A friend of mine recently shared an article about AI and mathematics that led me to think a little bit about the future of mathematics, particularly in regard to my own pursuits and interests in the field. The article itself is long, but incredibly interesting and shares many sentiments about the concerns of AI in a rapidly changing "mathematics economy."

For centuries, even millenia, humanity has considered mathematics insurmountable: there was always more to discover, and there always is more to discover (there might be some exceptions with particularly egotistical eras where people believed themselves to be exceptional, but this should be generally true). Now, when I use the word "discover," there might be some debate about my underlying assumptions about the universe: whether mathematics is a formalisation of existing structure, or whether it was entirely created by humans to describe phenomenon. I'm not sure if I've talked about this before, but I am in the school that believes mathematical formalism is a tool created to understand existing structure, and the only thing limiting our conceptual understanding in any mathematical direction is, as Bessis also agrees with, the human brain. After all, AI can generate so much stuff, mathematical or not.

The problem with unintelligible mathematics isn’t that it might be false. It is that it is literally meaningless, in the sense that it doesn’t compile on the only hardware that is currently able to make sense of it and appreciate its value—the human brain. — David Bessis

And this makes sense. Bessis describes how many people view mathematics as a puzzle to be solved, similar to Chess or Go. Pragmatically, this would be useful. If mathematics were as simple as a tool that could solve all of our technical problems, leaving the beauty and practicality of "human" things for the painters, architects, engineers, etc., then wouldn't the world be a better place? This is a societal view that is so prominent that most people don't even know what mathematics is. I've spoken to many people about what they think mathematics is, and to anecdotally support this claim, many can't even fathom what "research" in mathematics really is—it's solved, isn't it?

The advent of AI and its uses in mathematics are another matter, and from the outside, it seems incredible. As of now, many fields outside of mathematics have seen a jump in advancement—AI can optimise code, it can simplify some processes, and more recently, it can actually make contributions to mathematics research. Google DeepMind released a paper not too long ago that creates an AI model that can solve difficult problems. This is terrifying.

I like my chalk, thank you very much. I'm not doing any research now, but by the time I start doing research, what's to say that all the lowish-hanging fruit, and perhaps even more novel results, won't be already solved, either by AI or by some humans? I think there is some humility to the fact that we've grasped onto these traditionalist views of mathematics and something that takes time, dedication, and just plain thinking—now AI has seemingly reduced that entire ordeal and expression of mathematical innovation to some lines of code in Lean. Or has it? I certainly hope not.

Bessis' quote argues that AI may come up with new proofs for new results at a rapid pace, but at its basis, there is no existing mathematical syntax to actually understand what is meant by anything, no matter if it is correct. We are limited by ourselves. This puts us in a sort of limbo. Why should we care about mathematics if it can only be understood by some advanced AI model? Is the new dawn of mathematics just a race to creating new syntax to decipher previously AI-created results and theory? Well, that seems dystopian. No creativity. Are we just a bunch of stupid people clawing away at lines of code that seem to hold the answer to the Riemann Hypothesis? Bessis also mentions in his article an online object known as The Library of Babel, which I had actually heard about a long time ago—it contains an increasing list of every possible string of characters. What's to say that this library doesn't contain all mathematics—every possible field of academia, for that matter—whether known or unknown, and really we should be browsing this library with some gargantuan effort to find the bread crumbs for the mathematical secrets of the universe?

If this is the future of mathematics, I don't want to partake. I imagine both traditionalist mathematicians and current generation mathematicians, as well as young mathematicians, would absolutely agree. I think it's wrong to jump to conclusions now, but I think there is something greater than simply doing mathematics in this new era. I am for this new mathematical progressivism: we should adapt to change and yet continue to make mathematics something that remains useful, interesting, novel, but, most of all, human.

In its current state, the humanity of mathematics is already frugal: society doesn't view mathematics as crucial, nor does it view mathematics as social. We've already failed to make mathematics human. It's just lines of code, some tool for a physics or engineering problem. This view is harmful. I believe that if we completely lose the humanity of mathematics, the culture of human progression will become very, very linear.

But if AI ever “wins” at mathematics, then someone else will have to be the “loser,” and the only other player in the room is human thought. — David Bessis

Bessis questions whether perspectives like this are those of Luddites. I agree that it is not, and in fact there is something much more complex going on.

I think traditionalist mathematics is useless. Bessis says that we should "come clean about the nature of mathematics," and I could not agree more. I mean, isn't the very position of society on mathematics indicative of how elitist it really is? British scholars at Oxbridge in the 19th century seems to be the poster child of mathematics. It's outdated, primitive, and no longer serving the people who both benefit from it intellectually and practically. Mathematics is so much less popular than other fields because it is (1) not digestible, and (2) lacks connection with people. If cryptic symbols—which I admit I find pleasing from a self-asserted sense of "uniqueness"—is all that people think about when they think of mathematics, then we've already alienated millions from understanding truly novel and relevant concepts.

So, no. I'm not a Luddite. But I think if we want to maintain the culture of mathematics in this new era of AI, we need to rethink. Mathematical communication has not flourished enough in recent times. The mathematical community is still not in agreement on fundamental questions. If we can't even agree on how to express things, how can we even begin to communicate it to a wider audience?

So where does this place me? I've always seen the ideal route of a pure mathematician as this: undergraduate, graduate school, PhD, post-doc, then obtain a tenure position at some university conducting research and teaching. I don't think I'll ever lose a desire to learn more mathematics, but this new era raises a question. Many young mathematicians in my generation might already be looking to industry as a backup for pure mathematics, or perhaps computer science. I think this is fine and respectable, but I think it is also valuable to advocate for humanity in the future of mathematics.

And I believe it all starts from changing how we communicate mathematics.

Mathematics pedagogy needs change, and where I fit into that picture isn't exactly clear, but I think there is so much more merit to communication than people give it. If we are to reform mathematics, it is to extend ourselves beyond just, say, high school mathematics education, and to approach it from a new perspective. This isn't just changing curricula. We have to recognize our seemingly benign assumptions and create new movements that treat mathematics less as a commodity, and more as something so innately human and crucial that it cannot not be in our daily lives. Bessis puts this very well.

Many people hate math, and they tend to put AI in the same bag. They view anything with mathematics or computers in it as a threat to their humanity and subjectivity, their raw experience of being alive, immersed in this world, trying to make intuitive sense of it.


They might be surprised—and thankful—to find out that mathematicians are actually on their side, fighting the good fight. As Carl Jacobi once put it, “the object of mathematics is the honor of the human spirit.” — David Bessis

I think it is the responsibility of this generation of young mathematicians to make this reform.