Fields Medals 2022 | Hacker News Reader

Fields Medals 2022

mathunion.org

133 pointsmudil74 comments

This year's Fields Medals should be of great interest for this crowd: most of the winners study concepts very familiar to computer scientists, while their methods touch upon the deepest, most intricate areas of pure mathematics. From sphere packings, prime numbers and lattices to percolation theory to information complexity to point configurations and much more. They are studied using representation theory, matroids, automorphic forms, real algebraic geometry and probabilistic methods among many other tools. People should check both the popular expositions in the link and the laudatio for interesting information.

[paraphrased from a comment I made in another submission]

I always found it weird how it was dominated by the french, with very few germans in between (only 2!). What are they doing differently? It's not that math is unpopular here, a lot of students are studying mathematics and every university has a math department. But they are absolutely dominating and I can't really explain it.

It is at least partially due to the education system: MPSI -> MP -> ENS Cachan / Lyon / Ulm. Very hard entrance exams to make sure they get the best students. Small promotion (IIRC around 40 students per year for ENS Ulm FIMFA) = homogeneous level.

France has an insane system of hyper-elite universities, the Grandes écoles (https://en.wikipedia.org/wiki/Grande_%C3%A9cole). I have a friend who was in one, it's even crazier than it looks from the outside.

We have nothing comparable in Germany. If that's good or bad I don't know, but regarding super-elite competitions like the Fields-Medal I don't think there is another way.

but it's not the same picture for physics of chemistry, where we get our fair share of nobel prizes. It's somehow different for math.

I can tell you why.

In German 25 is five and twenty. 67 is seven and sixty. Annoying but bearable.

However, in French, 60 is sixty. 70 is sixty ten. 80 is four twenty. 90 is four twenty ten. 99 is four twenty nineteen.

Any French person is steeled by their crazy numbering system, from an early age, allowing them to reach the highest mathematical heights as they grow.

Q: What is 20 times 4?

A: 80 because multiplication is commutative.

Ok, I guess? I don't get it.

Read the names of the numbers in French

I speak French... I know what they mean. I still don't get your joke or reference. Or I don't find it funny? Unsure.

¯\_(ツ)_/¯

20 x 4 = 4 x 20 by commutativity. But the name of the number 80 is also basically 4 x 20. I guess the English equivalent would be something like ‘what is one thousand times one hundred?’ ‘One hundred thousand because multiplication is commutative’ but that is incredibly unfunny. I guess in English you think of one hundred thousand as being decomposed into a few numbers but maybe in French you just think of quatre-vingts as a single concept and will do a double-take when hearing the reason for the answer before noticing that the name of the number can be decomposed into quatre and vingt. Obviously if the joke was ever funny before it isn’t now.

Danish is worse, or at least as bad. Sixty is three twenties, so fifty is half three twenties. Eighty is four twenties, so seventy is half four twenties. Ninety is half five twenties, but a hundred is just a hundred. Sanity, at last! (The twenties have been abbreviated over the years to just an -s ending, so sixty is “tres” and so on. But still …)

> fifty is half three twenties

I'm confused. Wouldn't that be... thirty? :-)

I didn’t say it makes much sense. But it fits with how we talk about time in Norwegian and Danish both: When English speakers say half past five, we say half six. Which is a half hour before six. In the same way, I suppose half three twenties (halvtres in Danish) is short for half a twenty short of three twenties. So yes, there’s logic to this madness.

It's cultural. France has a long tradition of selecting and funnelling the brightest math students to elite schools and institutions. In particular, there's a system of "preparatory schools", 2 years right after high school, where students work hard to get to the best possible "Grande Ecole" (engineering school). Not only the incentive is high for the students to perform well, but maths teachers in these classes are extremely qualified.

I should add that the most selective "Grande Ecole" produce more managers than engineers. Maths is mostly a mean of selecting elite, since most of these students won't work in science or engineering.

Ironically, France students on average are getting worse and worse at maths. This system works well for some elite, but not for the rest of the country. I like to think it's the same for gastronomy. France has great restaurants, but a lot of French eat mostly pizza, Mac Donald's and junk food.

One outstanding fact is the disproportionate number of fields medalist that went to the École normale supérieure in Paris !

> École normale supérieure in Paris

That's a really cool name as well, like "Standard Deluxe" or so.

