13 ms·

The Fields Medal should return to its roots

122 points by adenadel 9y ago

maximumkek 9y ago
why don't we let the funders of the fields medal decide?
uptownfunk 9y ago
Ok so what awards ceremony selection process isn’t political? Any guess on who is in consideration of the 2018 prize? I imagine those under consideration are already at top tier institutions. Is no noteworthy mathematics being done at less prestigious institutions? (Loaded question I know) but it would be cool to see some undiscovered mathematician doing ground breaking stuff at a lesser known university.
- fantispug 9y ago
  Like Grigori Perelman did?
  - majos 9y ago
    It appears that Grigori Perelman was a well-known mathematician even before his work on the Poincare conjecture. He proved the wonderfully named "soul conjecture" almost a decade beforehand.
    - raincom 9y ago
      Even though he proved "soul conjecture", no university in the US wanted to give him a tenure job. Instead, they offered him a tenure track position. Once he proved the Poincare, every one wants him on their faculty. Because of this, Princeton offered Manjul Bhargava (another Fields winner) a tenure job right away without putting on the rigma role of tenure-track.
- impendia 9y ago
  (Professional mathematician here, indeed one at a less prestigious institution.) I would argue that medalists' universities have been reasonably diverse. For example, in the US since 1990, medals have gone to mathematicians from Rutgers and three separate University of California campuses. These are prestigious universities to be sure, but it's not like all the medalists are from the same two or three places. > it would be cool to see some undiscovered mathematician I think "undiscovered mathematicians" are very rare, for the reason that mathematics is an inherently social activity. We are constantly reading each other's papers, visiting each others' universities to give talks, and meeting each other at conferences. If you do excellent work, then in general your peers will learn about it and spread the word.
- rvo 9y ago
  Ciprian Manolescu or Peter Scholze (perhaps he is too young for it for this year).
  - tacomonstrous 9y ago
    I would be shocked if Scholze didn't win this year.
- yodsanklai 9y ago
  > Is no noteworthy mathematics being done at less prestigious institutions? People with high-potential are detected early on and can choose to work in the most prestigious institutions. It's like a pro-athlete. You don't expect Michael Jordan to be playing with a small local team.
  - opportune 9y ago
    I think people are psychologically averse to acknowledging this level of "filtering" even though it's mostly true, because it suggests an uncomfortable level of inequality. However I do think that there might be just a little too much focus on contest-math when it comes to identifying the country's best mathematicians. It's easily seen that the best contest mathematicians usually become the best professional mathematicians. In aggregate, though, most contest-math participants come from a very particular demographic (i.e. they live in big cities in wealthy areas, have very supportive/tiger parents (this is the key), go to magnet schools, obviously practice a lot, etc.). These people are still probably much more likely than average to become professionals, but it filters out a lot of bright people from less wealthy families or areas, or in regions where culturally math competitions are barely even a thing.
    - wbl 9y ago
      That's not that true. Plenty of non IMO/Putnam people have won Fields Medals.
      - opportune 9y ago
        I think you may have misinterpreted my comment, because I'm really in agreement with what you just said: placing near the top in prestigious math contests indicates that you'll probably be a good professional mathematician, but not having top contest-math scores does not preclude you from being a good professional mathematician. In general I think placement into top math undergrad/PhD programs (e.g. Harvard) should be less focused on contest math.
  - deleted 9y ago
    [deleted]
- cybertronic 9y ago
  https://www.quantamagazine.org/will-peter-scholze-win-the-fields-medal-in-2018-20160628/ https://www.quantamagazine.org/will-peter-scholze-win-the-fi...
- auggierose 9y ago
  How about: https://en.wikipedia.org/wiki/Yitang_Zhang https://en.wikipedia.org/wiki/Yitang_Zhang
mianos 9y ago
I am not sure awarding someone a prize 20 years after their work like the Nobel, would achieve the goal of 'encouragement'. It may be ageist due to that goal but that was the intent of Fields.
- majos 9y ago
  I don't think this article is arguing that the Fields medal should imitate the Nobel prize. Rather, it argues that the Fields medal should return to its early selection criteria: mathematicians who have 1. done good work, 2. look like they will do more good work/positively impact math, and 3. would find the Fields medal's recognition and prestige useful in doing future good work (e.g. in getting them collaborators or funding) The article argues that the <=40 cutoff is a poor proxy for points 2 and 3, and also seems to make a separate point that the habit of awarding mathematicians who are already professors at top institutions means point 3 may not be addressed well either. An example of the kind of person this might help is Yitang Zhang, who made substantial progress on the Twin Primes conjecture in his 50s after a relatively quiet math career as an untenured lecturer beforehand. Granted, his result was big enough to get him a MacArthur and a professorship at his university, so he may not need extra recognition. But perhaps there are similar, less-lauded cases.
Fibo144 9y ago
I think the age limit for the Fields medal reinforces this idea that "mathematics is a young mans game." It's one of many reasons why I got discouraged into entering mathematics when I was young because of this and math competitions. When I was younger , I would visit websites such as AOP , and ask questions and then be treated in a condescending way by students who were my age or younger who would then boast about their scores on Contests such as AMC. This just reinforced me that I probably shouldn't waste time pursuing mathematics as a career because I felt that I was drastically behind them, and I would be competing with them for positions that they could take. It took some time for me to realize that having encouraging parents who are academics/engineers helps significantly in guiding you in a career such as mathematics.
- throwaway0255 9y ago
