Fields Medal was never meant for ‘the greatest mathematical genius' (2018) | Hacker News Reader

Fields Medal was never meant for ‘the greatest mathematical genius' (2018)

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113 pointspaulpauper74 comments

As someone on the mathematics side, I had no idea this misperception existed. Why would the Fields Medal be capped to recipients under age 40, otherwise? It is idiotic to think that an award for "greatest mathematical genius" (which is a clumsy way of describing any prize) would just ignore accomplishments over a certain age, it is almost offensive. It has always been an award recognizing emerging talent, and it has always been entirely clear to anyone who paid attention to it.

The Abel prize (https://abelprize.no/) and Wolf prize (https://wolffund.org.il/the-wolf-prize/) exist to recognize general accomplishments in mathematics.

A perfect example is Sir Andrew Wiles, who proved the Taniyama–Shimura and thus resolved Fermat's last theorem, who received Abel and Wolf prize. But he was 40 when he began presenting his proof and was too old to qualify by the time he fixed his initial issues with Iwasawa theory. He was recognized by the Fields committee with a special "IMU silver plaque", instead.

You’ve godda understand, most of us don’t pay attention to medals. The Fields Medal is prestigious, and prestige breeds misconceptions. I’ve been vaguely interested in mathematics for decades and never knew the Fields Medal was anything but a recognition of the greatest mathematical achievement.

Thanks for the anecdote about Wiles. I had no idea mathematics didn’t have some way of properly recognizing achievements from the ancients over 40. So much for respect for one’s elders.

Did you read the parent comment? Wiles received two other prestigious prizes in addition to the "special IMU silver plaque" from the Fields committee, so I don't think you can say his achievement wasn't properly recognized.

the very same comment you are replying to mentions the Abel prize and the Wolf prize for recognizing general mathematics achievements, which if you look at the recipients over the last 2 decades, are almost all over 40 (usually white men who typically get tenured as mathematics professors and have the time and resources to focus on research).

I appreciate OP for explaining that the field recognized this pattern and made a step to try to encourage future mathematicians to have something to aspire to.

Actually, it's a bit of the reverse. The Fields medal was established in 1936, Wolf in 1978, and Abel in 2003. And Wolf and Abel filled gaps that Fields left because of its restrictions. Further, the first woman to get the Fields, Maryam Mirzakhani, was only awarded in 2014 (Abel, Wolf are worse). I don't think you can look at any of these awards and address the gender inequity in mathematics, either.

Give it based on the math, not based on gender.

It kind of tracks that Abel and Wolf would trail behind Fields in that regard.

As someone noted, since Fields is for the under-40 crowd, it'll be able to draw upon female mathematicians coming up into the field. Abel and Wolf would need to draw on the larger population. And thanks to all the biases, I'd imagine the number of women get smaller as the age gets higher.

That should correct itself in time.

Math (and I’m a math major) has a hard-on for youth. So does comp sci.

Everyone wants to pretend they’re Abel or Galois in Math.

And even Abel and Galois completed their most important work near the end of their lives.

I had to read up on these folks to understand that one of them was shot dead at 20, and the other attracted tuberculosis and died at 26.

Pretty sure you mean "contracted" TB, but the typo did provide a humourous mental image.

I probably did. ESL, in over my head.

Your first clause is complex and correct so you're doing just fine. :)

...so even at the end of their lives they would have still easily qualified for the Fields Medal. Maybe they should receive a posthumous honorary one. Or maybe they already did?

Yes I think Galois deserves a Fields in his name

Well, not the same, but Galois did get fields in his name, actually https://en.wikipedia.org/wiki/Galois_field . Is that what you intended?

Yes, that's the joke ;)

It's not a life changing amount of money, and if someone makes a huge finding they will still get tons of recognition and other forms of monetary compensation too. It's not like it's all or nothing.

That the Fields medal is in the public imagination at all is mostly due to its mention in the movie Good Will Hunting.

In which it is explained simply as "like the Nobel Prize for math".

