Is AI a mathematician?

I have just seen Terrence Tao on the BigThink Clipe video talk about the future of science and mathematics in the AI era. He didn’t sound worried, he sounded excited, saying that this new era has brought a lot of new proofs to check and that we need to re-stablish what it means to be a mathematician.

Barely a few hours had passed when I see the news: OpenAI solved the Navier Stokes equations problem. I could not believe it, earlier this morning I was trying to grasp the idea of mathematicians accepting AI and now this happens.

I am still a little shocked by that, and I will try to explain more about my background and my relation with mathematics in the following posts. This blog is my first thoughts and feelings about yesterdays news.

I am a mathematician, I fell in love with mathematics so much that I spent my 4 years of college basically just doing math, it is complicated to remember those days since I was in an institution that was very particular , but that is going to be content for another blog. The important thing here is that I really wanted to create new mathematics and I did not imagine a life without it during this time.

Ever since I discovered mathematics I felt like I was in a place with people that care about the same things as me. Don’t get me wrong, it was not all good, actually it was a little traumatic but not because of mathematics itself but because of the professors that sustained a non-healthy system of education and abuse of power at my college. In this post I will focus on the parts I enjoyed of being a math student.

As a freshmen I fell in love with not understanding anything, with being almost wrong all the time , with trying for the 10th time and failing, with spending much of my time alone thinking about the solution, but as much time discussing hard problems with my friends. I fell in love with opening a new book and learning new definitions and then proving lemmas just so we can prove theorems and so we can maybe, just maybe grasp the solution of the main problem and the main motivation of this book. I love how constructive it is and how many skills you need to master to understand the problem. I fell in love with chalks and with calligraphy.

“I fell in love with mathematics.”

At my senior year in college I started my undergrad research project, in my case, following the advice of my advisor, I was studying the Navier-Stokes equations. I know he was aware that I was not ready because I needed to take a couple or more advanced classes to comprehend the topic, but I knew he trusted me and my capacity to do things on my own and so I started to dig. After a year I had the confidence in myself that make me feel like I could do hard things, but also , made me realize that it takes a great, new, very cleaver, original idea to solve some problems and that these original ideas are incredibly hard to have.

At the end of the school year I presented my thesis and it was a weird moment, after a very intense 3 years at school this was the perfect ending. I have spent the last year and a half only with my parents at home (because of COVID), inmersed in these books and weird definitions and ideas that I could not comprehend, I remember sitting in the studio at night , my parents where asleep and everything was so quiet, you could only hear the sound of the grafite of my pencil go through the paper as I draw nonsense. Presenting my thesis about Navier-Stokes equations meant that this was the end of my time with my parents and all of these amazing nights of fun on my own. The Navier-Stokes equations are very special for me, this is why knowing that in the public eye an AI solved the problem instead of a mathematician or mathematicians pisses me off so much.

“It’s like stealing a great piece of cultural value to the mathematics community”

The whole point of the millenium prices is to motivate people to participate in mathematics, I don’t think is mainly about the problems. Doing mathematics is much more than solving the problem, mathematics is about what you create during this process.

“For mathematicians, the practice of mathematics is an end in itself” https://arxiv.org/abs/math/9404236

Remember Andrew Wiles? what makes Poincare’s Last Theorem so awesome and so legendary it’s the story! Is the many human stories behind it, the equation itself doesn’t mean anything, I mean in which context you would use that? the equation is so fascinating because of the context and the human stories behind it. It is a story of human braveness, intelligence, collaboration and resilience so awesome that it is almost like a celebration of the human experience.

After these years reading other stuff and not only mathematics I realize that there are two qualities that mathematicians appreciate the most.These qualities are originality and hard work. (Of course these are not particular for math)

So in order to accept what happened I am still trying to understand how an AI can be original or how can it be resilient and hard working. Is hard work the same if you don’t get tired? or if you don’t lose faith? Is originality the same if you have access to the whole human bibliography?

Is AI a mathematician?