There’s a sense of beauty when something is working well, almost an aesthetic to it.
This is a quote from the bestseller book, The Man Who Solved the Market , a biography dedicated to Jim Simons, who passed away on May 10th 2024. I don’t know Simons personally, hence what I know about him is not personal, but anecdotal, that is, from books and media. This makes my perspective of him the same as with figures like Caesar, Brutus, or Plato, etc. Despite these apparent disqualifications, I think it is safe for me to describe Simons as a towering figure and an icon for an aspiring mathematician / engineer like myself. Here I hope to reflect on his legacy and provide some of my own thoughts and commentaries.
This is going to be a very short article with concise observations and commentaries.
The Smart and The Rich
If you are smart, why aren’t you so rich? If you are rich, why aren’t you smart? Or can you be someone like Jim Simons?
It has now become more and more accepted (see here and here ) that being smart and being rich exhibits some correlations at a medium range of wealth, but above some point, they become uncorrelated. Of course, besides being naturally smart, a lot of factors like discipline, mental toughness, and relational intelligence comes into play, but suppose we put them all under the big umbrella of “being smart” (after all, emotional intelligence is intelligence), then still it is not necessarily true that being smart will result in being rich, or at least the correlation is growing like a concave function , if we plot “smart” as x-axis and “rich” as y-axis (let’s ignore the details of how to quantify for now). This means that if you are poor or in the lower-to-middle range of the American middle class, then being smart will make you richer, but above some level of wealth, it is likely that your increased effort won’t bring you more wealth (this is saying that your wealth is likely to be maintained at a level but not higher). The reason for it? From Taleb, it is too much randomness, and this observation maybe true (I have yet to experience it myself). There’s a catch to it though, since if you are mega-rich (i.e., billionaire), then the winner-take-all effect would elevate you to a status of financial dominance, hence the richer gets richer, poorer gets poorer effect. In other words, it is the tail of the income distribution that can defy this law.
We can make a first observation that Simons belong to the rare category of people who are both (super) smart and (super) rich. As a celebrated mathematician, he made serious contributions to differential geometry and won the Oswald Veblen Prize; as a financier, he funded the most successful hedge fund, Renaissance Technologies, that accumulated an average of $66 \perc$ annual return over a decade. He is incredibly gifted, smart, and lucky.
Since there are so many random factors at play, why study and reflect on the life of successful people at all? In particular, why should we care about Jim Simons? First and foremost, I must say that Simons as a mathematician and as a person who values math is perhaps (in my opinion) much more fascinating than him as a hedge fund manager (or the combination of these two). The archetype of mathematicians, especially those that work on abstract subjects (differential geometry is an abstract subject, unlike Euclidean geometry we learned pre-college), is that of a reclusive, Platonic figure; on the other hand, the archetype of a hedge fund manager, or a trader on Wall Street, is that of a guy who is wordly and highly competitive, sometimes perhaps even giving the impression of a Machiavellian character. Therefore, the synthesis of these two contrasting archetypes makes Jim Simons a truly remarkable and fascinating figure, and it is for this primary reason that I don’t see him just as another mega-rich guy, but as a figure to look up to: at least from the anecdotes and his public talks, you can see clearly a man with an elevated quality of mind, a giant of a figure. Moreover, his monetary contributions to fundamental research, exhibited in the Simons Institute and the Institute for Pure and Applied Mathematics (IPAM), is a noble one. A lot fewer people are willing to pay for research in pure math due to the current lack of applicability to real world.
Therefore, in no ways am I trying to learn and attempt to replicate his success–it is not possible! In fact, I deem it a fallacy to read people’s biography or writings about them and try to replicate their successes, as there are simply too many factors at play; I simply write this essay like how Plutarch would write a short note about Caesar on a rainy night in the Mediterranean: he may light a candle and enjoy some moments of silence, then carve the statue of a giant in his mind. Some people’s lives are so interesting that they may inspire you, or kindle a fire that will end up roaring–or it may not, but stories about these figures would draw inspirations for later generations to come.
The mind is not a vessel to be filled but a fire to be kindled.
—Plutarch
The Persistent Pursuit of Beauty
You can see the cigarette-smoking young fellow on the cover: that’s Jim Simons in his younger days (probably in his 30s). At that time he was a wild young man, traveling across the country for errands, and a promising mathematician working with Shiing-Shen Chern on differential geometry. The subject of differential geometry is a marvelous one, which combines the elegance of geometric objects with the richness and abstraction from algebra and differential forms, usually with some touch of functional analysis. The notation and the symbols in this subject can easily overwhelm a mathematician without sufficient prior exposure and often requires great maturity across different branches of pure math (This is a subject that I am constantly studying). In a 1974 paper, titled "Characteristic Forms and Geometric Invariants ", Simons and Chern published the result known as the “Chern-Simons Form”, designed to capture global invariance of a manifold. They invented this concept to solve a difficult problem in mathematics (as can be seen from their paper’s Introduction part). For people who are not familiar with pure math, this is quite a common way for abstract constructions to emerge: mathematicians usually try to invent new mathematical tools to solve some hard problems, which requires the build-up of intuitions (or correction of intuitions developed before), and these intuitions would then translate into definitions coupled with a bunch of desirable properties (laid out as theorems and lemmas). Unfortunately for my current level of mathematical understanding, I cannot yet make sense of their results.
