What's Math Anyway

Pavle Miha

Oct 25, 2026

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It’s been an incredible few weeks for Math haters - Tucker Carlson complained about letters in math, in a bit that’s been hacky for at least 50 years, and mathematicians have seen machines solve some of their most treasured problems, which one mathematician described as being “hit by trucks”.

Because of this, 25 Fields Medallists (a kind of math Nobel prize only people below 40 are eligible for) have signed a letter complaining that there is “A Severe Misalignment of AI in Mathematics”. Basically, that Anthropic and OpenAI’s recent ability to simply point tens of millions of dollars of compute at a problem and say is it true or false is actually getting in the way of the true purpose of mathematics. But what is math? And what is this true purpose? As a one-time recipient of the Portuguese Math Olympiad bronze medal, and completer of one year of Applied Math and Computation, I’m here to answer these questions. I think it’s useful to start with what math is and what it studies:

The letter defines math as “deal[ing] with understanding basic structures of shapes, numbers, and natural phenomena.” I think they have an interest in painting Math as down-to-earth, practical, and approachable.

On the other hand, my favourite definition I heard from Matt Parker, a youtuber, who I think got it from Douglas Hofstadter, not a youtuber, who said that math is, paraphrasing, “the study of things mathematicians enjoy doing”. Obviously there’s more to it, but math encompasses a lot of different formalised systems: number theory, games, knots, computers (even before computers existed!), geometry, cryptography, the study of formal systems themselves, and a lot of things that are quite far from basic structures or natural phenomena.

The medallists set out an important question: “how to make sure that, as AI changes the way work is done, we do not lose sight of what that work was meant to achieve in the first place.” But what was it actually meant to achieve in the first place? What is the study of these formal systems good for, and are these AI agents helping or harming these goals?

They state math “has built a large corpus of sophisticated ideas, methods, abstractions, and other tools to comprehend the mathematical landscape. In turn, modern technologies and sciences are based on mathematical tools”. This is surely true, Math’s areas of study are often motivated by problems in everyday life: you can see how trigonometry arises from the need to build and measure things, or how calculus was born out of Newton’s and Leibniz’s need to study continuous systems. Mathematicians then push these disciplines further than necessary for everyday life, which occasionally produces work that turns out useful in ways that we never even expected! When John Nash was studying games in the 2001 classic film A Beautiful Mind, it might have seemed to outsiders like a trivial pursuit (eyo), but things he discovered such as the Nash Equilibrium are now regularly used to reason about topics as varied as economic markets, international relations, and dating markets. Knot theory is apparently used in biology to model DNA and how enzymes affect it. Ironically the LLMs that caused this whole mess in the first place use a lot of Linear Algebra, a branch of mathematics initially developed by the Chinese in like 500BCE, and then Europeans in the 17th century, to study how to solve systems of linear equations (think of problems like “3 apples and a pear cost $5, 5 apples and 2 pears cost $9, how much do apples and pears cost?”).1

Obviously neither the Linear Algebrists in the 17th century, nor the Calculists of the 17th century could have predicted this is how their tools would be used, but here we are.

The thing is, for a lot of Math’s biggest problems, we basically know the answers won’t be useful, and it doesn’t seem to matter. For example, the recent solution to the Navier-Stokes problem by OpenAI - they found that if you use a set of continuous equations called the Navier-Stokes equations to describe a fluid, you can set it up such that it’ll become infinitely fast at some point - won’t change much about how we think about the physical world. In reality, fluids are composed of tiny bits of stuff, and these infinities just don’t happen, you get cavitation and other physical phenomena not described by the Navier-Stokes equations. OpenAI claims to have proved another 370 important results, and no one seems to think it’ll have even minor economic impact besides increasing OpenAI’s already stratospheric market cap.

Additionally, if you speak to Mathematicians, developing useful tools doesn’t feel like their main motivation. So much of Math is not useful we’ve defined a new name for math that is - Applied Mathematics. I think the development of useful tools, both incidental and deliberate, is a big reason why math is funded, but not the main goal of mathematics and its -ticians.

For the math that indeed is useful in our everyday lives, for physics, cryptography, etc, if these models continue improving, they will be able to do it autonomously, potentially as a by-product of simply trying to solve practical problems: the 2028 version of ChatGPT is asked, as a swarm of millions of superhuman agents, to give us the best theory it can find that explains all experimental phenomena, and it might develop new math that perfectly describes what we see, and then explain it to us in the best way possible if we so desire.

The letter states that “the most precious resources of our profession are students and ideas, and these we nurture with great care.”