So that's it. There you go

I enjoyed Good Will Hunting, it is easily the coolest commutative diagrams have ever been with the general public. It was also released 25 years ago, before approximately a quarter of the world's population was born. I don't think that is why.

It is definitely why. I know nothing about the fields medal beyond that movie.

It still holds a pretty compelling position in the cultural zeitgeist - it's become an object beyond an event, largely decoupled from its origination by virtue of its excellence.

But movies like these have the power to shape public perception for a long time. Even journalists who might have never seen the movie might just use the like the nobel prize, but for mathematics line. Last time I heard precisely this sentence was last time the fields medal was announced.

Out of that quarter of the world's population, how many know that the Fields medal exists?

And going further, how much mindshare does that quarter of the population have in "public imagination"? Surely, people under 14 not having watched <movie> does not preclude that movie from being influential?

Also, is if really true that people only watch movies made after they're born?

Some movies remain popular long after they were released though.

I'm not necessarily arguing it was GWH, but for sake of argument say it did have that effect, it then gets perpetuated by journalists, enters the public psyche, and goes on from there.

I don't think the suggestion was that everyone watched GWH and then had that misconception straight from primary source.

I probably view(ed) it a bit wrongly too, and I have seen GWH, but I'm pretty sure I'd read ('pop math'/news) about the award/it's winners before that.

And nobody that watched it ever spoke of it again, to anyone, ever. Especially about them apples.

> It was also released 25 years ago, before approximately a quarter of the world's population was born

Sure. Except that most people under the age of 25 probably haven't heard of the Fields medal anyway, unless it's from someone who watched GWH.

You would be astonished at how long phrases can last, with little sense behind it at all!

My favorite example is documented in Bully for Brontosaurus (see https://www.amazon.com/Bully-Brontosaurus-Reflections-Natura... if you want to buy it) in the essay, "The case of the creeping fox terrier clone." For close to a century, the first thing that everyone learned about the early horse Euohippus, officially known as Hyracotherium, was that it was "about the size of a small fox terrier". This despite the fact that essentially nobody knew what size a small fox terrier WAS. And despite the fact that later research found that the animal in question actually weighed several times what a fox terrier does! (But the shoulder height is indeed close.)

I've certainly seen the phrase "like the Nobel for mathematics" many times. I couldn't even have cited the original source. But it doesn't surprise me if this is the only thing most people have heard about the Fields medal. And it also doesn't surprise me that it would come from a movie.

Side note, is your screen name a reference to the Beaver?

> like the Nobel Prize for math

One recognizes individuals who are not too old and the other recognizes individuals who are not too old (i.e. dead).

This article says it's an artifact of cold war politics https://www.nytimes.com/2014/08/10/opinion/sunday/how-math-g...

I'm not personally familiar with the history, this just turned up when I googled the nytimes for "fields medal" and "nobel prize", but that query also turns up articles from 1986 and 1977.

On the other hand, if it's still part of the public imagination, it does seem more likely that its from Good Will Hunting and not the cold war.

Just want to ask from a layperson, between Abel and Wolf prize, which one is more 'prestige' like Nobel Prize for mathematics kind of prestige?

It is idiotic to think that an award for "greatest mathematical genius" [...] would just ignore accomplishments over a certain age, it is almost offensive

Unfortunately, nature - as ever - doesn't care about causing offence.

At the very highest creative level, maths - like pop music and physics - is a young person's game.

As somebody who does some 'mathy' theoretical CS work, I wonder if this will stay true forever, for the following reasons:

* The general population, but also academics, take increasingly more time to mature.

* The body of knowledge grows and mastering it takes more time.

* People (at least the privileged elites) spend more time taking care of their mental and physical health. For example, we see that athletes competing in team sports on top level may reach their peak in their mid-30ies, which is a relatively recent development. If one translates this to math (I know it is a shaky assumption, but why not speculate) and peak creativity is reached in the mid-30ies, the papers that result from it may be published years later.

* In some decades, people will most likely frequently use software tools as helpers.

Not that I think that these developments change things completely, but I would expect that we will see a substantial shift.