Constructing something novel in mathematics is Herculean feat; one can even argue that this achievement is as difficult, if not more so, as the already marvelous achievements Jim Simons made in finance. It seems that success in both fields require an insane amount of diligence, a great numbers of years of experience, and a splash of good luck. Although the luck part is not something one can control, the other two definitely are.
At the time of writing this article, I received the news of internship position in the summer. Provided with some financial certainty, I reward myself with a physical copy of Walter Rudin’s Real and Complex Analysis. Man I love math!
For Simons, he described in many occasions that his interests in math was natural, almost like how Aristotle would describe talent as an inbuilt function of man. At the age of ten, he started to have the intuition that corresponds to the famous Zeno’s Paradox, a thought experiment on the difficulty to comprehend the notion of infinitesimal in the real world. Interesting, Zeno’s Paradox was also the torch that ignited my passion in math. As a person who was first interested in philosophy rather than math, it took both Aristotle (who described this paradox) and my calculus teacher (who taught the concept of the infinitesimal) for me to question this fundamental assumption about the physical world. Still I can appreciate the fundamental nature of mathematics and the tools we use to describe the world, and it amazes me.
Philosophy begins with Wonder. – Aristotle
Or we can say, Science Starts with Wonder, and where does wonder start? I say the inherent curiosity we have and the innate beauty of nature.
From here I would like to make a little commentary of scientific research: as engineers and scientists, we look at research in different lenses: broadly speaking industries and academia say that some are applied and some are theoretical. As a practitioner, I tend to look at them from the perspective of a researcher and divide them by the motivations.
I say that some researches are motivated by Beauty, some by overall well-being, and some are motivated by pursuit of Fame and Resources.
Of these three kinds of motivations, perhaps the most widely acclaimed is the second kind, which is the pursuit to improve our overall well-beings. Examples are: biomedical researches that aim to develop efficient therapeutic drugs for cancer, HIV, and other terminal diseases; climate modeling and optimizations that can alleviate climate-related disasters (my current research direction), etc. The outcome of these kinds of research elevates the living conditions of the human society as a whole and can be seen usually as the goal of an idealist who’s just entering college (what happens next can be another story). Then more controversial are the first and the third kind: the pursuit of beauty is often deemed impractical and by some, a waste of intellectual resources, and the third one is straightforwardly a sad reality of current-day research.
The first kind, the pursuit of beauty, can be seen as esoteric by some. It is seen mostly as a trait of artists and musicians, for whom the pursuit of beauty is ingrained in their craft. Interestingly, mathematicians and some physicists also fall into the same category, even though we usually don’t call them artists, since appreciation of math’s beauty often requires a lot more formal training. Besides, mathematical research (and theoretical physics) usually face the challenges that their results are not readily applicable to solving real world problems, which can result in lack of research funding. Now, if a mathematician is purely driven by the beauty of math and takes the action of studying mathematics as reward in itself, then they may carry on their research, like Vincent van Gogh, who persistently pushed his style of painting without fearing the critics’ judgments, or they may fall into the third category, as unfortunately fame these days can result in more research funding. As a new researcher in the field of AI and deep learning, I observe that:
In particular, the current boom in AI and deep learning can be seen as both a great catalysis for the second kind of research and a threat to the first kind of research and a push for the third kind of research.
Therefore, I think researchers today need a lot more virtue than those in the past, given the advancement of material goods, the questionable allocation of research funding, and the never-ending media blast of fame and fortune. This makes me appreciate Jim Simons’ contribution to fundamental research more: he’s willing to fund the first kind of research, just like what he had been doing intellectually, and this helps to save the scientific world from collapsing into monopoly by pragmatism.
We must not forget how, when we start our journey of scientific research, the inherent curiosity and the beauty we saw.
Aim to Build a Legacy
So I can then say that one of Simons’ greatest legacy is his persistent pursuit of beauty, first by contributing to the subject of pure math, and then to the funding he contributed to fundamental research. This I deem the most remarkable achievements he made. His influence on math may be esoteric for most, but I can still feel his presence, every time I walk pass the IPAM building at UCLA campus.
One fun snapshot from The Man Who Solved the Market is that when Simons told his math colleagues that he decided to “make some money” and persuade them to join him, his colleagues lament that his gift in math would be wasted on something so mundane and material. Well, we see where a great sum of his earnings go–into funding for fundamental research; so, which contribution has the potential to push mathematics further? The Chern-Simons theory or the massive funding poured into mathematical research? Both are unmeasurable, but the second one has the potential to outshine the first one. The journey of Simons as a figure is a truly remarkable one, and his legacy is partly his scientific research, partly his status as a money-maker, but greatly (in my opinion) is his willingness to contribute to fundamental scientific research using his wealth, and I believe this legacy is something worth aspiring for.