Fields Medal

 

One of the biggest stories in mathematics when I was in secondary school was hearing that there was this guy in Princeton called Andrew Wiles who had been working very long and hard on Fermat's Last Theorem.

Back then, I was one of the more talented people at mathematics in my school, although I had been regularly accused of underachieving by my teachers. Mathematics was, for me, an easy A. I did hang out with the mathletes, took part in school competitions. But I never made it to the regular maths team. I wonder what it would have been like to been on track to be a maths quiz star. You had to be patient enough to study mathematics.

I didn't need patience to do the maths that appeared on regular homework. They were concepts that I grasped pretty quickly. I don't remember having to expend much effort on mathematics until I reached JC, and although I had to work for my As, it was relatively straightfoward. And it was easy because everybody around me was kicking and screaming, so I just had to progress at their pace, which I could well do with one eye closed.

So in hindsight, Andrew Wiles was an important parable for me at an important time. He locked himself away from the world and hammered away at a problem for 7 years until it got solved. Mathematics wasn't really about sprinting. It wasn't about Archimedes having a flash of insight and jumping out of his bathtub in joy. It was about taking a very long hike up a very tall mountain, and doing it over and over again.

Given the experiences I had as a teenager, it would be very churlish for me to wish that things were different, but I wish I managed to put together a successful run at being a mathlete, and I wish I had somebody to help me along with that. (I actually did, but I didn't know how to make use of that resource). I wish I had put together a regimen, where some form of intense focus and some ritual / regime helped me go up that mountain. I chose the more flashy route, which was an artistic life whose path was littered by flashes of inspiration. That is nice, but mathematics helps you think about structure, architecture and the intricate patterns behind putting things together.

Mathematics has gotten to the point where a lot of it is abstruse. It's easy to hide in a forest of complexity. The truly interesting results are the ones which lead to applications, or forming unexpected connections between superficially dissimilar instances. I wish I had at least learnt some fundamental results like Galois theory or saw the proof of the fundamental theorem of algebra (that polynomials always have complex solutions). I never learnt anything about diophantine equations. Those were the regrets I had about mathematics.

I heard about how mathematicians lived like recluses, and spent their days and nights chipping away at hard problems. There was June Huh, who was the very epitome of the tortoise brain, who worked slowly, but somehow always saw the deeper connections underneath the concepts.

There was Paul Erdos, and I remember Fan Chung describing him as somebody who always led you on an adventure that was very strenuous. There was Zhang Yitang, who had a story similar to Andrew Wiles: he toiled in obscurity for a long long time before coming up with his twin prime work.

Genius in mathematics wasn't so much the “AHA” flash of insights that come by. People have different styles of trying to find things out. I'm probably too messy a person to be a truly great mathematician, and after all, you need to have done most of your work before 40.

It's great that this time, the class of 2026 has 2 ethnic Chinese Fields medallists. The first two were Yau Shin Tung and Terence Tao, and they are legends. Yau Shin Tung didn't prove the Poincare conjecture: that was Grigori Perelman. But he laid down a big part of the foundations. Wang Hong and Deng Yu have big shoes to fill. Yau Shin Tung wasn't a Chinese national when he was awarded the prize, but he should be considered a mainlander too.

I'm more interested in prizes like the Fields Medal, the Abacus prize, the Turing prize and various other computer science and mathematics related work. I think that the Nobel prizes in Economics and Life Scences are still very vital. I am less sure about Chemistry and Physics. They gave the Chemistry Nobel to AlphaFold, and that to me was a bit like cheating, because why would you give a Chemistry prize to machine learning?