Jim Simons, A Tribute

This line comes from The Man Who Solved the Market, Gregory Zuckerman’s bestselling biography of Jim Simons, who died on May 10, 2024. I did not know Simons personally, so what I know of him is not personal but anecdotal, gathered from books and interviews. In that respect my view of him is no different from my view of Caesar or Plato. Despite this limitation, I think it is safe to call Simons a towering figure and an icon for an aspiring mathematician and engineer like me, and in this essay I want to reflect on his legacy and add some thoughts of my own.

The Smart and the Rich

If you are smart, why aren’t you rich? If you are rich, why aren’t you smart? Or can you be both, like Jim Simons? It has become more and more accepted (see here and here) that intelligence and wealth are correlated over a middle range of wealth but become nearly uncorrelated above some point. Many factors besides raw intelligence matter, of course, such as discipline, mental toughness and skill with people. But suppose we put all of them under the umbrella of “being smart,” since emotional intelligence is intelligence too. Even then, being smart does not guarantee being rich. At best the relationship looks like a concave function: if we plot “smart” on the x-axis and “rich” on the y-axis (setting aside how to measure either), the curve rises steeply at first and then flattens. If you are poor or in the lower or middle range of the American middle class, being smarter will probably make you richer, but above some level, more effort is unlikely to bring much more wealth, and your wealth tends to stay where it is. Taleb’s explanation is that there is simply too much randomness, and that may be true, though I have yet to experience it myself. There is a catch, however. At the very top, the winner-take-all effect can lift a few people into financial dominance, so that the rich get richer. The far tail of the wealth distribution defies the law.

Simons belongs to the rare category of people who were both exceptionally smart and exceptionally rich. As a mathematician he made serious contributions to differential geometry and won the American Mathematical Society’s Oswald Veblen Prize in Geometry in 1976. As an investor he founded Renaissance Technologies, whose Medallion Fund is often called the most successful investment fund in history. According to Zuckerman, it averaged a gross annual return of 66.1% from 1988 to 2018, or 39.1% after its very high fees.Some researchers have questioned how these figures were computed and argue the compounded return was lower. Even the skeptical estimates leave Medallion far ahead of any other fund on record. He was immensely gifted, and also lucky.

With so much randomness involved, why study the lives of successful people at all? And why Simons in particular? I should say first that, to me, Simons the mathematician, and Simons the person who valued mathematics, is far more fascinating than Simons the fund manager. The archetypal mathematician, especially one who works on abstract subjects (differential geometry is abstract, unlike the Euclidean geometry we learn before college), is a reclusive, Platonic figure. The archetypal hedge fund manager or Wall Street trader is worldly and fiercely competitive, sometimes even Machiavellian. Simons combined the two archetypes, and that combination is what makes him so remarkable. It is the main reason I see him not as another very rich man but as a figure to look up to. In the anecdotes and in his public talks you can see a man with an unusual quality of mind.

He also had principles that cost him. In the 1960s Simons worked as a codebreaker at the Institute for Defense Analyses, a research center that worked for the National Security Agency. In 1967, after the institute’s president defended the Vietnam War in The New York Times, Simons wrote to the paper to disagree, and he soon lost his job. He went on to chair the mathematics department at Stony Brook from 1968 to 1978. A Machiavellian would not have written that letter. Later in life, the money he made went largely to fundamental research, which few people are willing to pay for because its applications are so uncertain, and I return to this in the last section.

I am not trying to learn his methods or replicate his success, which would be impossible. In fact, I think it is a mistake to read biographies in the hope of copying someone’s success, since far too many factors are at play. I write about him in the spirit of Plutarch’s Lives, as a portrait of a life worth thinking about rather than a manual for success. Some lives are interesting enough to inspire us, to kindle a fire that may or may not catch, and stories about such people go on inspiring later generations.