  > It took some time to realize that having parents who are academics/engineers helps significantly in guiding you in a career such as mathematics. This is true of every good job. I'm trying to get hired at big 4 tech right now. Every person interviewing me is a rich kid. All of my competition is rich kids. Touring these big tech companies was discouraging. They're all very diverse. Rich white kids. Rich Asian kids. Rich female kids. Rich European kids. Rich Indian kids. I'm not sure there's anything I can ever do to make it past the social/socioeconomic judgment round of these interviews. These interviews make me feel like Red at a parole hearing in Shawshank Redemption.
  - ranman 9y ago
    I was in a similar position for a long time but then I found once you make it into one of the circles all of the others open up. It’s dumb. There’s so much untapped talent out there because tech giants are relying on “namebrand” schools or other companies to do their recruiting filters for them.
  - gmcballsonface 9y ago
    > Every person interviewing me is a rich kid. All of my competition is rich kids. Touring these big tech companies was discouraging. They're all very diverse. Rich white kids. Rich Asian kids. Rich female kids. Rich European kids. Rich Indian kids. Oh come on -- how could you possibly know this.
javiramos 9y ago
Shocking that 55/56 Fields Medals have been awarded to men. Maryam Mirzakhani has been the only female recipient. [0] [0] https://www.nytimes.com/2017/07/16/us/maryam-mirzakhani-dead.html https://www.nytimes.com/2017/07/16/us/maryam-mirzakhani-dead...
- laurentoget 9y ago
  putting an age limit of 40 is probably skewing the result as women who want to have children have a biological constraint to have them in their 20s or 30s when their fertility is higher.
- wheresmyusern 9y ago
  why is it shocking?
  - Hasz 9y ago
    If you accept the idea that a penchant for math is randomly distributed among all people, then the odds of 55/56 men winning by chance are very, very, very low.
    - lambdaphagy 9y ago
      If.
    - notzorbo3 9y ago
      > If you accept the idea that a penchant for math is randomly distributed among all people That would seem rather detached from reality.
      - bionsystems 9y ago
        Maybe he meant "Even if" ?
    - cycrutchfield 9y ago
      All it would require is just that the standard deviation for math ability in men (whether by nature or nurture, I am making no judgment either way) is only very slightly higher than for women. Since we are looking at the tail of the distribution, the result would not be surprising.
shem73 9y ago
I think this overlooks the fact that mathematics is very specialised, segmented. Enormous talent in one strain of maths does not mean that anybody, following a slightly different course, would recognise the talent. So, being an arbiter always means disappointing someone. I suggest several micro-Fields medals, each arbitrated by the cross-cut of the nebulously defined experts of this field.
throwaway5752 9y ago
He should institute a Barany medal instead. It's an interesting idea, but the Fields medal is what it is at this point. It would be very slow to change, and even though his article is well researched, it's a bit idealistic and the interpretation of the original intent isn't black & white.
- bionsystems 9y ago
  > He should institute a Barany medal instead. My thoughts exactly.
tremendulo 9y ago
Credentials and prizes are heading the way of the dodo because we're slowly realising that while neither knowledge nor significance can be measured our opinions can be swayed by prestige and politics.
- biohax2015 9y ago
  I would say charisma.. that gets people before they think about any of those things
pducks32 9y ago
I recently got to meet a fields medalist who will remain nameless but he mention a really really interesting statistic. No Field’s medalist has ever been the mentor to another Field’s medalist. I (my opinion here not his) think that this glorifies these young mathematicians who never go onto mentor or yield another similarly gifted mathematician. We should be finding great mathematicians who discover great math collaboratively.
- jhshah 9y ago
  Quibbling about the Fields Medal mentoring claim: Schwartz -> Grothendieck -> Deligne is a counterexample.
  - kkylin 9y ago
    Also Avila & Yoccoz: https://en.wikipedia.org/wiki/Artur_Avila https://en.wikipedia.org/wiki/Artur_Avila and https://en.wikipedia.org/wiki/Jean-Christophe_Yoccoz https://en.wikipedia.org/wiki/Jean-Christophe_Yoccoz.
  - ocfnash 9y ago
    Also Atiyah supervised Donaldson (albeit jointly with Hitchin), Mirzakhani was supervised by McMullen and others I'm sure.
- deleted 9y ago
  [deleted]
KKKKkkkk1 9y ago
Committee members started talking about criteria such as age and fields of study, even before suggesting nominees. Most thought that focusing on specific branches of mathematics was inadvisable. They entertained a range of potential age considerations, from an upper limit of 30 to a general principle that nominees should have made their mark in mathematics some time since the previous ICM in 1936. Bohr cryptically suggested that a cut-off of 42 “would be a rather natural limit of age”. By the time the first set of nominees was in, Bohr’s cut-off seemed a lot less arbitrary. It became clear that the leading threat to Bohr’s designs for Schwartz was another French mathematician, André Weil, who turned 43 in May 1949. Everyone, Bohr and Morse included, agreed that Weil was the more accomplished mathematician. But Bohr used the question of age to try to ensure that he didn’t win. Why let the committee argue whether the nuclear reactor needs to be built, when you can get them to argue about the color of the bikeshed. Stuff like that makes you wonder about the true significance of academic accolades.
- louithethrid 9y ago
  "..overall can not recommend weighting the Vain to be drowned down with golden medalls and recommend the return to a boulder/concrete bucket. How somebody who gives a scrap about the opionion of his fellow men is supossed to archive true greatness - in particular beyond the boundrys of the knowledge of his fellow men escapes my feable mind."
- coolgeek 9y ago
  This is not an example of bikeshedding. Bikeshedding is fighting over trivial details in order to delay or avoid a decision (perhaps subconsciously) This is an example of gaming the system in order to steer a decision in a particular direction. It is an example of organizational politics - perhaps even of corruption
sumanthvepa 9y ago
I think the equivalent of the Nobel prize for Mathematics is the Abel prize not the Fields Medal. The former rewards lifetime achievement.
- kkylin 9y ago
  Totally agree, but it should be pointed out that unlike the Fields Medal, the Abel Prize is relatively new, and perhaps intentionally set up in a way to invite comparison to the Nobel (whereas the Fields wasn't).