I had read up on HoTT/UF after Voevodsky passed away. It seemed promising, has it developed much? It seemed like coq / UniMath had a reasonable community.

I'm only very superficially aware of the Fields medal. I was not even aware it had an age limit.

I know it's given as a credential when someone wants to be shown as "good at math".

40 seems incredibly old for an "emergent" talent in Maths

It's just prizes guys. Everyone in mathematics knows that 'win a Fields medal' is not a realistic goal unless you're like Terry Tao or Peter Scholze - you need a lot of luck as well as talent.

There are other math prizes available that try to fill the gap with the Nobel prize - most notably the Abel prize, and the Wolf prize, these should possibly supplant the Fields medal (or maybe the Fields medal should just lose its age restriction). There are also other prizes available for young 'promising' mathematicians, for example the SASTRA Ramanujan prize in Number theory / combinatorics, or Clay research fellowships. I don't know if it makes sense to move the Fields medal closer to this now, given how it's outgrown its original prestige.

"maybe the Fields medal should just lose its age restriction"

I agree completely. The IMU should take a page from other academies and have prizes for lifetime accomplishments, substantial contributions during a year or some other period, and then maybe a more minor prize for new and upcoming mathematicians. The restriction that the Fields can only be awarded to a person once is equally arbitrary and needing to change. It particularly bothers me how the age 40 restriction puts women mathematicians who would like to have children at a disadvantage.

I am very surprised at the article as the Fields medal has always been promoted as such: encouraging promising young mathematical talents.

I am even more surprised that,of all places, here on HN I get to be the first to comment that.

How did the general audience get such a poor perception of the medal? Is it scientific communication gone wrong?

It's hard to argue that the spirit of the competition has not changed since it started. Roth would not have won the fields medal the way he did these days, he pretty much won it for a single paper.

> the Fields Medal, is often described as the Nobel Prize for math(s).

This is the problem

Is there a higher rank award in math?

It isn't about the rank in this case - it is about the difference in how both operate.

Equating the two, because of their similar prestige, misleads those to thinking the Fields Medal is awarded under the same merit of the Nobel Prize.

Surprisingly common given the multitude listed here:

List of prizes known as Nobel of X https://en.wikipedia.org/wiki/List_of_prizes_known_as_the_No...

Grothendieck is an interesting example of how quickly this changed [1]. If you have not heard of him, he is one of the two or three most important mathematicians of the 20th century, but his work was wildly abstract, so tends to be less well known.

He was passed over for the Fields medal in 1958 at age 30 because his advisor was on the committee, and wanted more of his work to be published to prove it wasn't favouritism. Then in 1962, he was deemed to be _too_ established for the medal, no longer an up-and-coming star. And then in 1966, the attitude of the committee changed to "the Nobel of math" and he won it!

[1] https://hsm.stackexchange.com/questions/14250/grothendieck-a...

But that "change" didn't persist. Another explanation is just that hewas an emerging talent, then he seemed to have done the thing mathematicians often do where he settled down to flesh out the brilliant ideas he'd already had, but then it became clear he was still producing innovative output!

Sorry not sure I understand you post, but if I follow:

- you're claiming that the Fields medal did not switch over in 1966 - I think many would disagree, that's generally cited as the year the change happened.

- you're claiming that a good explanation why Grothendieck didn't win in 1962 is because he was just fleshing things out? I think that is also incorrect - he introduced etale cohomology in 1960 - from 58-66 Grothendieck's output was pretty ridiculous.

After Perelman’s fiasco, many universities have started offering professorships without putting people on tenure-track. For example, manjul bhargava and June huh are two examples. Also add Yitang Zhang, an adjunct lecturer became a tenured professor.

Somehow, the American math tribe couldn’t offer a tenured position right away after his postdoc—-in fact, that’s what Grigori pereleman wanted.

> After Perelman’s fiasco

I couldn't find anything on this - any links?

https://mobile.twitter.com/luismbat/status/13611279484016148...

