Simons Says Quantitative Funds Win by Barring All Human Discretion

西蒙斯称量化基金唯有杜绝一切人工主观干预才能取胜 文艺复兴科技公司创始人吉姆·西蒙斯认为，系统化投资唯有在机构严格禁止人工主观干预并依赖聚拢微弱统计异常时方能成功。 在这场内容广泛的对话中，吉姆·西蒙斯梳理了自己的人生历程：从迷恋芝诺悖论的好奇孩童，到共同开创陈-西蒙斯理论的卓越微分几何学家。他讲述了在IDA从事冷战密码破译的转型期、因反对越战被解雇的经历，以及创立文艺复兴科技公司的过程；在那里，他开创了严格以模型驱动、协同合作的量化交易。西蒙斯还概述了退休后投身西蒙斯基金会的事业，致力于支持由好奇心驱动的长期基础科学，并剖析了美国数学教育的结构性困境。 吉姆·西蒙斯解释了文艺复兴科技公司如何通过机器学习捕获并汇聚微弱的统计异常，而非依赖单一主导信号，从而打破了有效市场假说。 (27:28) 与传统华尔街基金不同，文艺复兴完全基于算法运作，绝无人工主观干预，并推行终身保密协议，以保护那些若申请专利就会泄露商业机密的专有算法。 (36:43) 西蒙斯警告称，由于科技公司将合格人才从教师队伍中吸引走，美国数学教育正面临结构性危机；随着移居西方的外国毕业生减少，这种对外国H-1B人才的依赖是不可持续的。 (49:28) 西蒙斯基金会将80%至85%的预算投向纯粹由好奇心驱动的基础科学，以弥补日益注重短期转化成果、规避风险的联邦机构所留下的空缺。 (45:19)

Mathematician and Renaissance Technologies founder Jim Simons argues that breakthroughs across pure science, systematic investing, and education rely on giving talented individuals intellectual autonomy and long-term support rather than imposing rigid, top-down constraints. Aesthetic Pursuit in Geometry and Cryptography (7:25) Simons pursued mathematics out of aesthetic appreciation rather than competitive ambitions, finding inspiration in Stokes' theorem and differential geometry on curved manifolds. At Stony Brook University, while investigating characteristic classes, he isolated an unexpected mathematical term that led to the creation of the Chern-Simons invariants alongside Shiing-Shen Chern. Initially developed purely for mathematical interest, these geometric invariants were adopted a decade later across theoretical physics, condensed matter theory, and string theory. Simons also applied his algorithmic approach to practical problem-solving as a codebreaker at the Institute for Defense Analyses (IDA), targeting foreign ciphers. Although he achieved major classified successes there, his defense career ended abruptly when he publicly voiced opposition to the Vietnam War in an interview and letter to The New York Times, leading to his dismissal by General Maxwell Taylor. Systematic Modeling and Culture at Renaissance Technologies (27:28) After finding early discretionary trading emotionally draining, Simons shifted to quantitative finance by directly rejecting the efficient market hypothesis. He observed that financial markets contain identifiable anomalies, such as price momentum in commodities. Rather than relying on singular formulas, Renaissance Technologies developed machine learning models that aggregate thousands of faint, non-obvious statistical signals while strictly accounting for trading impact costs and portfolio volatility. Simons enforced a complete ban on human discretionary intervention, asserting that trading systems must adhere strictly to models because subjective hunches cannot be backtested or simulated. To safeguard this competitive edge, Renaissance relies on lifetime non-disclosure agreements, massive proprietary data, and internal profit-sharing that encourages scientific PhDs to collaborate openly rather than hoard research. Philanthropic Defense of Curiosity-Driven Basic Science (45:19) Through the Simons Foundation, established alongside his wife Marilyn, Simons allocates 80 to 85 percent of funds toward curiosity-driven basic science in mathematics, physics, computing, and biology. Simons argues that federal grant agencies such as the NIH and NSF have grown excessively risk-averse, favoring short-term translational research with predictable commercial outcomes over open-ended fundamental inquiry. To fill this institutional void, the foundation awards flexible 10-year investigator grants without mandatory deliverables, alongside collaborative programs tackling expansive questions such as the origins of life. Simons rejects the idea that his philanthropy is an obligatory repayment to society, explaining that he funds basic research purely out of a personal commitment to seeing scientific understanding advance. Structural Vulnerabilities in American STEM Education (49:28) Simons views the state of American K-12 mathematics education as an acute national crisis created by shifting labor economics. Decades ago, high school teaching attracted top mathematical minds; today, individuals with similar quantitative competencies are recruited into lucrative roles at technology firms and Wall Street banks that public school systems cannot match financially. He sharply criticizes federal policies that evaluate educators using statistically volatile standardized test metrics, advocating instead for raising teacher compensation and status. Through Math for America, the foundation provides $15,000 annual stipends to build peer communities and improve retention. Simons warns that relying indefinitely on foreign H-1B visas to offset domestic STEM shortfalls is unsustainable, noting that emigration from institutions like the Indian Institutes of Technology has declined from roughly 80 percent to 20 percent as domestic economic opportunities grow. Simons maintains that sustained innovation requires patient institutional backing for curiosity-driven talent, but leaves open the unresolved challenge of how the United States will address its domestic STEM teaching deficit as global competition for technical expertise intensifies.

数学家与投资家吉姆·西蒙斯（Jim Simons）在访谈中阐明了贯穿其学术、商业与慈善事业的核心范式：由审美与好奇心驱动的基础研究能够孕育出深远价值，而将严谨的科学方法、顶尖跨学科人才与利益共享机制相结合，能够打破传统经验主义并解决复杂的现实挑战。 纯粹数学审美与陈-西蒙斯不变量 (7:25) 西蒙斯强调自己投身数学并非为了追逐奖项或应用前景，而是纯粹为其内在的结构之美所吸引。在麻省理工学院（MIT）跳级并在三年内毕业后，他赴加州大学伯克利分校深造，被斯托克斯定理（Stokes' theorem）及其在微分几何与多维流形上的优雅推广深深打动。三十岁时，他出任纽约州立大学石溪分校（Stony Brook）数学系主任，历时六年完成了关于极小簇（minimal varieties）的基础性突破论文。在石溪分校自学示性类期间，他发现了一个无法消除却“极具生命力”的数学项，并借此定义了三维流形的不变量。在与陈省身（Shiing-Shen Chern）交流后，两人合作将该理论推广至任意维度，创立了著名的“陈-西蒙斯不变量”（Chern-Simons Invariants）并开拓了微分上同调领域。该理论在提出约十年后被物理学家广泛应用于弦论、凝聚态物理乃至天文学。西蒙斯以此指出，基础科学不可预测的转化过程正是人类认识世界的源头活水。 突破有效市场假说与量化模型驱动 (25:02) 学术生涯早期，西蒙斯曾在美国国防分析研究所（IDA）担任密码破译员，期间开发了多套破译算法；后因在《纽约时报》致信并接受采访公开反对越战，被管理层负责人Maxwell Taylor将军直接解雇。重返学界后，西蒙斯在与合作者遭遇长达两年的证明停滞期时，决定转战资金管理行业。起初的两年里，他与合伙人完全依靠主观直觉进行外汇和商品等标的的交易，尽管业绩优异，但西蒙斯直言其收益纯属运气，并坦言每日随行情剧烈波动的主观交易让人在“自认天才”与“自认蠢才”之间备受心理折磨。为此，他坚决否定了主张价格已反映全部信息的“有效市场假说”，指出真实市场存在可预测的统计异常（如商品市场的动量趋势）。文艺复兴科技（Renaissance Technologies）放弃人工主观判断与封闭大公式，转向利用机器学习算法对数十年历史价格数据进行严格回测，通过聚合金字塔般庞大且微弱的统计异常来获取超额收益，并辅以严密的概率统计来管理大资金交易引发的市场冲击成本与规模容量。 文艺复兴科技的协作机制与护城河 (32:36) 西蒙斯的管理哲学核心在于组织顶尖跨学科人才并打破信息壁垒。文艺复兴科技聘用了约100位拥有物理学、天文学、数学和统计学博士学位的科研人员，招聘时刻意避开传统华尔街金融背景，偏好具备扎实学术声誉的研究者。公司建立全员共享的合伙利润池，使得任何人取得的策略突破都能转化为全体成员的收益，从而营造出高度透明的协作文化。与许多仅将量化结果作为辅助参考、关键时刻仍依赖直觉干预的机构不同，文艺复兴科技坚持“100%模型驱动”，严禁任何主观臆断交易，因为主观决策无法进行科学回测。西蒙斯指出，公司的护城河在于数十年来积累的专有数据、高效的假设检验系统与严密的技术保密壁垒；量化交易策略因无法通过专利或版权进行公开保护，完全依赖内部商业秘密与终身保密协议维系。他谦逊地表示自己的核心才能在于凝聚优秀团队，并认为运气在巨大成功中占据了不可忽视的地位。 基础科学资助使命与数学教育危机 (45:19) 离开日常管理后，西蒙斯通过西蒙斯基金会（Simons Foundation）将80%至85%的预算投向数学、物理、计算机科学、神经科学及遗传学等纯基础科学，10%至15%投入教育与普及项目。基金会提供无预设成果限制的10年期资助以及探索生命起源等重大联合课题。西蒙斯批评美国联邦科研资助日益短视，指出国家卫生研究院（NIH）与国家科学基金会（NSF）在国会投资回报压力下变得高度规避风险，挤压了高风险、探索性的纯科学研究，私人慈善因而成为维系基础科学的重要支柱。与此同时，西蒙斯对美国K-12数学教育现状深感忧虑：科技巨头与华尔街的高薪待遇引发了严重的师资流失，导致公立高中缺乏真正精通数学的教师；而教育政策却热衷于基于统计无效的“增值测试”对教师进行惩罚性考核。为此，基金会通过“全美数学计划”（Math for America）为优秀教师每年提供15,000美元额外津贴并建立专业社群以重塑行业尊严。西蒙斯警示，长期依赖H-1B签证引进海外人才存在严重脆弱性（例如印度理工学院毕业生出国工作比例已由过去的约80%大幅降至约20%），若本土教育无法培育合格人才，国家科技根基将面临长期空心化风险。 西蒙斯的经历展示了严谨的数学逻辑与开放协作在探索科学前沿及金融工程中的巨大效力。然而，他所揭示的联邦基础科研资助短视化、美国本土中小学数学师资匮乏以及依赖外部科技移民的可持续性危机，仍是当前教育体制与国家创新政策尚未解决的深层矛盾。

## Background 该视频由 YouTube 频道 Numberphile2 于 2015 年 5 月 13 日发布，由布雷迪·哈兰（Brady Haran）主持采访。视频简介介绍吉姆·西蒙斯（Jim Simons）被誉为“世界上最聪明的亿万富翁”，他巧妙利用数学和计算机积累了巨额财富，如今是一位著名的慈善家并创立了西蒙斯基金会（The Simons Foundation）。 ## TL;DR 在这场深度访谈中，传奇数学家兼量化投资先驱吉姆·西蒙斯回顾了自己从童年直觉萌芽到攻克微分几何难题、开创“陈-西蒙斯理论”的学术历程。他详细讲述了自己在国防分析研究所（IDA）破译密码并因反对越战被解雇的往事，以及随后转向金融创办文艺复兴科技公司、开创 100% 模型驱动量化交易帝国的核心理念。晚年的西蒙斯将重心转向慈善事业，探讨了其基金会对基础科学的长远支持、对美国高中数理教育危机的深切担忧与干预策略，展现了他对探索未知的终身热爱。 ## Atmosphere & style 整场对话洋溢着睿智、从容且不乏冷幽默的松弛感。面对哈兰细致入微的追问，西蒙斯神态平和坦诚，毫无亿万富翁的傲慢架子，谈及年轻时死磕数学的执着与商业中的幸运时举重若轻、毫不伪饰。在触及美国基础教育困境与政府科研资助缩水等现实痛点时，他的语调严肃而尖锐，展现出一位顶尖学者对理性文明与人类认知边界由衷的关切与敬畏。 ## Bulletin - [27:28](https://www.youtube.com/watch?v=QNznD9hMEh0&t=1648s) 吉姆·西蒙斯从纯数学界与国防分析研究所密码破译领域起步，随后创立文艺复兴科技公司，凭借全自动统计机器学习模型颠覆了主流金融学的有效市场假说。 - [36:34](https://www.youtube.com/watch?v=QNznD9hMEh0&t=2194s) 文艺复兴科技公司坚持“100% 模型驱动”的原则，严禁主观干预交易，并将对市场冲击等交易成本的控制置于与价格预测同等重要的地位。 - [49:28](https://www.youtube.com/watch?v=QNznD9hMEh0&t=2968s) 西蒙斯警告美国初等与中等数学教育因科技大厂的高薪虹吸而面临严重师资危机，同时抨击仅以标准化考试评估教师的做法摧残了教学环境。 - [58:00](https://www.youtube.com/watch?v=QNznD9hMEh0&t=3480s) 面对联邦政府科研经费向短期“转化研究”倾斜的保守化趋势，西蒙斯基金会斥巨资对顶尖学者提供长达10年的无限制资助以守卫纯粹基础科学。 ## Key takeaways - [00:08](https://www.youtube.com/watch?v=QNznD9hMEh0&t=8s) 西蒙斯童年即展现出对无限与极限定理的敏锐直觉，四岁时通过汽车汽油永远用不完的构想独立触及了芝诺悖论的内涵。 - [07:24](https://www.youtube.com/watch?v=QNznD9hMEh0&t=444s) 斯托克斯定理将微积分基本定理拓展至高维流形边界，其展现的数学美感彻底坚定了西蒙斯深耕微分几何的研究志向。 - [12:48](https://www.youtube.com/watch?v=QNznD9hMEh0&t=768s) 西蒙斯与陈省身合作开创了陈-西蒙斯理论，该成果在十年后成为弦理论与凝聚态物理等现代物理学领域的关键基石。 - [18:12](https://www.youtube.com/watch?v=QNznD9hMEh0&t=1092s) 在冷战时期的国防分析研究所（IDA），西蒙斯为美国国家安全局破译密码并首次掌握算法设计，后因在媒体公开反战遭到解雇。 - [25:02](https://www.youtube.com/watch?v=QNznD9hMEh0&t=1502s) 转入投资初期的两年内，西蒙斯因纯直觉交易的情绪大起大落而心力交瘁，促使他下定决心转向量化数学与统计学建模。 - [27:28](https://www.youtube.com/watch?v=QNznD9hMEh0&t=1648s) 金融市场上不存在一招致胜的显性暴利规律，超额阿尔法收益来源于将海量极其微弱、隐蔽的统计学异常信号系统化融合。 - [29:44](https://www.youtube.com/watch?v=QNznD9hMEh0&t=1784s) 量化交易的核心瓶颈不仅是预测行情，还在于大资金进出对价格造成的市场冲击成本，因此核心大模型存在严格的资金容量上限。 - [33:57](https://www.youtube.com/watch?v=QNznD9hMEh0&t=2037s) 文艺复兴科技公司建立全员利益共享机制与极高的软硬件准入门槛，且坚守纯粹的模型驱动交易，彻底排除无法系统化回测的主观干预。 - [38:44](https://www.youtube.com/watch?v=QNznD9hMEh0&t=2324s) 西蒙斯认为文艺复兴闭门研发的成果属于高度特化的工程应用，对纯数学或基础科学的普遍理论推进并没有实际贡献。 - [49:28](https://www.youtube.com/watch?v=QNznD9hMEh0&t=2968s) 美国高科技产业的高薪大幅分流了潜在的数学师资，加之错误的标准化考试问责机制，导致美国基础数学教育面临系统性师资荒。 - [56:38](https://www.youtube.com/watch?v=QNznD9hMEh0&t=3398s) 美国长期依赖 H-1B 签证填补本土科技人才缺口，但随着印度等新兴经济体本土吸纳能力的飙升，海外人才输入模式未来难以为继。 - [58:00](https://www.youtube.com/watch?v=QNznD9hMEh0&t=3480s) 国会对科研投资回报率的政绩考核导致官方资助机构日趋保守，西蒙斯基金会通过纯粹资助顶尖人才来弥补基础科学的长远经费缺口。 - [59:26](https://www.youtube.com/watch?v=QNznD9hMEh0&t=3566s) 西蒙斯明确表示巨额资助基础科研并非出于财富“反哺”的道德负担，而是纯粹源于对科学突破的真挚热爱以及与顶尖科学家共事的精神愉悦。 ## Detailed walkthrough ### [00:08](https://www.youtube.com/watch?v=QNznD9hMEh0&t=8s) 童年时期的数学直觉与芝诺悖论 Jim Simons 回忆起自己的童年，坦言数学对他来说是一种非常自然的天赋，而且他一直都由衷地喜欢数学。小时候的他喜欢数数，还喜欢不断把一个数字乘以二，不过当一路翻倍算到 1024 之类的大数时，他就觉得“差不多够了”。大概在四岁的时候，Simons 在完全没有听过专业术语的情况下，自发领悟了类似于“芝诺悖论（Zeno's paradox）”的思想。当时父亲告诉他汽车可能会把汽油耗尽，这个概念让年幼的他感到十分不安： > “我父亲告诉我车可能会没油，这个概念让我很不安，我之前从未想过这点。但随后我想，车其实不应该会彻底没油：你每次可以只用掉现有汽油的一半，然后用剩下那一半的一半，接着再用剩下的一半，这样可以永远持续下去，所以油永远也用不完。” 虽然四岁的 Simons 当时还没意识到“车子这么开根本跑不了多远”，但在童年时期就能独立推导出“在原理上油永远用不尽”的想法，这对他而言是一个极具震撼力的深刻思考。 - **早期的计算习惯**：热衷于连乘 2，直到算至 1024 才作罢。 - **直觉与悖论**：四岁独立构想无限二等分过程，触及芝诺悖论与极限思维的核心。 --- ### [01:16](https://www.youtube.com/watch?v=QNznD9hMEh0&t=76s) 学生时代的粗心、热爱与立志成为数学家 当被问及是否在学校一直拿优异成绩时，Simons 坦诚表示自己确实很有天赋，也自知非常聪明，但同时存在一个巨大的毛病——粗心大意。他在算术测验中有时会因为算得太快或者字迹邋遢而把题目搞砸。即便如此，他对数学的一切都深深着迷：他很早就惊叹于球体体积公式 $\frac{4}{3}\pi r^3$ 的精妙；步入高中后，课程开始引入平面几何的定理与逻辑证明，这彻底抓住了他的心。Simons 坦言自己从来不是解题速度最快的那个人，但他具备一股非凡的韧劲与死磕精神，面对难题时会脚踏实地一步一步死磕到底。 与其他同龄男孩子梦想成为棒球运动员等体育明星不同，Simons 心中只有唯一的目标：成为一名数学家。 > “不，绝非如此，我唯一思考过的事就是我要成为一名数学家，无论那究竟意味着什么。” 在高中阶段，Simons 觉得科学课由于教学水平平平而缺乏吸引力；他热爱阅读历史和文学书籍，但他自认并不擅长写作。数学成了他唯一全心全意深爱着的学科。 --- ### [02:45](https://www.youtube.com/watch?v=QNznD9hMEh0&t=165s) 麻省理工学院求学与抽象代数的开窍时刻 凭借高中已修完部分大学先修课程的优势，Simons 进入麻省理工学院（MIT）后直接跳过了大学一年级的数学课，主修数学。到了大一第二学期，他在选课表上看到一门研究生级别的数学课，赫然写着“无先修要求（no prerequisites required）”。他当时心想既然没有先修门槛，那就选这门课。然而，这门课的内容异常高深，Simons 学得极为吃力，虽然最终勉强应付通过了课程，但他脑海中对那些抽象概念依然充满困惑。 转折点出现在随后的暑假。Simons 找来了一本专门讲解抽象代数（并非初等代数解方程，而是纯正的抽象代数）的书研读： > “不过那个夏天，我找来了一本关于这方面的书——这是代数，但不是解方程的那种代数，而是抽象代数。随后在一周之内，所有的东西在我脑海中全融会贯通了。我彻底理解了，不再感到困惑，我明白了他们为什么要做这一切。” Simons 总结道，数学中往往需要一定的时间去沉淀和领会概念背后的真正意图，一旦跨过那个坎，后续就会非常顺畅。最终，他仅用了三年时间就从 MIT 提前毕业。大一结束时，他也彻底明白了自己的职业蓝图——既然世界上有“专门付钱让你思考并创造数学”的职业，那么这条道路的终点就是去大学里当一名数学教授。 ```mermaid flowchart TD accTitle: Simons 的数学抽象理解路径 accDescr: 展示 Simons 从接触研究生课程产生困惑到通过研读教材顿悟代数本质的过程 subgraph Phase1["遭遇瓶颈"] A["选修研究生数学课<br>(标明无先修要求)"] --> B["概念晦涩困难<br>产生严重困惑"] end subgraph Phase2["突破与开窍"] B --> C["暑假研读抽象代数专著"] C --> D["一周内顿悟核心逻辑<br>彻底领会理论动机"] end subgraph Phase3["学业与职业确立"] D --> E["学业步入坦途<br>三年从 MIT 提前毕业"] E --> F["确立职业道路：<br>成为拿薪水思考数学的大学教授"] end ``` --- ### [04:35](https://www.youtube.com/watch?v=QNznD9hMEh0&t=275s) 数学的本质在于定义与伯克利之行 探讨这种“突然开窍（all the cogs move into place）”的现象时，Simons 解释说，在面对一个新概念时，学生最初总会纳闷为什么有人要提出这个概念、它的趣味性究竟在哪，直到通过大量思考与实例检验，才会意识到它的精巧。他特别指出，数学研究的极其关键之处在于“建立定义”： > “数学中很大一部分工作在于给出定义。