The Persistent Pursuit of Beauty

In photographs from his younger days, Simons is usually a young man with a cigarette in hand. He smoked heavily all his life, up to two packs of Merits a day. After graduating from MIT he rode a motor scooter from Boston all the way to Bogotá. Within a few years he had a doctorate from Berkeley, and by the early 1970s he was a promising mathematician working with Shiing-Shen Chern on differential geometry. Differential geometry is a marvelous subject. It combines the elegance of geometric objects with the richness and abstraction of algebra and differential forms, usually with a touch of functional analysis. Its notation can easily overwhelm a mathematician without enough prior exposure, and it demands maturity across several branches of pure mathematics. It is a subject I am still studying.

In a 1974 paper titled “Characteristic Forms and Geometric Invariants,” Chern and Simons introduced what are now called Chern–Simons forms. The paper’s introduction tells a story that I find very instructive. The work began as an attempt to find a purely combinatorial formula for the first Pontryagin number of a four-dimensional manifold, by integrating curvature over the pieces of a triangulation and pushing everything to the boundaries of those pieces. The attempt got stuck on a boundary term that refused to simplify. Rather than give up, Chern and Simons decided the obstacle was interesting in its own right and studied it, and the obstacle became the result. This is a common way for abstract constructions to emerge, though people outside pure mathematics rarely see it. Mathematicians try to solve a hard problem, build up intuitions along the way (or correct intuitions they had before), and the intuitions eventually become definitions, with their desirable properties laid out as theorems and lemmas. At my current level I cannot yet follow all of their results.

What happened next is the best argument I know for the pursuit of beauty. In 1989 the physicist Edward Witten showed that a quantum field theory built on the Chern–Simons form explains the Jones polynomial, a recently discovered invariant of knots, and the work was part of what earned him the Fields Medal the following year. Chern–Simons theory has since become a basic tool in physics, from the theory of knots to the topological phases of matter studied in condensed-matter physics. A boundary term that two geometers found too interesting to ignore turned out, fifteen years later, to describe something about the physical world.

Constructing something new in mathematics is a Herculean feat, and one could argue that it is as difficult as, if not more difficult than, Simons’s remarkable achievements in finance. Success in either field seems to require an enormous amount of diligence, many years of experience and some luck. Luck is out of our control, but the other two are not.As I was writing this article, I received the news of an internship for the summer. With some financial certainty, I rewarded myself with a physical copy of Walter Rudin’s Real and Complex Analysis. Man, I love math!

Simons often said that his interest in mathematics came naturally, almost the way Aristotle described a talent as an inborn function. When he was four or five, riding in the car with his father, he was told that they had to stop for gas. He objected that they never needed to run out: they could use half of the gas, then half of what was left, then half of that, and so on forever. As he later joked, it did not occur to him that they would also never get anywhere. He had rediscovered, as a small child, the intuition behind Zeno’s paradoxes about the infinitely divisible. Interestingly, Zeno’s paradox was also what first lit my own passion for mathematics. I was interested in philosophy before mathematics, and it took both Aristotle, who preserved and discussed the paradoxes, and my calculus teacher, who taught me about infinitesimals, for me to question this basic assumption about the physical world. I still marvel at how fundamental mathematics is, and at the tools we have built to describe the world.

Or, we can say that science starts with wonder. And where does wonder start? I would say in our inherent curiosity and in the innate beauty of nature.

From here I want to comment on scientific research more broadly. Engineers and scientists view research through different lenses. Broadly speaking, industry and academia sort it into applied and theoretical work. As a practitioner, I tend to look at it from the researcher’s side and to sort it by motivation.

Of these three motivations, the most widely praised is the second, the pursuit of better lives for everyone. Examples include biomedical research aimed at effective drugs for cancer, HIV and other deadly diseases, and climate modeling and optimization that can reduce the damage of climate disasters, which is my current research direction. The results of this kind of research improve living conditions for society as a whole, and it is usually what idealists entering college hope to do (what happens next can be another story). The first and third motivations are more controversial. The pursuit of beauty is often considered impractical, even a waste of intellectual resources, and the third is simply a sad reality of research today.