It's in the sense of norms or standards rather than normal as in unremarkable.

Yeah well getting into ENS Ulm is already such an outstanding feat, no surprise there.

Can anyone give a little insight into how some of these discoveries can have engineering applications? There are some abstracts, but has anyone looked at this and seen potential uses in computer science? I'm surprised there aren't more comments on this on Hacker News considering it's the Fields Medal.

One of the winners says that there are no concrete applications, but that some of the tools developed ("interpolation formulas") could potentially be useful for solving differential equations and signal processing, but doesn't go into detail.

https://youtu.be/V8icZM14v6Q?t=119

> I'm surprised there aren't more comments on this on Hacker News considering it's the Fields Medal.

Many would argue that looking for engineering applications in mathematics is not why mathematicians do mathematics. That mathematics does sometimes have engineering applications is a mysterious and beautiful side effect. It isn't the motivation behind doing mathematics.

Oh I know. I just thought that more people would be excited about this and maybe point out where engineering applications might be possible if at all.

Indeed, a possibly apocryphal tale holds that matrix algebra, while a beautiful mathematical construct, was considered by its inventor to be utterly useless. We know better today.

38 year old math PhD checking in. Guess I missed my shot. Oh well.

I'm only in my late 20s but have managed to rid myself of the pursuit/worry/desire/envy of being a great mathematician. What I worry about now is how to approach the subject with my children. Because on one hand I do not want them to not be ambitious as younglings. But I also do not want them to experience the crushing disappointment of realizing they are not talented, as that was one of the hardest bitter pills of my life.

When I read things like this I feel happy that I went to high school with some truly extraordinary people. I already grew up knowing I wasn’t that talented compared to the real talented people.

Now I’m at peace with being just a person. I don’t expect more from myself than just trying my best. I only get disappointed if my effort is lacking.

I had similar feelings of lack of talent when I was doing my higher maths/stats. Then I realized that I don't really love either; that realization prompted me to drop out and through a series of serendipitous events, I ended up learning computers. That is when I realized that I really love programming. And that ensured that I don't have any crushing disappointments with respect to the probable lack of my talent in programming; even though I am never going to be even close to being the best in the field, its fine - I just love it.

Honestly if you are a mathematician you are already at the top of humanity in terms of cognition. Saying that is not talent is quite something. But I guess I can understand if you see yourself in relation to other mathematicians.

You got a PhD in math. That alone makes you way smarter than me and the majority of the world population .

"Tie a donkey to a balcony in MIT and in 7y he has a PhD"

You've still got 2 years!

The Fields Medals are only awarded every four years.

me too!

(I got out of the research game two years after my PhD, so it's not like there was any doubt.)

It's interesting that the Field's medal award is quite a bit lower than the Nobel Prize's (~$15K vs ~$1mm) and is only awarded every four years, yet it still garners a lot of interest, speculation, and possibly envy from non-winners. Is there some kind of side-benefit to winning beyond the renown (which is probably a double-edged sword)?

Have to be under 40 too, so it isn't really an equivalent to the Nobel. Maths culture is weird though, long held belief that it is a young person's game.

There is the Abel prize, which so far has been awarded only to pretty old people. But it has only been around since 2003, so it does not quite have the weight of history behind it.

I know the Nobel Prize has had its share of upsets, but has anyone ever been deserving of a Fields Medal but been over the age of 40?

Andrew Wiles (for proving the Fermat-Wiles theorem as a consequence of the Shimura-Taniyama-Weil conjecture proof)

Andrew Wiles.

Thomas Hales, for proving the Kepler Conjecture both in a traditional way, and in a completely formalised way.

This is the shortcoming Abel prize is trying to fulfill, more like a lifetime achievement and as others mentioned Andrew Wiles is one of the recipients of the prize

I do like that the Fields Medal goes to people nearer to the start of their careers than the end like the Nobel awards.

I would be curious about, say, the next five people that didn’t make the cut. Is it common that they still go on to get a Fields Medal?

Also I wonder if there was ever a joint result that led to both authors being awarded a Fields Medal. I can’t find one but strong collaborations are not uncommon, so…

One of the medallists went to (equivalent of) high school with me - seeing his name pop up was... a surprise.

Reply on news.ycombinator.com