你会发现某些事物完全可以归纳在同一框架之下，于是你可以为这组概念定义出一个结构，这遵循着所有的特征。这是数学向前推进的一种极其强大的方式，因为当你把具备相似特性的事物整合在一起时，你就能尝试去证明关于这类一般性事物的定理，而不仅限于某个具体的特例。” 在 MIT 毕业前夕，由于 Simons 与 MIT 本校的教授们关系极为密切，导师们希望他换个环境去加利福尼亚大学伯克利分校（UC Berkeley），开拓视野并接触新的师资。更核心的原因是，数学大师陈省身（Shiing-Shen Chern）刚好在那一年加盟伯克利，MIT 方面认为 Simons 天资出众，极力主张他拿到伯克利的一份优渥奖学金去师从陈省身。 Simons 怀揣着与陈省身共事的渴望奔赴西海岸，然而现实却开了一个玩笑：陈省身为了庆祝加盟伯克利的第一年，直接申请了学术休假（sabbatical），根本不在学校。Simons 只能先跟着另一位导师开展研究。直到第二学年初，Simons 已经在博士论文项目上取得了相当深入的进展，正在做一个研讨会报告，突然一位身材高大的华人学者走进了教室： > “我正在伯克利二年级初做一次研讨会报告，这时走进来一位身材高大的华人。我问旁边的人：‘那是谁？’他说：‘那是 Chern。’我当时甚至不知道他是中国人。我以为 Chern 可能是 Chernawsky 之类的缩写，或者是个把名字缩短了的波兰人。如果是 Chen 或者 Chan 我会知道是中国人，但带有字母 r 的 Chern 我完全没概念。” Simons 与陈省身就此结识，尽管两人年龄悬殊，但迅速成为了忘年交，并在日后成为了名垂数学史的科研合作者。 --- ### [07:24](https://www.youtube.com/watch?v=QNznD9hMEh0&t=444s) 步入微分几何：流形与斯托克斯定理之美 Simons 随后深入浅出地阐述了他一生专注的研究领域——微分几何（differential geometry）。微分几何研究的是弯曲空间的几何学，它不局限于平面上的平坦形状，而是研究任何具有度量距离函数的空间，其基本研究对象被称为“流形（manifold）”。 为了通俗地解释流形，Simons 举例说明： - **流形的本质**：是由许多局部空间拼接（glued together）而成的结构。 - **球面的例子**：你无法直接拿一张单薄平整的纸折成一个完整的球面，但你可以把很多小块纸片剪裁拼接在一起形成一个球面。流形在局部微观区域看起来就像普通的平坦空间（略微带有弯曲），但在全局宏观结构上却可以截然不同。 - **拓扑差异**：汽车轮胎或甜甜圈的表面（环面）在本质上与球面完全不同，二者根本无法在拓扑上平滑变形为对方。 真正把 Simons 彻底引入微分几何世界的，是著名的斯托克斯定理（Stokes' theorem）。Simons 将其视为微积分基本定理在更高维度的极致推广： | 数学阶段 | 核心表达与运算对象 | 几何/拓扑意义 | |:--- |:--- |:--- | | **微积分基本定理** | $\int_{a}^{b} f'(x) dx = f(b) - f(a)$ | 对一维函数的导数进行积分，得到函数在两端边界上的差值。牛顿时代已发现此规律。 | | **斯托克斯定理（Stokes' theorem）** | 针对流形上的微分形式（differential forms）进行高维积分与外微分运算。 | 将“流形内部关于外微分的积分”等价转化为“流形边界上关于原微分形式的积分”。 | 谈及斯托克斯定理时，Simons 的语气充满了赞叹： > “将这种思想推广至高维空间……那条定理的一般化表述对我而言简直美得令人屏息。那条定理太美了，它成为了微分几何最基本的定理之一。” 当采访者 Brady Haran 问及他当时追寻这门学问究竟是感受到了一种优雅之美、还是把它看作一项可以去猎取的荣誉奖杯时，Simons 毫不犹豫地回答：“不，完全是它的美，纯粹是因为它的美感。”他学过大量的代数，但代数并没有真正触动他的灵魂，唯独几何学彻底震撼了他。来到伯克利之后，Simons 基于自己的敏锐观察做出了一些全新的数学推导，并向自己的指导教授展示，教授当即评价道：“哦，这真有意思。”这便拉开了他博士阶段重大突破的序幕。 ### [11:21](https://www.youtube.com/watch?v=QNznD9hMEh0&t=681s) 极小簇与转战石溪大学 在完成博士论文之后，吉姆·西蒙斯（Jim Simons）将目光投向了另一个方向。当时数学界流传着一个悬而未决的难题，许多人尝试求解均以失败告终。西蒙斯觉得极具吸引力便着手研究，但一位资深学者极力劝阻他放弃，理由是已有不少学术权威在此折戟，“那些都是大人物，而我只是个小人物”（“those were big shots and I was just a little shot”）。然而西蒙斯并没有听从劝告，而是埋头苦干、死磕到底，最终成功攻克了该问题。在此期间，他还研究了名为“极小簇”（minimal varieties）的数学领域，并撰写了一篇奠基性的论文。这篇论文耗费了他整整六年时间，甚至引来同行对其为何耗时如此之久的疑惑，但事实证明这是一篇极具分量的杰作。 大约在30岁时，西蒙斯前往纽约州立大学石溪分校（Stony Brook University）出任数学系系主任。石溪分校当时是一所成立不久的新大学，其物理系实力雄厚，数学系却相当薄弱甚至算得上糟糕。面对出任系主任的邀约，西蒙斯觉得这会是一件非常有趣的事，欣然接受了挑战。 ```mermaid flowchart TD accTitle: 西蒙斯学术与早期职业生涯轨迹 accDescr: 展示西蒙斯从攻克悬案、撰写极小簇论文，到担任石溪数学系主任及与陈省身合作的研究流程 subgraph Phase1["基础攻坚阶段"] A["挑战悬而未决难题<br/>（不顾劝阻独自攻克）"] --> B["耗时6年完成论文<br/>（极小簇研究奠基之作）"] end subgraph Phase2["石溪大学任职"] B --> C["30岁出任数学系系主任<br/>（面对基础薄弱的数学系）"] C --> D["自学示性类与拓扑学<br/>（探寻未解之谜）"] end subgraph Phase3["理论突破"] D --> E["推导中出现顽固项<br/>（定义三维流形不变量）"] E --> F["与陈省身合作推广至任意维度<br/>（陈-西蒙斯理论与微分上同调）"] end ``` ### [12:48](https://www.youtube.com/watch?v=QNznD9hMEh0&t=768s) 陈-西蒙斯不变量与跨学科的意外回响 在石溪任职期间，西蒙斯决定自学拓扑学中与几何学紧密相关的“示性类”（characteristic classes）。他从零起步，试图去解决一个曾吸引无数学者、但至今仍未被满意解决的问题。在推导公式的过程中，式子里反复出现一些无法消去的棘手函数项。西蒙斯原本急于摆脱它们以配平公式，却逐渐意识到这些项本身具有独立的生命力。顺着这条线索，他定义了一种针对三维流形的不变量，并用其证明了若干浸入定理（immersion theorems）。 西蒙斯将这一成果展示给著名几何学家陈省身（Shiing-Shen Chern）。陈省身看后敏锐地指出，由于自己对该领域的熟稔，完全可以将其推广到所有维度。两人随即展开深入合作，共同构建了完整的数学结构。陈省身随后在70年代初的国际数学家大会（ICM）上展示了这一成果。后来西蒙斯又与杰夫·奇格（Jeff Cheeger）合作引入了“微分特征”（differential characters），开创了如今被称为“微分上同调”（differential cohomology）的研究分支。大约十年后，物理学家们意外发现了“陈-西蒙斯不变量”（Chern-Simons invariants）的巨大价值，发现它能够完美解决理论物理中的症结，其应用迅速席卷弦理论、凝聚态物理乃至天文学。对于这种数学成果在其他领域开花结果的现象，西蒙斯深有感触地总结道： > “基础科学是人类认识世界的良种。”（“Basic science is at the you know, it's the seed corn of our knowledge of the world.”） - 当被问及当时是否觉得这项研究很冷门偏僻时，西蒙斯表示自己从未觉得它只是个小消遣，他纯粹出于对数学本身的热爱而研究，压根没考虑过实际应用。 - 西蒙斯曾向石溪分校的诺贝尔物理学奖得主杨振宁（C. N. Yang）展示过这些数学结构，询问其对物理是否有用，但杨振宁当时并未接话，西蒙斯因不懂物理便未再深究。 - 对于十年后理论在物理界引起的轰动，西蒙斯坦言这让他感觉非常好，但他从不认为自己凭此“彻底变革了物理学”，只当是自己留下的一份坚实成果。 ### [18:12](https://www.youtube.com/watch?v=QNznD9hMEh0&t=1092s) 国防分析研究所的密码破译岁月 在37或38岁彻底离开纯数学界之前，西蒙斯曾在位于普林斯顿的国防分析研究所（Institute for Defense Analyses, IDA）工作了四年。那是一个为美国国家安全局（NSA）服务的高度机密机构，核心任务是破译外国对手（主要是苏联）的密码机与密码系统。在那里，西蒙斯不仅继续推进他的极小簇数学研究，还首次接触到了计算机与算法。 西蒙斯坦陈自己是一个极度糟糕的程序员，但在设计破译算法方面极具天赋。他负责构思突破密码的算法逻辑，交由他人编写程序并在计算机上运算验证。他在那里取得过一项极为出色的机密破译成果。当被问及几何拓扑学专业是否对密码工作有帮助时，西蒙斯直言“完全没关系”。他之所以接受这份工作，纯粹是因为“他们给的钱多”（“They paid money”）。当时他对单纯的大学学术生活感到些许厌倦，加上极小簇长达六年的研究周期让他看着同行频频发文而产生落差。国防分析研究所开出的薪水更为优厚，而且不设教学任务，允许研究人员一半时间做自己的数学研究，另一半时间攻关军方课题，这恰好满足了他的需求。 - 在国防分析研究所的四年里，西蒙斯体验到了构建计算机模型的巨大乐趣，这为他日后的量化投资思路埋下了伏笔。 - 因涉及国家最高机密，西蒙斯对他在密码破译中所取得的具体突破始终守口如瓶。 ### [20:46](https://www.youtube.com/watch?v=QNznD9hMEh0&t=1246s) 反对越战与突遭解雇 西蒙斯在国防分析研究所的职业生涯在第四年戛然而止，原因是他被解雇了。当时正值越南战争时期，西蒙斯内心对这场战争极度反感，即便他所在的研究机构并不直接参与支持前线作战。当时国防分析研究所的最高负责人是身在华盛顿的退役陆军名将麦克斯韦·泰勒将军（General Maxwell Taylor）。泰勒在《纽约时报杂志》（The New York Times Magazine）发表了一篇封面文章，宣称美军在越战中胜券在握，只要坚持下去就能大获全胜。 西蒙斯认为这通言论纯属胡说八道（“a lot of baloney”），随即给《纽约时报》写了一封公开信，直言不讳地指出并非所有为泰勒将军工作的人都支持其观点。这封立场鲜明的信件很快被报纸刊登。起初机构内部风平浪静，没有任何管理层当面责备他，但他心知肚明自己已经被列入了监控名单。西蒙斯当时并未觉得自己此举鲁莽，认为这只是个人观点的表达且与本职工作无关。大约三四个月后，《新闻周刊》（Newsweek）的一名记者找上门来，表示正在采写一篇关于国防部内部反战员工的报道，因极难找到愿意受访的人而请求采访西蒙斯。面对记者的邀请，年仅29岁、从未接受过采访的西蒙斯跃跃欲试，当即答应了接受采访。 ### [22:52](https://www.youtube.com/watch?v=QNznD9hMEh0&t=1372s) 幽默的“五五分”算法与被 IDA 解雇 在接受一位记者的采访时，对方追问吉姆·西蒙斯（Jim Simons）在国防分析研究所（IDA）面对越战的工作态度和政策究竟是什么。西蒙斯当时半开玩笑但又十分契合实际地编造了一套说辞：在 IDA，研究人员原则上需要将至少 50% 的时间投入军方的加密与破译工作，剩下 50% 的时间则可以自由从事个人纯数学研究。西蒙斯于是告诉记者自己的全新“算法”：“我的算法是，在越南战争结束之前，我把 100% 的时间都花在数学上；战争结束后，我再把 100% 的时间花在他们的工作上，直到这两部分时间重新扯平为止。”当时他确实将绝大部分精力投入到了纯数学研究中，军方的项目只做了一点点。 采访结束后，西蒙斯觉得自己应该向当地的主管报备一下。主管听完西蒙斯原原本本地复述了对记者说的这番话后大惊失色，连忙给自己的上司马克斯韦尔·泰勒将军（General Maxwell Taylor）打电话汇报。打完电话后，主管把西蒙斯叫回办公室，当面宣布他被解雇了。西蒙斯当时非常不解，反驳称自己的头衔可是“终身研究员”（Permanent Member），之前从临时成员晋升为终身成员，怎么能说开除就开除。主管幽默地回应道：“临时成员有合同，终身成员没有合同。”西蒙斯当时并没有合同在身，因此立刻就被扫地出门。不过西蒙斯对此毫不担心，因为他刚攻克了困扰数学界六年的极小次流形难题，学术界声誉正盛，找一份新教职易如反掌。 - 西蒙斯受聘于 IDA 时，由于保密协议，官方甚至不能对外公开其研究内容属于“密码与破译”（codes and ciphers），只能含糊称作“他们的业务”（their stuff）。 - 泰勒将军直接下达了开除西蒙斯的指令。 - 面对失去工作的境地，西蒙斯回忆道：“我刚刚解决了之前跟你们聊过的那个长达六年的重大数学难题，我知道自己能非常轻松地找到工作，所以我其实一点都不担心。”（“I had solved this big math problem that I told you about the six year thing. I knew I was going to get a job very easily, so I wasn't really worried about that.”） --- ### [25:02](https://www.youtube.com/watch?v=QNznD9hMEh0&t=1502s) 转战石溪大学、学术瓶颈与涉足投资 被 IDA 解雇后，西蒙斯接受了纽约州立大学石溪分校（Stony Brook University）的邀请，出任数学系主任。在石溪期间，他先是与陈省身合作开创了著名的“陈-西蒙斯理论”（Chern–Simons theory），随后又与数学家杰夫·奇格（Jeff Cheeger）联手攻坚另一个数学难题。然而，西蒙斯和奇格在这一研究上彻底陷入了僵局，苦战整整两年却一无所获。西蒙斯直言，如果能感觉到自己在向前推进，研究做再久也没问题，但在这项难题上他们完全是在原地踏步，这让他感到极其沮丧。 恰逢此时，西蒙斯的父亲做生意赚了一笔钱，西蒙斯获得了一个打理这笔资金的机会。初次涉足投资让西蒙斯产生了浓厚兴趣，他萌生了彻底转行的念头，决定投身于资产管理领域。起初，他用父亲的钱、一些家族资金以及其他几位投资人的资金启动了业务。令人意外的是，西蒙斯在最初的整整两年里完全没有使用任何量化模型，而是像普通交易员一样凭借宏观直觉和直觉判断，在货币、大宗商品以及各类金融工具（当时尚未涉及股票）中博弈。虽然团队凭借纯粹的运气取得了惊人的盈利，但这种传统交易方式让西蒙斯感到心力交瘁：每天清晨走进办公室，如果行情顺应预期，就会觉得自己是个无所不能的天才；而一旦市场反转逆行，整个人瞬间又觉得自己像个彻头彻尾的蠢货。这种大起大落的心理煎熬促使他重新审视价格走势中的内在模式，开始思考是否能够通过数学和统计学方法来预测市场。 ```mermaid flowchart TD accTitle: 西蒙斯早期职业路径与交易方式的转变 accDescr: 展示从 IDA 解雇、石溪大学学术瓶颈，到非模型投资，最终走向统计建模的转变过程。 subgraph 学术与早期探索 A["被 IDA 解雇"] --> B["出任石溪大学数学系主任"] B --> C["与陈省身合作 (陈-西蒙斯理论)"] C --> D["与杰夫·奇格合作遭遇两年瓶颈"] end subgraph 初涉金融 D --> E["受挫后转行：打理父亲与家族资金"] E --> F["前两年：纯直觉交易<br>(无数学模型，大宗商品与货币)"] end subgraph 转向模型化 F --> G["情绪如坐过山车：天才与蠢货的心理内耗"] G --> H["观察价格形态：启动数学与统计预测模型"] end ``` - 西蒙斯形容那两年的直觉交易过程极为折磨：“这是一个非常揪心的行业。早上走进来你觉得自己是个天才，市场完全顺应你；第二天早上你走进来又觉得自己像个蠢货，市场与你背道而驰。”（“This was a very gut-wrenching business. You know, you come in one morning, you think you're a genius, the markets are for you... and the next morning you come and you feel like a jerk, the market's against you.”） - 早期团队主要交易外汇（currencies）、大宗商品（commodities）和衍生金融工具，未涉及股票市场。 --- ### [27:28](https://www.youtube.com/watch?v=QNznD9hMEh0&t=1648s) 打破有效市场假说：寻找微小异常与构建预测模型 当主持人询问作为数学家的西蒙斯为何在起步两年后才开始建模时，西蒙斯解释说，自己其实很早就萌生了量化建模的想法，并早早找来了一位同样出自 IDA 密码破译机构的优秀学者。然而，这位搭档逐渐对基本面分析产生了更浓厚的兴趣，甚至断言纯数学模型在金融市场上难有作为，导致早期的建模工作停滞不前。西蒙斯坚信建立预测模型是完全可行的，于是相继引入了更多数学家以及顶尖的计算机专家，才真正打造出了切实行之有效的量化交易系统。 在构建模型的过程中，西蒙斯直面并推翻了主流金融学界的“有效市场假说”（Efficient Market Theory）。该假说认为资产价格总是反映了所有已知信息，价格历史数据中不可能包含任何预测未来的有效线索。西蒙斯坦言：“在某种意义上价格总是对的，但那根本就不是真的。”他指出历史价格数据中真实存在着各类统计“异常”（anomalies）。例如，大宗商品在过去往往具有明显的趋势性，只要能捕捉到这种微弱的趋势并顺势下注，从概率上就能赚多赔少。然而，市场上不存在任何能够让人一口吃成胖子的显性规律，因为显而易见的规律早就被其他交易者套利抹平了。真正的超额收益来源于大量极其隐蔽、微弱的异常信号。 - 随着研究的深入，西蒙斯的量化团队挖掘到了越来越多的市场异常模式。 - 西蒙斯总结了多信号融合的核心思想：“没有任何单一异常是如此压倒性的，以至于你能靠某一个特定异常大发横财，因为如果是这样的话，其他人早就发现了；所以它们必须是非常微妙的东西。你把这些微妙异常的集合拼凑在一起，就能得到一个预测得相当不错的系统。”（“None of them is so overwhelming that you're going to clean up on a particular anomaly, because if they were, other people would have seen them. So they have to be subtle things. And you put together a collection of these subtle anomalies, and you begin to get something that will predict pretty well.”） --- ### [29:44](https://www.youtube.com/watch?v=QNznD9hMEh0&t=1784s) 机器学习、交易成本与文艺复兴科技的管理哲学 针对预测系统是否像毕达哥拉斯定理那样由几个精巧公式构成的疑问，西蒙斯澄清道，文艺复兴科技（Renaissance Technologies）的现代系统结构极其复杂庞大，但它的核心并非深奥的巨型公式，而是机器学习（machine learning）的运作范式。研究人员会针对某些潜在的预测因子提出假设，随后将其放入海量的长期历史价格与多维度数据中进行严格的回测检验；如果该特征具有统计预测力，就将其并入统一系统，若无效则果断抛弃。更重要的是，西蒙斯强调在量化交易中，预测价格仅仅是整体系统的一部分，甚至不是最困难的部分。另一个关键支柱是对交易成本（尤其是市场冲击成本）的精确把控：普通散户购买 200 股对市场价格毫无影响，但如果要建仓 20 万股，订单本身就会大幅推高买价；如果交易把价格扭曲得太厉害，原本微弱的利润空间就会被自身造成的冲击成本彻底吞噬。此外，如何构建一个能将整个投资组合的波动率降至最低的仓位系统，需要极度精密的现代应用数学、概率论和统计学算法。 西蒙斯透露，他们的核心大模型存在严格的“容量限制”（capacity），即资金管理规模存在一个最佳甜蜜点（sweet spot）。一旦管理的资金规模过度膨胀，进出市场的订单就会对价格造成不可承受的冲击，导致阿尔法收益衰减。正因如此，文艺复兴的自营基金不会无限膨胀成吃掉整个市场的超级巨兽。在团队构建与管理层面，公司聚集了大约 100 位拥有博士学位的顶级科学家。西蒙斯分享了他数十年来贯彻始终的人才算法：召集最聪明的人，给予他们充分的探索自由，创造所有人平等交流、绝不在个人角落里自扫门前雪的完全开放氛围；同时为他们提供业界最强悍的计算机硬件与基础设施支持，并让所有人成为公司的合伙人，共享丰厚的收益。在招聘时，他们完全不看重金融背景，唯一的筛选标准是应聘者是否在物理学、天文学、数学或统计学等硬核科学领域受过严格的科学训练，发表过扎实论文，并且展现出绝顶的聪明才智。 - 西蒙斯明确了团队所运用的数学工具：“主要是统计学，还有一些概率论。但我们是无所不包的，我们随时调用任何可能奏效的工具。”（“It's mostly statistics and some probability theory... but we reach for different things that might come that might be effective. So we're very universal.”） - 西蒙斯总结了他执掌文艺复兴科技的核心组织原则：“我的算法始终是：把聪明人聚在一起，给予他们充分的自由，营造一种大家彼此敞开交流的氛围——他们不会躲在角落里搞自己的小算盘，而是与所有人交流——并为人们提供最好的基础设施和最好的计算机，同时让每个人都成为合伙人。”（“My algorithm has always been: you get smart people together, you give them a lot of freedom, create an atmosphere where everyone talks to everyone else—they're not hiding in a corner with their own little thing, they talk to everybody else—and you provide the best infrastructure, the best computers and so on that people can work with, and make everyone partners.”） - 招聘标准直截了当：博士毕业后工作过几年、发表过优秀学术论文、拥有扎实科学研究背景的物理学家、天文学家、数学家或统计学家。 ### [33:57](https://www.youtube.com/watch?v=QNznD9hMEh0&t=2037s) 文艺复兴科技公司的协作文化与高准入门槛 詹姆斯·西蒙斯（James Simons）虽然已经离开文艺复兴科技公司（Renaissance Technologies）的日常管理岗位六年了，但他目前仍担任董事会主席，并每月参加一次董事会会议。他指出，公司的士气和凝聚力依然非常高昂。这得益于一种极佳的科学协作氛围——这是一种大规模的集体努力。在文艺复兴科技公司，所有员工都参与利润分享，因此每个人都乐见同事取得突破。西蒙斯笑着解释这种心理：“好吧，你可能希望那个证明自己有多聪明的人是你，但不管怎样，太好了，他做到了，我也能从中赚钱。” 当被问及为什么其他同样精通数学和计算机的人没有取得像他这样的成就时，西蒙斯谦虚地承认，确实有其他人做出了非常优秀的模型，文艺复兴科技公司并非独占鳌头，但他确信自己的公司做得更好。他指出，该行业存在极高的准入门槛： - **历史数据集**：公司多年来收集并积累了极其庞大的数据集。 - **专有测试软件**：为了让研究人员能够极其轻松地测试各种假设而专门编写的程序。 - **顶尖的基础设施**：经过多年摸索、调整至最佳状态的软硬件支持系统。 此外，公司的人才流失率极低。员工一旦加入极少离开，即使离开也会彻底转行。所有员工都签署了永久保密协议（NDA）。西蒙斯解释说，他们对自己的工作方法高度保密，因为这些交易算法无法申请专利或版权保护。一旦申请专利，细节就会公开，竞争对手只需稍作修改和调整，就能轻松绕过专利。因此，这些知识产权必须作为绝对机密锁在公司内部。 --- ### [36:34](https://www.youtube.com/watch?v=QNznD9hMEh0&t=2194s) 100% 模型驱动与对模型的“宗教般信仰” 西蒙斯强调，文艺复兴科技公司的投资操作是“100% 模型驱动”的。这与许多将模型仅作为“参考建议”的量化基金（可能只有80%或90%依赖模型）有着本质区别。在那些公司，决策者看着模型给出的建议，有时会选择忽略。但在文艺复兴科技公司，绝对没有交易员会走进交易室说：“嘿，我们买点 IBM 吧，这绝对稳赚”，或者“谷歌的股票太多了，我们得做空它”。 这种对模型的“宗教般信仰”是维持这家公司运转的唯一方式。西蒙斯解释了其中的逻辑：你无法在历史数据中去模拟那个突然走进来大喊“谷歌太高了，赶紧卖掉”的交易员的行为，因为这种主观决策是无法被系统化复盘的。相反，数学模型或新的预测指标却可以在历史数据中进行严密的模拟测试，以验证其过去的表现。 当主持人问及，将所有成功都归功于计算机，是否会伤害到聪明人的虚荣心时，西蒙斯予以了否定。他认为计算机只是工具： > “一个优秀的细木工不会说这全是因为我那把精妙的凿子。” 就像优秀的摄像设备无法直接决定一个导演的成功一样，同样的设备在平庸之辈手中只会拍出一团糟。计算机只是在执行人类给它的指令。 ```mermaid flowchart TD accTitle: 100%模型驱动交易与主观交易对比 accDescr: 展示文艺复兴科技公司完全依赖数学模型进行系统化模拟与交易，排除了无法被模拟的人类主观决策。 subgraph Renaissance ["文艺复兴科技公司 (100% 模型驱动)"] A["开发数学模型/预测器"] --> B["利用历史数据进行系统模拟 (Backtesting)"] B --> C["模型生成交易指令"] C --> D["计算机自动执行交易"] end subgraph Discretionary ["传统/主观交易 (无法系统模拟)"] E["交易员直觉/消息 (如：'买入IBM')"] --> F["主观决定交易"] F --> G["无法在历史数据中准确模拟该决策的影响"] end style Renaissance fill:#f9f,stroke:#333,stroke-width:2px style Discretionary fill:#bbf,stroke:#333,stroke-width:2px ``` --- ### [38:44](https://www.youtube.com/watch?v=QNznD9hMEh0&t=2324s) 商业机密与数学研究的界限 数学是一门高度依赖学术共享和共同构建的学科。主持人提出一个疑问：文艺复兴科技公司在紧闭的大门背后，是否发现了一些本可以推动数学或科学界整体进步的成果，却为了商业利益而选择秘而不宣？ 西蒙斯非常明确且坦率地否定了这一猜测： > “据我所知，我们在文艺复兴科技公司紧闭的大门背后所学到的东西，没有任何能对数学或科学的普遍领域有所帮助。” 他们所做的工作是高度应用性的，专注于市场微观结构和数据模式，这些发现对于基础科学或纯数学理论的拓展并无直接益处。 --- ### [39:10](https://www.youtube.com/watch?v=QNznD9hMEh0&t=2350s) 运气、管理才能与科学家的威信 在探讨成功的原因时，西蒙斯认为运气起到了极大的作用，而人们往往低估了运气的成分。他指出了一种常见的人性弱点： > “通常情况下，如果有人失败了，他会说‘我运气不好’；而如果他成功了，他就会说‘我是个聪明人’。” 西蒙斯承认自己是在正确的时间出现在了正确的地点。但他认为自己真正的核心才能并非数学天才，而是管理和组织能力： > “我认为我所擅长的是让优秀的人一起工作。” 他表示，自己虽然算是个聪明人，也确实提出过几个预测算法，但公司里许多人都做出了算法，他很清楚自己不可能包揽所有创意。不过，他的学术背景为他赢得了员工的尊重。因为他曾是一位优秀的科学家，员工们会觉得：“他有时可能表现得挺糊涂，但我们知道他其实非常聪明。”这种科学家的威信在管理这群顶尖聪明人时发挥了关键作用。 --- ### [40:51](https://www.youtube.com/watch?v=QNznD9hMEh0&t=2451s) 数学成就与商业成功的抉择 当被问及在前半生的数学学术成就与后半生的商业帝国之间，他更以何者为傲时，西蒙斯表示自己同样自豪。他为自己做过一些对学术界有积极影响的数学研究而欣慰，也为创立了一家出色的企业而骄傲。此外，他现在将主要精力放在了与妻子共同创立的西蒙斯基金会（The Simons Foundation）上。该基金会由其妻子于1994年用他的资金创立，如今已成为他的主业，他也为此感到非常自豪。 主持人抛出了一个极具启发性的问题：“你是否愿意用你全部或部分的商业成功，去换取成为那个破解黎曼猜想（Riemann Hypothesis）的人？” 西蒙斯沉思片刻，承认这是一个极好的问题： > “我可能会愿意交换其中一部分……对于黎曼猜想，我想，能解决它当然会是一件令人极其兴奋的事。” 但他随即表示，自己对目前的职业生涯走向感到非常满意。他从不回头看，也从不后悔自己在商业上做过或没做过什么。 --- ### [42:52](https://www.youtube.com/watch?v=QNznD9hMEh0&t=2572s) 并非典型的商人：减法的艺术与圣路易斯分销商的启示 西蒙斯直言，自己并不适合管理普通的商业公司。如果要他去管理一家大型制造企业，他会觉得那些繁琐的行政细节极其枯燥，而且他自认不是一个组织纪律性极强的人，很快就会感到厌倦。他表示：“我不是那种典型的商人。”文艺复兴科技公司之所以能成功，是因为它的运行方式对他而言非常自然。 谈到商业，西蒙斯幽默地分享了他对商业中数学的理解： > “我总是说，商业中最重要的数学技能是减法。你必须明白你的收入何时会超过你的成本。” 他吐槽说，有些创业者只盯着收入增长，却忽视了每天都在亏损的事实，还天真地以为“问题过阵子自己就会解决”。 为了证明自己确实不适合传统商业，西蒙斯分享了一段往事：他曾因投资关系，不得不亲自去管理一家陷入困境的计算机领域小微企业，前后维持了三到六个月，期间每周通勤去费城。虽然他做得比前任好，但他深知自己并不擅长。他回忆起当时与一位来自圣路易斯的分销商开会时的场景，自己心里一直在想：“我到底在干什么？把时间花在和圣路易斯的分销商扯皮上？这根本不是我想过的人生。”最终，他们聘请了一位真正的专业经理人，西蒙斯才得以解脱。 如今，西蒙斯基金会是他倾注心血的地方。该基金会主要致力于支持基础科学研究，同时也资助了一项庞大的自闭症研究项目（包含大量基础科学研究，并以寻找治疗方法为最终目标）。 ### [45:19](https://www.youtube.com/watch?v=QNznD9hMEh0&t=2719s) 西蒙斯基金会的慈善模式：支持基础科学与应对不确定性 吉姆·西蒙斯（Jim Simons）详细阐述了西蒙斯基金会（Simons Foundation）的资金投向。基金会重点资助数学、物理、计算机科学，以及神经科学和遗传学等各类生物学的基础科学领域。西蒙斯明确指出，这是他们真正热爱的事业：“大约 10% 到 15% 的资金用于拓展和教育，但 80% 到 85% 基本上都是支持基础科学。” 面对主持人的追问——基础数学研究本质上无法预知成果，这是否就像“把钱扔向墙壁看能粘住什么”，西蒙斯承认某种程度上确实如此。基金会推行了西蒙斯研究员资助计划（Investigator Grants），为顶尖的数学家、物理学家和计算机科学家提供长达 10 年的长期资助。学者们可以用这笔钱聘请博士后或推进日常研究。西蒙斯解释说，他们并不预设学者必须产出什么具体成果，只看重过往学术成就和顶尖实力。此外，基金会还资助大型合作项目，设定宏大但相对宽泛的目标。例如“生命起源”课题汇聚了四五十位学者，研究从原始有机分子如何一步步演化出人类智慧。西蒙斯风趣地总结道： > “我们并不指望未来五年能彻底弄清起源的所有奥秘，但我们会对这条从原始有机分子走向如今坐在这里接受采访的道路了解得更多。” ```mermaid flowchart TD accTitle: 西蒙斯基金会资助结构 accDescr: 展示西蒙斯基金会在教育推广与基础科学之间的资金分配与项目模式 subgraph FundAllocation["基金会资金分配"] A["总资助预算"] --> B["10% - 15%<br>教育与科普拓展"] A --> C["80% - 85%<br>基础科学支持"] end subgraph EducationPrograms["教育拓展"] B --> D["Math for America<br>(美国数学计划)"] end subgraph BasicSciencePrograms["基础科学两大支柱"] C --> E["西蒙斯研究员项目<br>(10年无限制资助/选拔顶级人才)"] C --> F["前沿合作课题<br>(如生命起源等宏大科学问题)"] end ``` ### [47:36](https://www.youtube.com/watch?v=QNznD9hMEh0&t=2856s) 商业与慈善的异同，以及对风险的真正态度 主持人提出疑问：这种不问产出、任由学者探索的慈善模式，与西蒙斯在文艺复兴科技公司（Renaissance Technologies）强调收入、成本与盈利的对冲基金运营似乎背道而驰。西蒙斯对此作出了辩证的剖析。他指出，两者的相通之处在于招募人才时同样不设限： > “当把顶尖人才招进文艺复兴公司时，我们也不知道他们具体会做什么。我们只是希望他们能提出好点子，让公司变得更好；我从不会规定某个人必须发现某种特定的东西。” 两者的区别在于，商业运作最终收敛于极具针对性的狭窄结果，而基础科学则是完全开放的“自由探索”。谈及对风险的理解，主持人询问曾打造出以降低风险为核心的量化帝国、却又敢于放弃终身教职下海创业的西蒙斯，究竟是风险承担者还是风险规避者。西蒙斯坦言，随着年龄增长人可能会变得相对保守，但他骨子里一直是个敢于冒险的人。更重要的是，他有一套管理风险的方法论： > “我一直都算是个冒险家，但我拥有良好的品味，尤其是在识人方面。而且我几乎总是与他人合作合伙，这有效降低了风险。” ### [49:28](https://www.youtube.com/watch?v=QNznD9hMEh0&t=2968s) 美国数学教育的危机与高薪产业的人才虹吸 转向学术与教育现状时，西蒙斯对全球前沿数学研究的发展感到非常乐观，认为新思想源源不断、交叉学科蓬勃兴旺。然而，谈及美国的初等与中等数学教育，他的语气沉重下来，直言其状态“非常不健康”。危机的根源在于懂数学、懂科学的合格教师严重匮乏。 西蒙斯对比了时代背景的巨大变化。在三四十年前，如果一个人掌握了足以教授高中的数学知识，除了留校做教授外，社会上并没有太多其他职业出路，当中学老师是一份极具吸引力且受人尊重的体面工作。但在当下，同样掌握这些数学知识的人，转头就能去 Google、IBM 或 Goldman Sachs 获取高薪职位： > “如今高中的数学师资水平下降了，原因很简单：如果你懂得足够多的数学去教高中，你就懂得足够多的数学去 Google 上班，而高中给不了那样的薪水。” ### [51:18](https://www.youtube.com/watch?v=QNznD9hMEh0&t=3078s) 解决之道：Math for America、教师待遇与尊严 要解决公立学校留不住理科人才的难题，西蒙斯指出必须从人类行动的根本动力出发——物质报酬与社会尊重。他举例说，联邦最高法院的大法官并非为了发财而工作，而是源于崇高的社会威望与自我认可。面对无法完全抹平的薪资差距，西蒙斯创立的 Math for America（MƒA）提供了一套行之有效的解决方案： - **直接经济补贴**：在教师原有的常规薪资基础之上，每年额外发放 15,000 美元的津贴。 - **打造专业共同体**：汇聚数学与科学教师，破除教师在普通学校里孤立无援的处境，建立极具凝聚力的集体荣誉感（esprit de corps）。 - **极低的流失率**：在常规教师离职率居高不下的背景下，该项目参与者的离职率极低。 西蒙斯以芬兰为例，那里的数学教师是极具社会声望的专业群体，享有很高的社会地位。而在美国，舆论环境充斥着对教师的贬低与问责，只关注如何淘汰所谓的“不合格教师”。西蒙斯批评道： > “如果经营一家企业，清理不称职的人固然重要，但更重要的是认可那些表现优异的员工，奖励并赞赏他们，让他们获得成就感。我们对教师却根本没有这么做，只是一味地抨击、抨击、再抨击。” ### [53:45](https://www.youtube.com/watch?v=QNznD9hMEh0&t=3225s) 标准化考试评估的荒谬与“自发市场调节”的幻灭 深入探讨美国教育困境的成因时，西蒙斯指出了大约十年前兴起的错误问责机制——单纯依靠学生的标准化考试成绩和所谓的“增值模型”（value-added）来评估甚至解雇教师。他直指这种做法在统计学和教育实践上都是彻底的灾难：学生的统考成绩是一个非常薄弱的统计指标，其跨年度表现的相关性极低。这种一味依靠惩罚手段来逼迫教学质量提升的逻辑，让西蒙斯联想到了英国皇家海军的一句老谚语： > “英国海军有句老话叫‘鞭打将持续进行，直到士气好转为止’，我们现在的做法就跟这差不多，纯粹是在摧残这些教师。” 西蒙斯指出，正确的出路是树立“特级教师”（Master Teacher）的晋升通道与行业标杆，让教师获得应有的报酬、体面与社会威望。面对主持人提出的疑问——西蒙斯作为自由市场的信徒，这一短缺难道不能依靠市场供求关系自发纠偏（例如科技公司招不到本土数学家自然会倒逼教育改革）吗？西蒙斯干脆利落地打破了这种幻想，揭示了美国当前残酷的现实捷径： > “不，我们现在是怎么解决人才短缺的？我们直接从国外引进人才。” ### [56:38](https://www.youtube.com/watch?v=QNznD9hMEh0&t=3398s) 本土人才匮乏与全球科技人才流动的变局 吉姆·西蒙斯深入探讨了美国高科技人才短缺的深层困境。当前美国极度依赖 H-1B 签证从世界各国引进具备扎实数理与科技知识的专业人才。各大科技企业不断向政府游说施压，要求发放越来越多的 H-1B 签证配额，其根本原因在于美国本土培养的技术人才储备严重不足，根本无法满足科技产业日益扩张的需求。西蒙斯指出，这种完全仰赖海外人才输送的模式短期内尚可维持，但绝非长久之计。 全球人才流动格局正在发生剧烈转变。西蒙斯以印度理工学院（IIT）为例说明：大约十二三年前，该校大约有 80% 的顶尖毕业生选择离开印度，远赴欧美寻找就业机会；而如今这一比例已骤降至 20% 左右。这是因为印度本土的经济与产业蓬勃发展，国内涌现出海量的高技术岗位，年轻人才完全可以留在家乡施展才华，不再需要背井离乡奔赴英国或美国工作。西蒙斯严肃地警告道：“来自其他国家的人才正在涌入，我们目前确实从中受益，但终有一天，我们本土将没有足够多具备这种专业知识的人来承担这项工作。” - **H-1B 签证依赖**：美国科技企业因缺乏足够的本土培养人才，长期高度依赖 H-1B 签证输入海外数理科技精英。 - **印度理工学院（IIT）人才留存变动**：IIT 毕业生的海外流出率从十几年前的高达约 80% 大幅下降至现今的 20%，体现出新兴国家本土高科技产业对顶尖人才的强大吸附力。 --- ### [58:00](https://www.youtube.com/watch?v=QNznD9hMEh0&t=3480s) 联邦基础科研经费收紧与慈善事业的关键角色 谈及科研资助现状时，西蒙斯指出基础研究是“人类知识以及对世界认知的源头活水”，但美国联邦政府对基础科学的投入却日益受限。这一危机体现在两个层面：一方面，联邦政府拨给整体科学研究的总体资金预算本身就在持续缩水；另一方面，各科研资助机构正表现出越来越严重的功利倾向，将有限的资金大举倾斜于所谓的“转化研究”（Translational Research），而不断压缩纯粹的基础研究空间。 ```mermaid flowchart TD accTitle: 联邦科研资助机制的保守化演变 accDescr: 展示国会考核压力如何导致科研机构倾向于支持短期转化研究并冷落基础研究 subgraph 考核压力 A["美国国会 (Congress)"] -->|"要求短期可见回报与明确成果"| B["资助机构 (NIH / NSF)"] end subgraph 资助取向分化 B -->|"偏好明确商业前景"| C["转化研究 (如3年内攻关癌症疗法)"] B -->|"保守规避风险，冷落大胆假说"| D["基础研究 (如探索细胞基本机制)"] end D -.->|"经费缺口亟待填补"| E["民间慈善资助 (西蒙斯基金会等)"] ``` 在官僚体制下，转化研究更容易获得审批，例如申请人承诺三年内研发出某种癌症疗法，就能轻易获得拨款；但若申请人只是试图探索细胞最底层的运作机制，资助机构就会以“应用前景过于遥远”为由予以回绝。西蒙斯解释说，国会不断敦促美国国家卫生研究院（NIH）与美国国家科学基金会（NSF）拿出切实的回报与立竿见影的成果。这种自上而下的考核机制迫使评审机制极度保守化，那些大胆、狂野但前景未知的探索性假说越来越难拿到资助。西蒙斯直言不讳地指出：“政府在支持基础科学方面做得并不够好，因此慈善事业有了用武之地，而且慈善事业正扮演着越来越重要的角色。” - **转化研究挤压基础研究**：政府科研资金偏好周期短、回报明确的临床与应用类课题，使得探索生命与物理底层规律的远期课题面临资金枯竭。 - **资助机构风险厌恶**：在国会追求投资回报率（ROI）的政绩压力下，NIH 与 NSF 等官方机构行事日趋保守，极具创新性的颠覆性构想遭到边缘化。 --- ### [59:26](https://www.youtube.com/watch?v=QNznD9hMEh0&t=3566s) 资助科学的纯粹动力、最爱的数字与数学家 布雷迪·哈兰提出了一个耐人寻味的问题：西蒙斯如今倾注巨资支持基础科学，究竟是因为自己凭借数学取得了巨大财富而心怀感激、意图“回馈”科学，还是出于某种单纯的信念？西蒙斯坦诚且直率地打破了这种常见的道德崇高化叙事。他平静地回应道：“我做这件事是因为它让我感觉很好。我喜欢科学，我喜欢看到它蓬勃发展，我喜欢与科学家们在一起，我也喜欢学到新知识。我的妻子也有同感，她也热爱科学，所以我们非常乐于做这件事情。”当被追问是否有“回馈”的心理包袱时，西蒙斯干脆地表示：“我是否觉得自己在回馈？并没有特别这么觉得。要知道，我能回馈的方式有很多，除了支持科学，我还能做许多别的事情。”对他而言，资助科学研究纯粹源于发自内心的智性热爱与精神共鸣。 在访谈尾声，布雷迪提出了两个经典的轻量提问。首先，当被问及最喜欢的数字是什么时，西蒙斯几乎毫不犹豫、干脆利落地脱口而出：“7。下一个问题。”其敏捷冷幽默的反应引来现场一阵笑声。随后，布雷迪询问他心中最崇敬的数学家是谁。西蒙斯稍作思索后回答道：“阿基米德（Archimedes）和欧拉（Euler）是我目前的最爱。我对这两个人印象极其深刻。”访谈在轻松愉快的氛围中画上句点，面对布雷迪由衷的感谢，西蒙斯微笑着总结道：“好啊，这确实挺有意思的。” - **慈善驱动力**：西蒙斯与妻子玛丽莲·西蒙斯（Marilyn Simons）投身科研慈善的核心动力是享受与顶尖学者交流并见证知识边界的拓宽，而非出于道德绑架式的“报恩”或“反哺”心态。 - **最喜欢的数字**：7。 - **最崇拜的数学巨匠**：古希腊先贤阿基米德与18世纪数学大师莱昂哈德·欧拉。 ## Notable quotes > [42:52](https://www.youtube.com/watch?v=QNznD9hMEh0&t=2572s) 商业中最重要的数学技能是减法。你必须明白你的收入何时会超过你的成本。 — Jim Simons > [49:28](https://www.youtube.com/watch?v=QNznD9hMEh0&t=2968s) 如今高中的数学师资水平下降了，原因很简单：如果你懂得足够多的数学去教高中，你就懂得足够多的数学去 Google 上班，而高中给不了那样的薪水。 — Jim Simons > [39:10](https://www.youtube.com/watch?v=QNznD9hMEh0&t=2350s) 通常情况下，如果有人失败了，他会说‘我运气不好’；而如果他成功了，他就会说‘我是个聪明人’。 — Jim Simons > [47:36](https://www.youtube.com/watch?v=QNznD9hMEh0&t=2856s) 我一直都算是个冒险家，但我拥有良好的品味，尤其是在识人方面。而且我几乎总是与他人合作合伙，这有效降低了风险。 — Jim Simons > [58:00](https://www.youtube.com/watch?v=QNznD9hMEh0&t=3480s) 政府在支持基础科学方面做得并不够好，因此慈善事业有了用武之地，而且慈善事业正扮演着越来越重要的角色。 — Jim Simons > [51:18](https://www.youtube.com/watch?v=QNznD9hMEh0&t=3078s) 如果经营一家企业，清理不称职的人固然重要，但更重要的是认可那些表现优异的员工，奖励并赞赏他们，让他们获得成就感。我们对教师却根本没有这么做，只是一味地抨击、抨击、再抨击。 — Jim Simons > [12:48](https://www.youtube.com/watch?v=QNznD9hMEh0&t=768s) 基础科学是人类认识世界的良种。 — Jim Simons ## Mentioned Jim Simons, Brady Haran, Shiing-Shen Chern, Jeff Cheeger, C. N. Yang, Maxwell Taylor, Marilyn Simons, Archimedes, Leonhard Euler, Massachusetts Institute of Technology (MIT), University of California, Berkeley, Stony Brook University, Institute for Defense Analyses (IDA), National Security Agency (NSA), Renaissance Technologies, The Simons Foundation, Math for America (MƒA), National Institutes of Health (NIH), National Science Foundation (NSF), Google, IBM, Goldman Sachs, Indian Institutes of Technology (IIT), Chern-Simons theory, Stokes' theorem, Riemann Hypothesis ## Video description Shorter version: https://youtu.be/gjVDqfUhXOY More about The Simons Foundation: http://bit.ly/SimonsFoundation James Harris Simons has been described as "the world's smartest billionaire", amassing a fortune through the clever use of mathematics and computers. He is now a renowned philanthropist. NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile Videos by Brady Haran Support us on Patreon: http://www.patreon.com/numberphile Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ A run-down of Brady's channels: http://www.bradyharan.com Sign up for (occasional) emails: http://eepurl.com/YdjL9 [Source](https://www.youtube.com/watch?v=QNznD9hMEh0)

[42:52] Jim Simons: 商业中最重要的数学技能是减法。你必须明白你的收入何时会超过你的成本。 [49:28] Jim Simons: 如今高中的数学师资水平下降了，原因很简单：如果你懂得足够多的数学去教高中，你就懂得足够多的数学去 Google 上班，而高中给不了那样的薪水。 [39:10] Jim Simons: 通常情况下，如果有人失败了，他会说‘我运气不好’；而如果他成功了，他就会说‘我是个聪明人’。 [47:36] Jim Simons: 我一直都算是个冒险家，但我拥有良好的品味，尤其是在识人方面。而且我几乎总是与他人合作合伙，这有效降低了风险。 [58:00] Jim Simons: 政府在支持基础科学方面做得并不够好，因此慈善事业有了用武之地，而且慈善事业正扮演着越来越重要的角色。 [51:18] Jim Simons: 如果经营一家企业，清理不称职的人固然重要，但更重要的是认可那些表现优异的员工，奖励并赞赏他们，让他们获得成就感。我们对教师却根本没有这么做，只是一味地抨击、抨击、再抨击。 [12:48] Jim Simons: 基础科学是人类认识世界的良种。

[49:28] Jim Simons: if you know enough to teach in high school you know enough to work for Google [42:48] Jim Simons: I always say, what's the important mathematics skill in business? It's subtraction: you have to understand when your revenues are going to exceed your costs. [39:11] Jim Simons: It's typical that if someone fails at something, he'll say, ‘I had bad luck,’ and if he makes a success, he'll say, ‘I was a smart guy. [39:11] Jim Simons: I really think what I'm good at is getting good people to work together. [29:31] Jim Simons: You have to know what your costs are when you trade. You're going to move the market when you trade.

[0:08] should we start at the beginning [0:09] okay [0:11] as a child [0:12] were you [0:13] good at mathematics like was was [0:15] mathematics a natural thing for you [0:16] which yeah it was very natural [0:18] and i always liked it i like counting [0:22] i like continually multiplying things by [0:24] two [0:25] although by the time i got to 1024 or [0:28] whatever it is i was [0:29] had enough of it [0:30] uh [0:31] but uh i like i like math i discovered [0:36] as a very young [0:38] kid maybe four [0:40] something called zeno's paradox you ever [0:42] hear of xenos paradox my father told me [0:46] that the car could run out of gas [0:49] and i was [0:50] disturbed by that notion that never [0:52] occurred to me but then i thought well [0:55] it shouldn't run out you could always [0:56] use half of what it has and then you [0:58] could use half of that and then half of [1:00] that and it could go on forever and so [1:02] it would never run out [1:03] so now it didn't occur to me yes but it [1:05] wouldn't get very far either but [1:08] but the idea that in principle you [1:10] didn't have to run out of gas was uh [1:13] kind of a profound thought for a for a [1:16] very little boy were you a talented [1:17] student were you always getting really [1:19] good grades [1:20] well [1:22] i was a pretty talented student i knew i [1:24] was very smart somehow on the other hand [1:26] i was very careless [1:28] so i sometimes screw up arithmetic tests [1:30] just because i did it too fast or [1:32] sloppily but i liked everything about it [1:35] i liked everything about math i loved [1:37] learning [1:38] the formulas for the volume of a sphere [1:41] four thirds pi r cubed i always thought [1:44] that was a great uh a great formula when [1:46] i got to high school [1:49] we started with you know plane geometry [1:51] proofs and theorems that's where i [1:53] really