Some see the first kind, the pursuit of beauty, as esoteric. We usually think of it as a trait of artists and musicians, for whom pursuing beauty is part of the craft. Mathematicians and some physicists belong in the same category, even though we do not usually call them artists, because appreciating the beauty of mathematics takes much more formal training. Mathematical research and theoretical physics also face the problem that their results are rarely applicable to real-world problems right away, which can leave them short of funding. A mathematician driven purely by beauty, who treats the study of mathematics as its own reward, may carry on regardless, like Vincent van Gogh, who kept developing his style of painting without fear of the critics. Or they may drift into the third category, since fame these days can bring more funding.

The classic defense of the first kind is G. H. Hardy’s A Mathematician’s Apology (1940). “Beauty is the first test,” Hardy wrote: “there is no permanent place in the world for ugly mathematics.” Hardy went further and took pride in the uselessness of the mathematics he loved. He wrote that no one had found any warlike purpose for the theory of numbers, and that it seemed unlikely anyone would for many years. He was wrong within a few decades. Number theory became central to cryptography, the field in which Simons himself would work as a codebreaker, and it now protects nearly every message sent over the internet. The history of Chern–Simons theory points the same way: mathematics pursued for its beauty has a way of becoming useful later, in ways no one could have planned. That is not the reason to pursue it, but it is a good reason for the rest of the world to pay for it.

As a new researcher in AI and deep learning, I also observe the following:

So I think researchers today need much more virtue than those in the past, given the abundance of material goods, the questionable allocation of research funding and the constant media attention to fame and fortune. This makes me appreciate Simons’s support for fundamental research all the more. He was willing to fund the first kind of research, the kind he had once done himself, and that helps keep the scientific world from being taken over entirely by pragmatism.

Aim to Build a Legacy

So I would say that one of Simons’s greatest legacies is his persistent pursuit of beauty, first through his contributions to pure mathematics and then through his funding of fundamental research. I consider this his most remarkable achievement, and the funding is easy to underestimate. In 1994 he and his wife, Marilyn Simons, founded the Simons Foundation, which has since become one of the largest private funders of mathematics and basic science in the world. In 2004 he founded Math for America, which supports outstanding mathematics and science teachers in public schools. In 2008 the foundation gave $60 million to create the Simons Center for Geometry and Physics at Stony Brook, a fitting home for the meeting of geometry and physics that Chern–Simons theory represents. In 2012 it gave $60 million to Berkeley to found the Simons Institute for the Theory of Computing, now one of the main centers of theoretical computer science. Its autism research initiative, begun in 2003, has become one of the largest private funders of autism science. In 2016 it opened the Flatiron Institute in New York, where scientists develop computational methods for astrophysics, biology, neuroscience and other fields. It publishes Quanta Magazine, which is how many people outside mathematics first hear about its newest results. And in 2023 it gave Stony Brook University a $500 million endowment gift, which the foundation described as the largest unrestricted gift to an institution of higher education in American history.

His influence on mathematics itself may be esoteric to most people, but his influence on the conditions of research is felt by thousands of scientists who never met him, including people in my own field. The Simons Institute has run semester-long programs on the theory of machine learning, and Simons Foundation grants support a great many of the mathematicians and theoretical computer scientists working today.

One story from The Man Who Solved the Market is that when Simons told his colleagues in mathematics that he had decided to go “make some money,” and tried to persuade some of them to join him, they lamented that his gift would be wasted on something so mundane. We can now see where much of that money went: into fundamental research. So which contribution has the greater potential to push mathematics forward, Chern–Simons theory or the funding he poured into mathematical research? Neither can be measured, but the second has the potential to outshine the first. His legacy lies partly in his scientific research and partly in his success as a money-maker, but mostly, in my opinion, in his willingness to use his wealth for fundamental science, and I believe that legacy is worth aspiring to.

I first wrote this tribute in May 2024 and revised and expanded it in October 2026.