Grabbed a relevant reference from Wikipedia: https://archive.ph/tL5oD

Perelman solved the Soul Conjecture. Then he wanted a tenured/research-only position, but Princeton only offered a tenure track job, so he declined. And then he took a (research-only) job elsewhere (in Russia), which gave him requisite time/space to prove the Poincare conjecture. So Princeton would have benefited from giving him tenure when he asked for it.

I wonder if those people taught Google the idea of insisting famous candidates solve their pet leetcoder challenge before they can go another round of interviews?

Perelman, when asked for his CV, "You have heard my lecture why would you need anymore information?" Then proceeds to leave.

Google needs a million perelkids not one perelman

Thanks for the link. I still do not understand why people call it "Fiasco" though. Princeton at least tried, pretty sure many other universities knew about the soul conjecture, but did not make any effort.

I think it meant "fiasco" for Princeton specifically and not in general - they had him ready to accept a immediately full-tenure position which they didn't offer and later he went on to solve the Poincaré Conjecture. Sure, one can say that they couldn't have known the future but considering the Soul Conjecture is described as an extraordinarily difficult problem that he solved in a short 4-page paper, they could have tried harder. Anyway, granted, hindsight is 20/20.

It almost seems inevitable. When a prize is new maybe you have the freedom to give it to young and relatively unknown mathematicians. But as the reputation and the coverage of the award grows, you end up leaning towards the more traditional pick.

The thing is, mathematics is nowadays almost the only science where someone can make a name for themselves at a young age, because they don't need as much funding (except to pay their own bills), research grants, associates to do grunt work etc. etc. So if the Fields Medal would really go to "the traditional pack", it would be especially unfair. Of course it's also unfair that many of the biologists, physicists etc. doing the grunt work for their higher-ups don't get recognized either until they manage to climb to the top, but such is life...

What are the other sciences? I'd say CS

A good way of ending this article: "I was fascinated by the way in which the personal agendas of committee members were clothed in seemingly reasonable attempts to place restrictions on the prize," says Christopher Hollings, a historian of mathematics at the University of Oxford in the United Kingdom, who attended Barany's talk. "It is a nice and interesting reminder that mathematicians are people, too."

It’s worth noting that the Bohr mentioned in the article is Niels’ brother, so he certainly would understand the ramifications of the award using similar qualification standards as the Nobel Prize.

He was also, on an unrelated note, a silver medalist in the Olympics of 1908 as a soccer player.

Nobel prize itself deviated quite a lot from original vision of worthy nominees. It’s pretty well covered in “Losing the Nobel Prize” book

Barany published his findings as a short article in Nature [1]. He also talked about the topic in an episode of the podcast “My Favorite Theorem” [2].

[1]: https://www.nature.com/articles/d41586-018-00513-8 [2]: https://kpknudson.com/my-favorite-theorem/2020/11/12/episode... (from 21:40 to 30:44).

It's a pervasive misunderstanding. See, e.g., yesterday's ArsTechnica headline on an article about the Fields Medal: "How one institution keeps claiming math’s highest award: One institute has had 12 math faculty, and eight of them have won the Fields Medal."

https://arstechnica.com/science/2022/07/how-one-institution-...

Delightfully relevant HN thread: https://news.ycombinator.com/item?id=35079

Thank you for pointing out this nugget!

The problem with "promise" is that it is ageist and hard to measure. And to be honest, being "promising" can actually put more psychological pressure on the recipient.

I think in general societies should strive to have equal and realistic opportunities across the board rather than try to fix it with a prize for selected young men.

To be fair, it's not awarded on "promise". It is awarded based on contribution, the Fields medal is phenomenally prestigious in that respect. It is just restricted to recipients under age 40, among other things.

Also is there something of a pure-maths fixation with the fields medal? Did anyone win it for Wavelets( like Ingrid Daubechies for example) or compressed sensing?

Popular culture mis-informs a lot of things. Look at how people understand 'Turing Test' -benedict cumberbatch did an awesome job of being AT. Does that mean everyone understands the turing test? No.

So blame Russell Crowe for mis-understanding of the fields medal.

The 0th tier is a prize named after you.

Title needs (2018).

Reply on news.ycombinator.com