got gripped that i really loved [1:55] that i loved [1:57] working on [2:00] some of the problems were harder than [2:01] others and i liked i liked doing that [2:04] i was never the fastest guy in the world [2:06] but i would plod through it [2:09] and uh with uh [2:12] determination i just i just liked it did [2:14] it feel like this was where your career [2:16] was going to take you or were you like [2:17] another boy who dreamed of being a a [2:20] baseball or something no no no no the [2:22] only thing i thought about was i would [2:24] be a mathematician whatever exactly that [2:26] meant [2:27] i didn't know quite what it meant except [2:29] that [2:31] mathematics was the only subject i [2:32] really liked [2:33] science was okay but it wasn't very well [2:36] taught where i went to high school at [2:37] least i don't think so [2:39] and [2:40] history english i love to read [2:43] but i wasn't a good writer [2:45] i read a lot when i went to mit [2:48] i majored in mathematics of course and [2:50] skipped the first year because i had [2:52] some of those courses in high school and [2:54] i even took a graduate course in my [2:56] freshman year of a second semester [2:58] uh [3:00] in math because it said [3:02] no uh prerequisites required oh no [3:06] prerequisites i'll take that course had [3:08] a very hard time getting my arms around [3:10] that course i finished it okay [3:13] but i i was very puzzled by some of the [3:16] concepts [3:17] however that summer [3:19] i got another book i've got a book on [3:22] this this is algebra [3:24] but not algebra like solving equations [3:26] it was [3:28] abstract algebra and then in a week [3:32] everything came together for me i [3:34] understood i was no longer puzzled i [3:37] understood why they did everything other [3:39] parts of math [3:41] got me stymied for a while [3:44] but typically it would take [3:46] some time for me to sort of grasp what [3:49] it was what they were trying to do and [3:51] then [3:52] uh then it would go very smoothly so i [3:55] graduated early from mit in three years [4:02] did you imagine you would be a professor [4:04] sitting in a university or like what you [4:06] didn't had no grasp before i didn't [4:09] yeah by by the time that my freshman [4:11] year was over i i kind of realized [4:13] that's that's what it would mean that [4:15] someone would pay you for thinking about [4:17] mathematics and creating mathematics [4:19] what i thought earlier was i would would [4:22] do something that involved mathematics [4:24] but [4:25] it was mathematics that i wanted to [4:28] major in and and [4:29] i could see quickly that well that's the [4:31] way [4:32] if you're going to do that you're going [4:33] to be a professor somewhere and uh [4:35] profess you also talked about this week [4:38] of algebra where everything sort of fell [4:40] into place yeah is that a common thing [4:42] is there is there like is this a a thing [4:44] that always happens there's this moment [4:46] where all the all the cogs move into [4:48] place and it's like oh i get it now [4:50] uh i think yeah there are moments like [4:52] that [4:54] sometimes you're introduced to a new [4:56] concept and it's [4:58] you wonder what's [4:59] why wh why are they [5:01] talking about this why is this concept [5:03] interesting and then [5:05] you're thinking you see some examples [5:08] and they say oh yeah okay this is this [5:10] is really this is really good a lot in [5:12] mathematics is making definitions [5:17] you'll see [5:18] things that [5:20] really could come together under one [5:22] aegis [5:23] and and you can define [5:26] this set of notions and sometimes just [5:28] uh a structure which which [5:31] follows all these notions and that's a [5:33] great way that mathematics has advanced [5:35] because when you put a lot of things [5:37] together that have similar [5:38] characteristics then you can try to [5:40] prove theorems about the the general [5:43] set of things rather than some [5:45] particular example [5:47] and that turns out to be a very powerful [5:49] approach so uh making a good definition [5:52] is a [5:53] is a good thing [5:58] they wanted me to go to berkeley and get [6:00] away from mit [6:01] meet some new [6:02] faculty because i was quite close to the [6:04] mit faculty and they thought [6:06] i think they didn't want to get rid of [6:08] me so much as [6:10] they thought i was probably pretty good [6:12] so i should get exposed to [6:15] a certain guy [6:16] named chern who was just coming to uh [6:20] berkeley that year [6:22] and i got this very nice fellowship and [6:23] i went there i was very eager to work [6:25] with churn me turned except he wasn't [6:27] there [6:28] he celebrated his first year at berkeley [6:31] he had just come to berkeley and he [6:32] celebrated that first year by taking a [6:34] sabbatical [6:35] so he wasn't there [6:37] so i work with another guy which which [6:39] was fine [6:41] and by the time churn came [6:43] in the second year i was [6:45] already [6:47] pretty far along with the with the [6:49] thesis project i was giving a seminar at [6:52] the beginning of my second year at [6:53] berkeley and in walk this tall chinese [6:55] guy [6:56] and i said to [6:58] kai next me who's that i said that's [7:00] churn that's churn i didn't know he was [7:03] chinese i thought churn was probably [7:05] short for chernowski or something or he [7:07] was probably some polish guy who who had [7:09] shortened his name to churn if it had [7:11] been chen or chan i would have known it [7:13] was chinese but churn with the r i know [7:16] but anyway uh [7:17] so i met chern then and we became uh [7:20] friends because i was much younger than [7:22] he but we became friends and later [7:23] collaborators can you give some idea [7:25] about what your area of specialization [7:28] is at this point what what are you [7:29] zeroing in mathematically on well at [7:32] that point and pretty much thereafter [7:35] the field [7:37] that i worked in was called differential [7:39] geometry differential geometry is [7:40] geometry but it's the geometry of curved [7:43] spaces it's not flat things in the plane [7:46] it's it's any any shape or or form but [7:50] typically with a with some distance [7:53] function so that you knew how far apart [7:55] things were and the basic object to [7:57] study is what's called a manifold [7:59] and a manifold is a lot of pieces of [8:02] space [8:03] glued together [8:04] so for example the surface of a sphere [8:07] is a manifold now you can't just take [8:10] one little sheet of paper and make a [8:13] sphere out of that but you could glue a [8:14] bunch of pieces of paper together and [8:16] make a sphere so a manifold is something [8:19] that locally in your neighborhood looks [8:22] like it's just regular space maybe it's [8:24] curved a little bit but globally [8:26] it's uh it could be quite different so [8:29] and the surface of a tire [8:32] of a doughnut for example [8:34] is fundamentally different from the [8:36] surface of a spear you can't deform one [8:39] into the other what really got me onto [8:41] it [8:42] is a certain theorem [8:44] which is called stokes theorem [8:47] now stokes theorem [8:49] is the ultimate i think [8:52] generalization of what was originally [8:54] called the fundamental theorem of [8:56] calculus now i don't know if you studied [8:58] calculus but [8:59] the basic [9:00] theorem [9:02] is [9:03] if you integrate the derivative of a [9:06] function so you take a function you take [9:07] its derivative [9:09] first derivative and then you integrate [9:11] that let's say [9:12] from a to b [9:15] well that gets you back the original [9:17] function the answer when you integrate [9:20] the derivative is [9:22] of f it's well it's f of b minus f of a [9:26] that's the answer if you integrate [9:29] the derivative of a function you'll get [9:31] back the value of the function well that [9:33] was [9:34] the fundamental theorem of calculus [9:36] presumably newton knew that [9:38] now that had been generalized into [9:41] higher dimensions so there were other [9:42] things you could integrate [9:44] and differentiate and go from boundaries [9:47] to interiors and so on and the general [9:50] statement of that theorem [9:52] was [9:53] to me almost breathtaking [9:56] it was so beautiful [9:58] that theorem and that's a a bit one of [10:00] the basic theorems in differential [10:02] geometry and [10:04] it's about integrating something [10:07] over the [10:08] boundary [10:10] uh [10:11] and that's the same as integrating [10:13] something [10:15] else over the interior something related [10:17] to it it's derivative in effect it's [10:19] called it's differential so there's a [10:22] whole calculus of things called [10:24] differential forms and [10:25] integration and all that and that [10:28] takes place in manifolds in general and [10:31] anything that [10:32] looks like pieces of space [10:35] so i love that theorem and uh that's [10:38] what got me into differential geometry [10:40] so was it was it a beauty or an elegance [10:42] you saw or was it a trophy and a prize [10:44] you saw that could be chased no it was [10:46] just a beauty [10:48] it was just the beauty of it [10:50] i just liked it i i learned a fair [10:52] amount of algebra and that was fine but [10:54] it didn't grab me [10:56] but the geometry did [10:58] so that's what i uh [11:00] specialized in [11:02] and and when i got to berkeley [11:04] uh [11:06] i was fooling around and started [11:10] i'd made some observations and i [11:12] mentioned them to [11:14] my thesis advisor the guy i was i was [11:16] going to work with [11:18] and he said oh that's interesting [11:21] that makes me think about such and such [11:23] a problem [11:24] that was there was a [11:26] problem floating around [11:28] that uh [11:30] people had been trying and failing to [11:32] solve but i i thought oh [11:35] that's very interesting so i started [11:37] working on that and he [11:39] advised me not to [11:40] because so-and-so had tried and someone [11:42] else had tried it and these those were [11:43] big shots and i was just [11:46] a little shot but uh i didn't pay much [11:48] attention to him [11:50] and i i solved it and uh just worked [11:54] through it and worked through it and you [11:56] know [11:58] had a little [11:59] help along the way with for people but [12:01] uh but basically i drove that i had done [12:04] some other mathematics after my thesis [12:06] work on something called minimal [12:08] varieties and it was kind of a [12:09] fundamental paper it took me six years [12:11] to write that paper [12:13] people were i think thought how could i [12:15] be take six years but anyway it did and [12:18] and that turned out to be [12:20] a very good paper that was where i was [12:23] coming from at roughly that time frame [12:25] or a year or two afterwards i went [12:28] when i was 30 to stony brook to be [12:31] chair of their [12:33] math department stony brook university [12:35] was a very new university they had a [12:37] rather poor math department in fact it [12:39] was very bad but an excellent physics [12:41] department they offered me this job as [12:43] being chairman and i thought that would [12:44] be a lot of fun in that time frame [12:48] i had decided to try to learn something [12:50] about an area of topology which is [12:53] related to geometry it's the kind of [12:57] handmaidens of each other [12:58] called characteristic classes whatever [13:01] that might be and i thought i'm going to [13:04] just learn these [13:05] classes because i didn't really know it [13:07] and it was important and i wanted to [13:09] learn about it so i [13:11] kind of started from the beginning and [13:14] worked my way up and [13:17] i was [13:18] trying to [13:21] solve a problem [13:22] as as i later discovered had [13:27] intrigued many people [13:28] and it's never been solved [13:30] satisfactorily so [13:32] since i say that you know i didn't solve [13:34] it either but in the course of trying to [13:37] do that [13:39] certain terms came up [13:42] certain [13:44] functions of a sort [13:46] that [13:47] began to look just very interesting to [13:50] me [13:51] and uh [13:53] i saw well [13:55] so they were a pesky term that i [13:58] couldn't get rid of i needed to get rid [13:59] of that term in order to make this [14:01] formula that i wanted but the term [14:03] seemed to have a life of its own [14:05] and [14:07] one thing led to another i defined a [14:10] certain invariant of a three-dimensional [14:12] manifold [14:14] and [14:16] use that [14:17] to prove some what's called immersion [14:20] theorems whatever those are this was a [14:22] very handy thing [14:24] and i showed it to churn [14:26] said look at these results [14:28] in three dimensions and he looked at it [14:30] and said oh well we could do this in all [14:32] the dimensions because it was an area [14:34] that he really knew about [14:36] not the results that i'd gotten but the [14:38] whole the general area so we worked [14:40] together [14:41] and we came up with uh with uh well uh [14:46] this [14:47] these results this whole structure [14:50] in fact there's [14:53] that's uh [14:54] the [14:55] slides of the presentation that churn [14:59] made in uh at the international congress [15:02] in [15:03] the early 70s it was very nice geometry [15:07] i pushed on with it and we [15:09] defined some things called differential [15:10] characters which was another chapter [15:14] uh with working with a guy named chiger [15:16] but [15:16] the chern simons invariants about 10 [15:19] years later [15:21] the physicists got a hold of it and it [15:24] seemed to [15:26] be very good for what ailed them [15:28] or whatever what might have hailed them [15:30] and so [15:32] and it wasn't just string theory [15:34] as i subsequently developed it was kind [15:35] of all areas of physics including [15:37] condensed matter theory [15:40] even some [15:41] astronomers seem to want to look at [15:43] those terms that's really what's great [15:45] about basic science in this case [15:47] mathematics i mean i didn't know any [15:49] physics [15:50] it didn't occur to me that this material [15:53] that chern and i had developed would [15:55] find use [15:57] somewhere else altogether this happens [16:00] in basic science all the time [16:03] that one guy's discovery [16:05] leads to someone else's invention and [16:07] leads to another guy's machine or [16:09] whatever it is uh you know so [16:13] basic science [16:15] is at the [16:16] you know [16:18] it's the seed corn of our of our [16:20] knowledge of the world what did it feel [16:22] like at the time you were coming up with [16:23] it did it just feel did it feel obscure [16:26] and just like a little diversion and [16:27] then ten years later it felt special but [16:30] it never felt like a little diversion i [16:31] really liked the uh i really liked the [16:33] results i i loved the subject but i [16:36] liked it for itself i didn't i wasn't [16:38] thinking of applications [16:41] you know i mentioned to uh [16:43] cn yang who was at stony brook at the [16:45] time who was a nobel prize winning [16:46] physicist of great renown [16:49] i said i've got these things [16:52] maybe they'd be useful in physics [16:53] because [16:54] i knew the physicists were looking in [16:57] the same places [17:00] using certain mathematical structures [17:02] but he didn't bite and i didn't know how [17:06] it would be useful so i just [17:08] left it alone but i was very pleased [17:10] with the math and then it led to [17:14] another [17:15] set of definitions [17:17] and some math that i did with this guy [17:19] jeff chiger [17:21] which started as sort of a mini field [17:23] although i didn't realize it at the time [17:25] called it's now called differential [17:27] cohomology [17:28] and so that there's a fair amount of [17:31] people working in that area what does [17:32] that make you feel does it become like [17:34] vindication or what i did was more [17:36] useful than i thought or like what do [17:39] you think when it gets used 10 years [17:40] later or by then are you divorced from [17:42] it and you're like do what you want with [17:43] it oh it's always made me feel very good [17:45] of course naturally you like to think [17:47] that something you did had far-reaching [17:50] uh ramifications you know it was nice [17:53] but it wasn't [17:55] i didn't go to bed dreaming about ah now [17:57] i've revolutionized physics with first [17:59] of all i didn't revolutionize physics [18:01] but but did some stuff there and [18:06] but sure it made me feel good [18:12] actually in the middle of my mathematics [18:15] career which ended when i was about 37 [18:17] or 38 [18:19] was that i spent four years at a place [18:21] called the institute for defense [18:22] analyses [18:23] down in princeton which was a [18:26] super-secret government based national [18:29] security agency based [18:31] a place for [18:33] code cracking [18:35] trying to break [18:37] the enemies whoever it was russia i [18:40] guess code machines and cypher machines [18:42] i spent four years there in princeton [18:44] during that time i was working on this [18:46] remember i said i took me six years to [18:48] work through all this [18:50] stuff in [18:51] minimal varieties i did a lot of it [18:53] while i was there but i also learned [18:56] about computers [18:57] and algorithms [19:00] in the code cracking [19:02] field [19:03] i was no good as a programmer terrible [19:05] but i was pretty good at coming up with [19:07] algorithms [19:08] and uh and trying to you know and i [19:11] found that very exciting to [19:13] think oh this might help crack this cold [19:16] here's an algorithm which could work [19:18] someone else would program it up [19:20] then it would run on the computer [19:22] uh and maybe it would work and maybe it [19:24] wouldn't and i did one thing there that [19:26] was quite good because i can't tell you [19:28] what it was it's all classified so i had [19:31] a good career there both doing [19:32] mathematics and [19:34] learning about the fun [19:36] of computer modeling let's say was that [19:39] specialization that you'd had during [19:41] your phd the manifolds and the topology [19:44] was that related to the algorithms were [19:45] the two or three oh completely so why [19:48] were you drafted in for that in the [19:49] first place then they paid money [19:53] i was getting kind of bored [19:55] simply being an academic [19:58] and also [19:59] this work [20:00] this six-year project was [20:02] maybe making me feel [20:05] gosh other guys are publishing papers [20:06] and i'm not but i i wasn't thrilled with [20:10] being an academic [20:12] and this place hired mathematicians a [20:15] handful [20:16] you could do mathematics [20:18] half your time and the other half of [20:20] your time you were supposed to work on [20:22] their stuff [20:24] there was no teaching so it was like oh [20:26] i could do as much mathematics as i was [20:27] doing anyway [20:28] and and they and they paid better [20:32] and i thought this would be interesting [20:34] and a nice change and it was [20:37] and i i enjoyed it [20:40] i did a lot of good math or that i [20:42] thought was good and [20:44] it did good work for them but [20:46] that ended after four years because i [20:49] got fired [20:50] and uh well you can't you can't just [20:52] leave it at that you got fired okay [20:55] why did you get fired [20:57] well [21:00] i got fired [21:03] because this was in the middle of the [21:04] vietnam war [21:06] uh which i [21:08] didn't like [21:09] the war [21:10] not that we were doing anything to [21:12] support the war in this particular [21:14] organization but nonetheless i just [21:16] didn't like it and the head [21:17] of the organization [21:20] he was down in washington [21:22] he was a big shot named maxwell taylor [21:24] general maxwell taylor he wrote an [21:27] article in the new york times magazine [21:29] section of a sunday magazine a cover [21:31] story how we're really winning the war [21:34] in vietnam we just have to stay the [21:36] course and it's all going to be great [21:39] and i thought that's a lot of baloney [21:42] so i wrote a letter to the time saying [21:44] not everyone who works for general [21:46] taylor supports his views [21:49] and uh in my opinion blah blah blah it [21:51] was a good letter and they published it [21:54] right away of course because it was [21:56] unusual that someone would write such a [21:58] letter in his situation [22:00] i didn't hear a peep [22:02] no one said anything uh at the company [22:05] they didn't say [22:06] you shouldn't have done that but i was [22:08] clearly on the watch list did you did [22:10] you when you wrote it did you know you [22:12] were doing something reckless no [22:14] i didn't really think it was reckless [22:16] because it was my opinion and it really [22:18] didn't have anything to do with my work [22:21] but then [22:22] about three or four months later a guy [22:24] from newsweek magazine [22:29] came to see me and he said he's doing an [22:31] article [22:33] about people who work for the defense [22:35] department who are opposed to the war [22:37] and he says i have a lot of trouble [22:39] finding such people but could i [22:41] interview you [22:43] well i was 29 years old no one had ever [22:45] asked to interview me before it sounded [22:47] like hey maybe i'll i'll be interviewed [22:49] okay you can interview me [22:51] so [22:52] we asked this and that but [22:54] he really wanted to know so what is your [22:56] policy [22:57] so i sort of made up a policy although [22:59] it was [23:01] pretty much true [23:02] i said well you know here [23:06] at ida [23:07] you [23:08] have to spend uh [23:11] at least 50 percent of your time on [23:13] their stuff [23:14] in those days it was secret that it was [23:17] even [23:17] codes and ciphers so i just said their [23:19] stuff [23:20] uh but you could spend 50 of your time [23:22] in mathematics and so my algorithm now [23:25] is [23:26] until the vietnam war is over i will [23:28] spend all my time on mathematics and [23:30] then [23:31] after it's over i'll spend all my time [23:34] on their stuff until the two things [23:36] match up again and then uh [23:39] and that was kind of largely true i was [23:41] doing mostly mathematics but i i was [23:43] doing a little of their stuff [23:44] so [23:46] then [23:47] it occurred to me to tell my local boss [23:49] that i gave this interview [23:52] and he said well what'd you tell him i [23:55] said well i told him what i just said to [23:57] you he said you did [23:59] he says oh i better call taylor [24:02] his boss [24:03] and he called taylor [24:06] and i came back into his office and he [24:08] said you're fired [24:10] he said i'm fired [24:12] yes you're fired taylor fired you [24:14] taylor told me to fire you [24:17] so [24:18] well i was fired i said you know [24:20] i don't know how you can fire me my [24:22] title [24:23] is permanent member [24:25] which was [24:28] i started as a temporary member [24:31] and then i became a permanent member [24:33] and the boss was very funny he said well [24:36] here's the difference between a [24:37] temporary member and a permanent member [24:40] a temporary member has a has a contract [24:43] a permanent member doesn't [24:45] i had no contract so i was out of there [24:48] and it was amusing i mean i i wasn't [24:51] i had solved this big math problem that [24:53] i told you about the six year thing i [24:56] knew i was going to get a job very [24:58] easily so [24:59] i wasn't really worried about that [25:02] you've honed your skills with algorithms [25:04] yeah and you've learned a lot about [25:05] computers so i'm seeing the writing on [25:07] the wall here for where things go next [25:08] how how do we progress to yeah so uh at [25:11] a certain point [25:13] now i wasn't then i went to stony brook [25:15] after this it was chair [25:17] and uh did this work with churn [25:20] and did some work with chiger and and we [25:22] got stuck we were trying to [25:24] prove something [25:26] uh mathematical thing and it was very [25:28] very frustrating worked on it for about [25:30] two years we got nowhere [25:32] i mean it's okay to work for a long time [25:34] if you feel you're getting somewhere but [25:36] we have we got absolutely nowhere [25:38] uh on this problem [25:40] and uh [25:44] my father had made a little bit of money [25:46] and [25:48] um [25:50] i [25:51] have had the opportunity to [25:53] try investing it [25:55] and that [25:57] was interesting [25:59] and i thought you know i'm going to try [26:01] another career altogether [26:04] and so i went into the [26:06] money management business so to speak so [26:10] you started [26:11] with some of your dad's money and that [26:12] got you a taste of an interest in it [26:14] some family money and then some other [26:16] people put up some money and uh [26:19] i did that [26:21] uh no models [26:22] no models for the first two years so [26:24] what were you doing then you were just [26:25] using cunning and uh you know just no [26:29] like normal people do like normal people [26:31] do [26:32] and i brought in a couple of people to [26:34] work with me and [26:37] we were extremely successful i think it [26:39] was just plain good luck but nonetheless [26:41] we were very successful but i could see [26:45] but this was a very gut-wrenching [26:47] business you know you come in one [26:48] morning you think you're a genius the [26:50] markets are for you we were trading [26:51] currencies and commodities and [26:54] financial instruments and so on not [26:55] stocks but those kinds of things [26:58] and the next morning you come and you [26:59] feel like a jerk the market's against [27:01] you it was very gut-wrenching and in [27:03] looking at the patterns of prices i [27:06] could see [27:08] that there was something we could study [27:09] here that there may be some ways to [27:11] predict prices [27:13] mathematically or statistically [27:15] and [27:16] i started working on that and then [27:18] brought in some other people [27:20] and gradually built models [27:22] and the models got better and better and [27:24] finally the models replaced the [27:26] fundamental stuff so it took a while i [27:28] would have thought with your background [27:30] and mathematician this would have almost [27:33] occurred to you immediately like you [27:34] would have straight away saying this [27:36] what what was the two-year delay well [27:38] two things i saw it pretty early [27:42] but [27:44] and i brought in a guy who was a [27:46] wonderful [27:47] guy also from the code cracking place [27:50] and he was uh i thought together we'll [27:53] we'll start building models that was [27:55] fairly early but it wasn't right away [27:58] but he got more interested in the [28:00] fundamental stuff and he says the models [28:01] aren't going to be very strong and so on [28:03] and so forth so [28:04] we didn't [28:06] get very far [28:07] but i knew there were models to be made [28:08] then i brought in another mathematician [28:10] and a couple more and a better computer [28:13] guy and then we started making models [28:15] which really worked but you know [28:19] the [28:19] the general [28:21] uh there's something called the [28:22] efficient market theory [28:25] which says that [28:27] there's nothing in the data let's say [28:30] price data [28:31] which will indicate anything about the [28:34] future because the price is sort of [28:37] always right the price is always right [28:39] in some sense [28:40] but that's just not true [28:42] so there are anomalies in the data even [28:44] in the price history data for one thing [28:47] uh [28:48] commodities especially [28:50] used to trend [28:53] uh not dramatically trend but trend so [28:56] if you could get the trend right you'd [28:58] bet on the trend and you'd make money [28:59] more often than you wouldn't whether it [29:01] was going down or going up that was an [29:03] anomaly [29:05] in the in the data but gradually we [29:07] found more and more [29:09] and more and more anomalies none of them [29:12] is so overwhelming that you're going to [29:14] clean up on a particular anomaly because [29:17] if they were other people would have [29:18] seen them so they have to be subtle [29:20] things [29:21] and you put together [29:23] a collection of these subtle anomalies [29:27] and you begin to get something that will [29:29] predict pretty well how elaborate are [29:31] these things because in my head i'm [29:32] imagining you know some equation like uh [29:35] like pythagoras equation you put a few [29:36] numbers in and something spits out but [29:38] are these giant beasts of equations and [29:41] algorithms or are they are they simple [29:42] things [29:43] uh [29:44] well the the system [29:46] as it is today is is extraordinarily [29:49] elaborate but it's not a whole lot of [29:51] quite you know it's it's what's called [29:52] machine learning [29:54] so you find [29:57] things that are predictive [30:00] you might guess oh [30:02] such and such [30:04] should be predictive might be predictive [30:06] and you test it out in the computer and [30:07] maybe it isn't maybe it isn't you test [30:09] it out on long [30:11] term historical data [30:14] and uh price data and other things and [30:16] then [30:17] you add to the system this if it works [30:19] and if it doesn't you you throw it out [30:22] so [30:22] there aren't elaborate equations [30:25] at least not for [30:27] the prediction part but the prediction [30:29] part is the only it's not the only part [30:31] you have to know what your costs are [30:34] when you trade [30:36] you're going to move the market when you [30:38] trade now the average person will [30:41] make a buy 200 shares of something and [30:43] he's not going to move the market at all [30:45] because it's too small but if you want [30:46] to buy 200 000 shares you're going to [30:49] push the price how much you're going to [30:50] push the price how are you going to [30:52] you know are you going to push it so far [30:54] that you [30:56] you can't make any money because you've [30:57] distorted things so much so you have to [30:59] understand costs [31:01] and that's something that that's [31:02] important and then you have to [31:04] understand how to minimize the [31:06] volatility of the whole [31:08] of the whole assembly of positions that [31:10] you have and [31:12] be [31:13] uh [31:14] so you have to do that that last part uh [31:18] takes some fairly sophisticated applied [31:20] mathematics [31:22] not uh [31:23] earth-shattering but but fairly [31:25] sophisticated what discipline of [31:27] mathematics or disciplines is it [31:28] multi-disciplinary or are we talking [31:30] mostly statistics it's mostly statistics [31:34] and uh [31:36] some [31:37] uh [31:38] some probability theory [31:40] and [31:41] but i can't get into you know what [31:43] things we do use and what things we [31:45] don't use we [31:47] reach [31:48] for different things that might come [31:50] that might be effective [31:53] so we're very [31:54] universal we don't have any any uh but [31:58] it's a big computer model for one thing [32:00] there's a there is a capacity [32:02] to the major model [32:05] it can manage a certain amount of money [32:06] which is rather large but it can it [32:09] can't manage an enormous amount of money [32:11] because you're pushing you're going to [32:12] end up pushing the market around too [32:14] much so it was kind of a sweet spot as [32:16] to how much it's reasonable to manage [32:18] therefore it would never grow into some [32:21] behemoth [32:22] which would uh you know take everybody [32:24] out and you'd be the only player i mean [32:26] well of course you were the only player [32:27] that'd be known to play against there [32:29] are there are limitations at least [32:32] the way the way we [32:34] the way we see it [32:36] but we keep we keep improving it we have [32:38] about a hundred phds working for the [32:40] firm that's what i mean i mean how did [32:42] you get to that point did you start to [32:43] think we need this we need that what did [32:45] we just hired smart people my [32:48] my algorithm has always been you get [32:50] smart people together [32:53] uh [32:54] you give them [32:56] a lot of freedom [32:59] create an atmosphere where [33:02] everyone [33:03] talks to everyone else they're not [33:05] hiding in a corner with their own little [33:07] thing [33:08] they talk to everybody else [33:11] and [33:12] you provide the best [33:15] uh infrastructure the best computers and [33:17] so on that people can work with [33:20] and make everyone partners so that was [33:24] the model that we used in in in [33:26] renaissance so we would bring in [33:28] smart folks and uh [33:31] they didn't know anything about finance [33:33] uh [33:34] but [33:36] they learned what was your employment [33:38] criteria then if they knew nothing about [33:40] finance what were you looking for in [33:41] that someone with a phd in physics and [33:43] who'd had uh [33:44] five years out and had written a few [33:46] good papers and was obviously a smart [33:48] guy or in astronomy [33:50] or in mathematics or in statistics [33:55] someone who had done science [33:57] and done it well [33:59] and was interested in [34:01] you know [34:03] applying [34:05] his mind or her mind although it was [34:08] mostly his [34:09] to uh [34:11] you know modeling markets and making [34:13] money but it's a very good spirit now [34:16] i've [34:17] been six years away from the company so [34:19] i i'm not running it anymore but [34:22] i'm the chair of the board and i [34:25] go to a monthly board meeting i think [34:27] the the morale is very good the spirit [34:29] is good [34:30] and [34:32] it's really [34:33] a very good way [34:35] to work scientifically [34:37] a it's a big collaborative effort [34:40] and uh and everyone [34:43] is happy to see someone else come up [34:46] with something good [34:47] because he the first person is going to [34:49] share in that because because everyone's [34:51] shared in the profits so uh [34:54] so okay [34:55] you might wish it was you to show how [34:57] smart you were but nonetheless [34:59] good he did it i'm going to make money [35:00] from it i would imagine lots of people [35:02] want to be financially successful most [35:05] most people want that of course i [35:06] suppose and lots of people are good at [35:08] mathematics and know a lot about [35:10] computers like you know [35:12] at your level i would imagine why did [35:14] you do it why didn't someone else do it [35:15] i don't know well first of all some [35:17] other people have done it [35:19] uh i think that we're [35:21] uh [35:22] our firm is [35:24] better but nonetheless uh i'm pretty [35:26] sure of that but nonetheless other [35:29] people have done some very [35:31] good modeling and so we're not alone [35:35] but it's not easy to do [35:37] and there's a big [35:39] barrier to entry [35:41] for [35:42] example huge data sets that we've [35:45] collected over the years programs that [35:47] we've written to make it really easy to [35:50] test hypotheses and so on [35:53] the infrastructure is exceptionally good [35:56] so everything is tuned right it took [35:59] years to learn how to do that people [36:01] don't leave our firm or if they do they [36:04] believe to [36:06] just do something else altogether [36:08] everyone has signed a forever [36:10] non-disclosure agreement and so on [36:12] because we're you know we're very [36:13] secretive about what we do because you [36:15] can't patent that stuff or copyright it [36:18] because then everyone would see what it [36:19] is and someone will just work around it [36:21] and say oh that patent's no good look [36:24] i've made this twist and that tweak and [36:26] it's different so you can't [36:28] you [36:29] what you have is [36:31] your intellectual property and you have [36:32] to keep that to yourself so [36:35] uh yes we were very successful continue [36:38] to be [36:39] as i say there are others [36:41] but most [36:43] very few [36:45] uh investment operations are a hundred [36:48] percent because this is a hundred [36:49] percent model driven it's not ninety [36:51] percent or eighty percent some people [36:53] have models [36:54] and for uh [36:57] you know for advice [36:59] so what does the model say oh yeah let's [37:00] go oh i don't forget that i i don't want [37:03] to pay attention to that so uh [37:06] but [37:07] you know uh [37:09] renaissance is 100 model driven no trade [37:12] is ever made because someone walks into [37:14] the trading room and says hey let's buy [37:16] ibm [37:17] it's a sure winner or anything like that [37:20] uh you know we got too much [37:22] uh [37:23] google we got to show it [37:26] nobody does that [37:27] it may be that we had too much google [37:29] but nonetheless uh he might have been [37:31] right [37:32] but uh it's just what the model says and [37:35] that [37:36] religious sticking to the model is the [37:39] only way you can run such a business [37:41] because you cannot simulate [37:43] that guy who walked in and said hey [37:44] let's [37:46] google's too high let's sell it how can [37:47] you simulate that you don't know what [37:49] might have happened [37:50] but you can simulate a you can [37:53] come up with a model or a new predictor [37:56] and you can simulate it in the past and [37:58] see how did it do [37:59] so [38:00] you have to stick to it i know you guys [38:03] made the model so [38:05] you do have the ownership of it and feel [38:07] proud of it but is it hard to follow the [38:09] model [38:10] religiously like is it hard for your ego [38:12] to think all the successes because of [38:14] the computer like and i just i just sat [38:16] there and watched no the computer's just [38:18] a tool that we used to i mean it's uh [38:22] a good cabinet maker doesn't say it's [38:24] all because of my wonderful chisel you [38:26] know you may have great film equipment [38:29] but that's not why you're a success at [38:31] doing what you're doing you you're [38:33] working with good equipment but uh [38:34] another guy would make a mess of it with [38:36] the same equipment so [38:38] no we don't we don't feel [38:40] oh the computer is doing everything the [38:42] computer does what you tell it to do [38:44] mathematics is very collaborative and [38:46] things that are learned are built upon [38:48] by sharing are you learning things [38:50] behind the locked doors at renaissance [38:52] that could help mathematics [38:54] but you're not sharing because you want [38:57] to keep them a secret to help the [38:58] business [38:59] no [39:01] there was there's nothing [39:02] there's nothing that we're learning [39:04] behind locked out doors and renaissance [39:06] that would help the general field of [39:08] mathematics or the general field of [39:09] science as far as i can tell do you [39:11] think there's something about your [39:13] personality that made you able to do it [39:16] or is it just [39:17] this is luck well i think a lot of it's [39:19] luck i probably have a good personality [39:22] for running a group of people but there [39:23] are other people who are maybe even have [39:26] a better personality for doing that we [39:28] underestimate [39:30] uh the role of luck [39:32] it's typical that if someone fails at [39:34] something he'll say i had bad luck [39:37] and if he makes a success he'll say i [39:39] was a smart guy [39:41] and uh [39:42] oh i was just lucky uh people don't [39:45] usually say that uh when when uh [39:48] if they make a big success and of course [39:51] obviously not everyone can make a big [39:54] success but [39:55] i think the luck played a role i was in [39:57] the right place at the right time [39:59] but i i really i think what i'm good at [40:02] is [40:03] getting good people [40:05] to [40:06] work together [40:08] so [40:08] it was more you would think it would [40:10] more your managerial ability than your [40:12] mathematical genius that resulted in it [40:14] definitely wasn't my mathematical genius [40:16] i think i'm a you know i'm a pretty [40:18] smart guy i can understand this stuff so [40:21] uh but i wasn't and i did come up with a [40:24] few predictive algorithms so that was [40:26] fine but uh many people did [40:30] that's [40:31] i knew i wasn't going to come up with [40:32] all them so that's why we have all these [40:34] folks uh so it wasn't my mathematical [40:37] genius but i think people respected me [40:40] because i was a a good scientist so they [40:42] said well [40:44] he may act stupid but we know he's [40:46] really smart so [40:48] you know you had you had a few runs on [40:49] the board i would say yeah are you given [40:52] that given that you will put some of it [40:54] down to luck what are you more proud of [40:57] all of this in the business or the or [40:59] the mathematics [41:00] from that first half of your career oh [41:05] to the extent that i'm proud [41:10] i think i'm proud of both i i think [41:14] you know i've done some mathematics and [41:16] some of it's had a positive effect and [41:18] i'm i guess i'm proud of that [41:20] and i've built a nice business and i'm [41:22] proud of that i don't say i'm prouder of [41:24] one than the other and now for the last [41:27] number of years i've been working with [41:29] my wife on this foundation which she [41:32] started actually in 94 [41:34] with my money but nonetheless she [41:36] started the foundation and then i joined [41:40] i got [41:40] more and more involved with the [41:42] foundation as [41:44] time went on and now that's my main [41:46] thing and i'm pretty proud of the [41:47] foundation let me focus your focus you [41:50] more on which the mathematics versus the [41:52] business then would you would you trade [41:54] any of your [41:55] any or all of your business success for [41:58] for being the man who cracked the [41:59] riemann hypothesis or something like [42:01] that no that's a good question [42:07] would i trade that for [42:12] well i probably trade some of it i mean [42:14] for the riemann hypothesis it would [42:16] certainly uh [42:17] i guess be a thrill to to [42:20] solve three men hypothesis i'm pleased [42:23] mostly with what [42:25] with [42:26] the way my career has gone [42:30] so [42:32] would i trade part of it for something [42:35] i don't know it's i've never looked back [42:38] and said i wish [42:40] at least in business i wish i hadn't [42:43] done that or i wish i had done this and [42:45] not that whatever it is i've never [42:47] looked back that way i guess the thing [42:49] i'm getting at is what do you define [42:50] yourself as a businessman or a [42:51] mathematician [42:53] well [42:55] i would not be very good [42:57] at running an ordinary business [43:00] if i had to run [43:02] a big manufacturing business or [43:04] something like that i don't think i'd be [43:06] very good at there's a [43:08] level of detail that i would find [43:10] tedious uh i'm not the best organized [43:14] person in the world and frankly [43:16] i would be bored [43:20] so [43:21] i'm not your [43:22] typical businessman [43:24] the kind of business that i did [43:27] run [43:28] was very natural to me so in that sense [43:30] i was a businessman i [43:32] i like business sort of i you know i [43:36] i like i [43:39] i always say what's the important [43:41] mathematics skill in business is [43:43] subtraction [43:45] you have to understand when your [43:47] revenues are going to exceed your costs [43:51] you know some some people they just look [43:53] at revenues hey we're growing yeah but [43:55] you're losing money every day well [43:57] that'll take care of itself after a [43:58] while so um but [44:01] i i don't think i'd be uh [44:04] i once [44:06] had to for about six months [44:09] run a small business [44:10] in the computer area a business that we [44:12] had started [44:14] uh or invested in and then [44:16] uh wasn't going well and we had to get [44:18] rid of the head and find someone new and [44:20] i found myself running it [44:22] for about [44:24] three to six months commuting to [44:25] philadelphia [44:27] and [44:28] i came to the conclusion [44:30] i'm doing a better job than the guy was [44:33] there before but i'm not doing a very [44:35] good job [44:36] and i found myself in business meetings [44:38] like with the distributor from st louis [44:41] at some [44:43] and i remember saying i think what am i [44:45] doing spending my time with some [44:47] distributor from st louis i mean this is [44:50] not the way i want to [44:51] run my life finally we got someone in he [44:54] really knew how to run a business and uh [44:56] then that that was his [44:58] that kind of a business [45:02] the foundation is focused [45:04] on support of scientific research [45:07] primarily basic science but not [45:09] completely because we have a large [45:11] autism project which [45:13] involves a lot of basic science but the [45:15] but [45:16] treatments are a goal but the rest is [45:19] support of mathematics physics computer [45:22] science [45:23] biology [45:25] of all sorts neuroscience genetics we [45:28] support basic science and [45:31] that [45:32] is what we like to do there's a certain [45:34] amount of outreach we we have a math for [45:36] america pro we spend maybe [45:38] 10 or 15 percent on uh outreach outreach [45:42] and education but uh 80 85 [45:45] is uh [45:47] support of basically basic science [45:49] almost the nature of basic mathematical [45:51] research is you can't really know where [45:52] it's going to go that's right so what [45:54] are you do you just are you are you [45:57] throwing [45:58] money at a wall and seeing what sticks [46:00] or like how targeted are you about well [46:01] to some extent yes uh we have [46:06] investigator grants which give [46:08] outstanding mathematicians and [46:10] physicists and computer scientists uh [46:13] 10-year [46:15] run [46:16] where they they have support for [46:18] for 10 years and they can use that money [46:21] to [46:22] for a post doc or something like that to [46:24] help their work along [46:26] we don't know what work it's going to be [46:27] we we have no i well we know what the [46:29] guy has done but it's it's it's not [46:32] these are very very competitive [46:35] and they're just the best people and [46:37] it's helping their careers whatever they [46:39] might do we also have collaborative [46:42] projects that we support there there is [46:44] a goal [46:46] um but it can be a rather vague goal [46:49] like one is origins of life well we'd [46:51] like to know how we all got here what [46:54] how did life originate outside [46:57] inside what what was the path [46:59] to life [47:00] uh so there's [47:02] i don't know 40 or 50 people working on [47:04] that [47:05] and uh it's a very [47:08] exciting project we're making some [47:10] progress so there's a goal [47:12] but do i think that in the next five [47:14] years we're going to know everything [47:15] about the org no i don't think so [47:17] but we'll [47:18] learn more about this path that [47:21] started with [47:22] you know primitive organic molecules and [47:25] ended up with uh an interview like this [47:27] one [47:29] so [47:30] there there is a goal but it's a but [47:32] it's a [47:34] relatively big goal [47:36] this model of philanthropy of of [47:38] supporting the basic research and not [47:40] knowing where it's going to end up [47:41] almost seems the opposite of what you [47:43] were talking about with your business [47:44] totally you were talking about with [47:46] business you know revenues and costs and [47:48] making sure yeah [47:50] well [47:51] yes and no [47:53] when we would bring smart guys into [47:55] renaissance [47:57] we didn't know what they were going to [47:58] do [47:59] we hoped that they'd come up with some [48:01] good ideas to make the firm [48:04] better [48:05] but i didn't say oh this guy is going to [48:07] discover i want this guy to discover [48:10] this thing i don't know what he's going [48:11] to discover [48:12] uh so [48:14] but it's it's of course very focused on [48:16] a narrow set of outcomes whereas uh the [48:20] other [48:21] basic science anything goes [48:23] is uh is very different from that what's [48:26] your attitude to risk because you you [48:28] almost have created a business that's [48:30] based on removing