Opinion 168: The Downside of Fields Medals

By Doron Zeilberger

Written: Aug. 12, 2018

Less than two weeks ago, the "World Cup" of Mathematics, took place in Rio, where four new inductees got Fields medals. Less than four weeks ago, the real World Cup, that of Soccer, took place, where France was declared the best team in the world. While billions of people could enjoy the Soccer World Cup, regardless of their soccer-playing ability, very few could appreciate and enjoy the "game" of the Math champions. At least, I could not. Below are links to talks of the four new Fields medalists that are easily found on YouTube.

While I could see that the brilliant speakers made a great effort to be lucid, (and except for Figalli, to my pleasant surprise, all were blackboard talks), I could not really see "what it is all good for". Of course the official citations, and the ICM press releases made something up, but the works of the four (admittedly brilliant) new Fields medalists are really championship play in four completely different games, with their own rules and cultures, and each of them can be really appreciated and judged by ≤ 100 people in the whole world (and that is probably not a sharp inequality).

I am willing to bet that each of these Fields medalists' understanding of the other ones' work is not far greater than mine. In our sins, the God of mathematics made mathematics into a Babel of an almost disjoint union of little mathematical tribes, where each tribe can't really understand, let alone appreciate, any of the languages of the other tribes.

I also went to arxiv.org and browsed a random sample of the new winners' papers. I did not understand any details, and while the content of their articles were very different, they all shared two things in common.