This is also surely true. Mathematics as a community, like other branches of Academia, seems to provide unusually long and dedicated mentoring and training. A research mathematician can expect 4 years of undergraduate studies, 2 years of a masters and then 3-4 years of PhD before they become a productive member of mathematical society. Mathematicians’ interest in developing more mathematicians seems two-fold, more mathematicians advance their fields faster, but they also become consumers for mathematics, basically the only people in the world who can understand the work of their colleagues.

These mathematicians are also, it seems, unusually useful in the world - they often leave academia, where spots are scarce and pay is often disappointing, and move on to revolutionise financial markets, found AI companies, and preside over Romania.

a) There’s something inherent in mathematics, in the content of these fields, that gives insight into non-math-related realms, or

b) studying math is really hard, and by doing it for years mathematicians get smarter, or

c) a lot of people study math and the people who are the best at it are probably just very smart in general. I read recently a quote from a British politician, arguing in 1833 for judging public servants on their knowledge of Greek and Latin - his point was that it wasn’t that Greek or Latin were actually important, but they were good measures of intelligence because they were something lots of people cared about:

If astrology were taught at our Universities, the young man who cast nativities best would generally turn out a superior man. If alchemy were taught, the young man who showed most activity in the pursuit of the philosopher’s stone would generally turn out a superior man.

I don’t know how much weight to give each of these explanations, but it’s clear that having mathematicians around is useful. Of course, it’s useful right now, if machines get better at the exact kind of thinking mathematicians are good at, perhaps we should be training more people to be good-taste-havers, or masseuses or something.

It’s pretty clear to me that this new age spells trouble for the way new mathematicians are developed - there will be no low hanging fruit for them to get started on, and they’ll have to rely on artificially constructed toy problems, and simply not consulting the chatbots to develop their own understanding, something that seems to be impossible for people.

The letter mentions the role of mathematicians in taking what they’ve learned, and basically digesting it for other mathematicians and even, sometimes, the rest of us:

At the end of this process, one will ideally find a textbook presentation of the results suitable for any graduate or even undergraduate student to study. Some of the mathematical ideas pursue their journey even further to become, decades or centuries after, tools that are understood and used by the whole population.

Even perhaps outside of the “tools” the writers mention, there is some utility in hearing back from what those mathematicians are up to. I enjoy it, and many other people watching 3blue1brown on youtube enjoy it too. Math news pretty regularly makes it onto the front pages of most news sources, and it’s just fun to hear about these conceptual astronauts, miles above the surface, reporting back on wonders we’ll never witness directly. But - will the machines just get really good at this too? Why wouldn’t they also be better at explaining concepts, if they’re better at examining them?

This one they understandably didn’t mention in the letter, but I think of a lot of things as being, basically, like the unpopular Olympic Sports - mostly government funded, highly competitive, and highly insular, its audience often being other practitioners. I think European arthouse cinema production is like an Olympic sport in this way - mostly funded by governments, to be displayed at festivals mostly attended by other filmmakers and not something the market seems to want bad enough to pay for it. I think a lot of academia is like this.

I think the way I’ve put it is quite insulting, but I don’t think this is necessarily bad! This work is perhaps not essential to our survival as a species - if a comet was coming towards us and we needed all hands on deck, we might conscript some of our finest beret-ed film directors, but honestly a lot of the work most of us do is non-essential in this way. We’re simply at a point as a species where it’s not necessary for all of us to work on the bare essentials.

The fact that the market can’t support a lot of these jobs is interesting, but perhaps fine too - a lot of people work for the government in more or less direct ways. The amount of money spent by governments on all of these non-essentials combined is pretty low in the grand scheme of things, compared to pensions and benefits, and governments do have some interest in doing well in these areas. Medal counts in the actual Olympics, winning the bizarrest Oscar category, having prominent academics all serve, in some unmeasured way, to advertise a country to outsiders as a serious and successful place, and to signal to insiders that things are going well. There’s a theory that gazelles prance around inefficiently as a way to signal to predators that hey, I’m so fast and energetic that there’s no point in even trying to chase me - something it seems that has been studied with game theory.

And, much like mathematics, the people who come out of these fields often do become net-contributors on a pure tax level. Your arthouse cinema director today could be your Christopher Nolan of tomorrow, and a thriving film industry is, in general, a good thing for a country.

Perhaps this goal can remain, more explicitly as an “organic, robot-free” discipline, where the best mathematicians are the best at solving problems without LLMs, as competitions like the IMO operate today. These are not problems that actually matter, but countries could still put some resources in making sure they perform well.

The signers of the letter have an obvious vested interest: one of the main goals of mathematics for them is to pay their bills. But I think perhaps the truest and most important part of the letter, is what they describe as the core of the purpose of math: “the primary goal of conceptual understanding