risk [48:32] reducing it reducing risk uh and yet you [48:35] took a risk by leaving tenure to go and [48:37] start business i mean are you are you a [48:39] risk taker or are you a risk minimizer [48:42] or were you [48:43] you don't you probably don't need to [48:44] worry about well i suppose as we get [48:46] older we get a little less a little more [48:48] risk averse i don't know [48:50] uh [48:52] i'd always been something of a risk [48:54] taker i think [48:56] uh [48:57] but [48:59] but i've had uh good taste [49:02] and uh especially again as i say in [49:05] people [49:06] and uh [49:07] have pretty much always partnered up [49:09] with people [49:10] so uh that that cuts the risk [49:14] so uh but i did i i certainly when i [49:18] started the company i had to finance it [49:20] myself [49:21] and uh i didn't know whether it would [49:23] succeed or not [49:24] and [49:25] but i was pretty sure it would but i [49:27] didn't know you put a lot of money into [49:28] mathematics so you're you've got some [49:30] right to comment on it how are you [49:31] feeling about it oh i think mathematics [49:34] is [49:34] is really uh going quite well uh [49:36] worldwide uh the research then a bit uh [49:40] a lot of new ideas are [49:42] coming up new fields or sort of are [49:45] are flourishing [49:48] it feels [49:49] like a pretty healthy enterprise to me [49:52] what's not healthy is the state of [49:54] mathematics education in our country [49:57] that's very unhealthy [50:00] for young people [50:02] that's why we have [50:03] we started this thing called math for [50:05] america and so on [50:06] but [50:07] we don't have enough teachers of [50:08] mathematics who know it [50:10] who know the subject [50:12] and even of science and and that's for a [50:15] simple reason [50:16] uh 30 40 years ago [50:20] if you knew some mathematics enough to [50:22] teach let's say in high school [50:23] there weren't a million other things you [50:25] could do with that knowledge oh yeah [50:27] maybe you could become a professor but [50:28] let's suppose you're not quite at that [50:30] level but you you're good at math and so [50:32] on being a math teacher was a nice job [50:35] but today if you know that much [50:37] mathematics [50:38] you could get a job at google you could [50:39] get a job at ibm you could get a job in [50:41] goldman sachs i mean there's plenty of [50:44] opportunities that are going to pay more [50:46] than being a high school teacher right [50:49] there weren't so many when i was going [50:51] to high school [50:52] such things so the quality [50:56] of high school teachers in math has [50:58] declined [51:00] uh [51:01] simply because [51:02] if you know enough to teach in high [51:04] school you know enough to work for [51:06] google [51:07] and well they're not going to pay that [51:09] much in high school so how do you [51:12] redress that how do we redress that as a [51:14] country [51:18] well [51:19] you have [51:21] so we work [51:23] a person works for a combination of [51:26] financial reward and respect [51:29] right so a guy becomes supreme court [51:31] justice [51:32] he's not doing it because he's going to [51:34] make a fortune uh he'll be well paid i [51:37] suppose but you know supreme court [51:39] justice everyone says [51:41] it's a big deal you have a lot of [51:42] respect and you respect yourself [51:44] presumably [51:45] uh [51:47] so [51:49] there are many so you [51:51] can't pay [51:53] let's say high school teachers of math [51:55] as much as they would get at google [51:58] but you can give them a bump [52:01] pay them more [52:02] we give people fifteen thousand dollars [52:05] a year more than they [52:06] would make their regular salary but we [52:09] also create a community [52:12] of math and science teachers [52:15] uh [52:15] which [52:17] they love [52:18] and it makes them feel important and [52:20] they are important [52:22] they interact with each other they don't [52:25] they're not [52:26] forlorn you know stuck in some high [52:28] school no one to talk to so we've [52:30] created a community with a great esprit [52:32] de corps and these people [52:34] don't walk out of the field but turnover [52:36] is very very low whereas [52:38] ordinarily the turnover is quite high so [52:43] in finland for example which has very [52:45] good [52:46] mathematics uh teaching [52:49] those are real professionals and they [52:51] they have [52:52] a lot of status societal status [52:55] a teacher in finland [52:58] here in the united states teachers don't [53:00] have such good societal status [53:02] and and of course [53:04] the [53:06] the whole thing of [53:09] uh getting rid of these bad teachers or [53:13] get them out so on and so forth okay [53:15] maybe we have some bad teachers [53:17] but there's no nothing said about hey [53:19] let's reward and and and recognize the [53:22] really good ones [53:24] right so if you're running a business [53:26] yeah you want to get rid of the dead [53:28] wood if there are people who just aren't [53:29] doing the job but most more important is [53:33] to recognize [53:34] the people who are doing a good job and [53:36] reward them and extol them and make them [53:39] feel good in one way or another we don't [53:41] do that at all with teachers we're just [53:43] bashing them and bashing them in passion [53:45] why has that happened in the united [53:47] states but but not in finland [53:49] well and it has hasn't happened in most [53:51] of the european countries why [53:55] well for one thing we have teachers [53:56] unions but that shouldn't be the reason [53:58] because finland probably has unions too [54:00] i don't know [54:01] uh [54:02] there's been a [54:04] shift [54:05] and it's [54:07] uh [54:09] about maybe started about 10 years ago [54:13] that [54:16] we have to [54:18] measure these teachers by outcomes [54:21] all right fair enough [54:23] yeah well what outcome oh well we're [54:25] going to give their students [54:26] standardized tests [54:29] if they have value added and so on and [54:32] well then then they're good and if they [54:34] don't have value [54:35] well it turns out judging people on [54:37] standard [54:38] student standardized tests is a disaster [54:41] it's a very very weak statistic it's not [54:43] very highly correlated with how they're [54:44] going to do the next year by the same [54:46] measure [54:47] and uh [54:49] and [54:50] the the but somehow [54:52] the theory is we have to measure these [54:54] people if they're not doing a good job [54:55] we have to get rid of them somehow or [54:57] other we have to get these people out of [54:59] the schools [55:01] well [55:02] there's a old saying [55:04] in the british navy you know floggings [55:07] will continue until morale improves [55:10] and that's kind of what this this is [55:13] we're just beating these people up so uh [55:16] how did it start i don't know someone [55:18] got the idea that we can measure output [55:22] but we can't or at least we this is [55:24] we've imposed a system [55:26] which stinks for measuring output [55:29] and uh if we the longer we stick with [55:31] this system of rating teachers on [55:33] performance of their students [55:35] on standardized tests [55:37] though the worse it's going to get and [55:39] the solution is you put it sounds to me [55:41] like [55:42] just [55:43] respect them a bit more and make them [55:45] feel good about themselves yeah and and [55:47] recognize and reward the very best ones [55:50] and that encourages people to say hey i [55:51] could get maybe i could rise up and and [55:54] and and get one of those become a master [55:56] teacher or whatever and and uh or [55:59] someone could even come into the field [56:00] and say hey that [56:02] my cousin is a master teacher there new [56:05] york he's having a good life so yes [56:08] uh but it's gonna take a [56:11] we're doing it in new york pretty [56:13] successfully but it needs to be all [56:15] around the country and it needs to be [56:17] bigger than it is in new york too you [56:18] seem to be a believer in markets markets [56:21] in that though is this not something [56:22] that would correct itself like over time [56:24] like if the if the teaching drops and [56:26] then the google can't get the [56:28] mathematicians and they have to improve [56:29] the team will this not take care of [56:31] itself does it need [56:32] no artists [56:34] here's how we're taking care of it now [56:36] we're importing people [56:38] h1 visas [56:40] and we're bringing in [56:41] guys from other countries who do have [56:44] this knowledge [56:45] and all the technology companies [56:48] only want [56:49] more and more h-1 visas because they [56:52] can't get [56:54] enough home-grown talent [56:57] the talent that they need so [57:00] now that's okay for a while [57:02] but [57:04] about 12 or 13 years ago for example [57:09] of the graduates from the indian [57:11] institute of technology i whatever they [57:14] call it indian iit [57:17] about 80 percent of them [57:20] left india and would come to europe and [57:22] united states to to get jobs [57:26] now it's 20 [57:28] because india is doing much better [57:30] there's plenty of technical jobs in [57:32] india so hey i can stay home i don't [57:34] have to run to england or i don't have [57:35] to run to [57:37] united states uh to work [57:39] so well there are people [57:41] from other countries who are coming and [57:43] we're taking advantage of that but the [57:45] day will come when [57:47] we just don't won't have enough people [57:49] here [57:50] uh of our own folks [57:53] who uh who know [57:56] enough to to do this work basic research [58:00] is as as i have said the sort of the [58:02] wellspring of uh [58:04] human knowledge [58:06] knowledge about our [58:08] world and [58:11] but the [58:13] federal funding [58:14] for basic research has [58:16] become restricted [58:18] for one thing federal funding for [58:20] science has come down anyway [58:23] overall [58:24] and [58:26] second of all [58:28] there's increasing tendency [58:31] for these agencies to fund what's called [58:34] translational research rather than basic [58:36] research translational means okay you're [58:39] working on cancer great you know we're [58:41] going to have a [58:42] cure for this in three years you're okay [58:44] fine we'll give you money [58:45] you're working on how the basic cell is [58:47] working uh well you know [58:51] that applications are too far away so [58:54] there's less [58:56] the congress pushes the nih and [58:59] the nsf too probably to hey you know [59:03] we want to see some return on this money [59:05] we want to see results [59:07] so [59:08] they're more conservative wild ideas [59:11] less often get funded because you know [59:14] so [59:15] the government's not doing such a good [59:17] job at supporting basic science [59:19] and [59:20] so there's a role for philanthropy [59:23] an increasingly important role of [59:26] philanthropy do you give your money to [59:28] basic research because you feel somehow [59:32] indebted to it for your own success or [59:34] do you do it just out of like a belief [59:35] or do you do you feel like you're giving [59:37] something back to us to what gave [59:38] something to you that's an interesting [59:40] question [59:42] i do it because it feels good i like [59:44] science [59:45] i like to see [59:47] it flourish [59:48] i like to be around scientists i like to [59:51] learn some new things my wife feels the [59:54] same way she loves science so [59:57] we're very happy to [59:59] to do this do i feel i'm giving back [60:02] not especially [60:04] you know [60:07] i could give back in a lot of ways [60:08] there's a lot of things i could do [60:10] besides support science do you have a [60:11] favorite number seven next question [60:16] do you have a favorite mathematician [60:21] well [60:23] archimedes and euler [60:26] are my current favorites [60:28] but uh maybe you met somebody [60:32] i'm very impressed with those two guys [60:34] thank you so much for so much of your [60:36] time [60:36] all right well this was kind of fun [60:42] you