122 points by adenadel 9y ago

why don't we let the funders of the fields medal decide?

Ok so what awards ceremony selection process isn’t political? Any guess on who is in consideration of the 2018 prize? I imagine those under consideration are already at top tier institutions. Is no noteworthy mathematics being done at less prestigious institutions? (Loaded question I know) but it would be cool to see some undiscovered mathematician doing ground breaking stuff at a lesser known university.

fantispug 9y ago
Like Grigori Perelman did?
- majos 9y ago
  It appears that Grigori Perelman was a well-known mathematician even before his work on the Poincare conjecture. He proved the wonderfully named "soul conjecture" almost a decade beforehand.
  - raincom 9y ago
    Even though he proved "soul conjecture", no university in the US wanted to give him a tenure job. Instead, they offered him a tenure track position. Once he proved the Poincare, every one wants him on their faculty. Because of this, Princeton offered Manjul Bhargava (another Fields winner) a tenure job right away without putting on the rigma role of tenure-track.
impendia 9y ago
(Professional mathematician here, indeed one at a less prestigious institution.) I would argue that medalists' universities have been reasonably diverse. For example, in the US since 1990, medals have gone to mathematicians from Rutgers and three separate University of California campuses. These are prestigious universities to be sure, but it's not like all the medalists are from the same two or three places. > it would be cool to see some undiscovered mathematician I think "undiscovered mathematicians" are very rare, for the reason that mathematics is an inherently social activity. We are constantly reading each other's papers, visiting each others' universities to give talks, and meeting each other at conferences. If you do excellent work, then in general your peers will learn about it and spread the word.
rvo 9y ago
Ciprian Manolescu or Peter Scholze (perhaps he is too young for it for this year).
- tacomonstrous 9y ago
  I would be shocked if Scholze didn't win this year.
yodsanklai 9y ago
> Is no noteworthy mathematics being done at less prestigious institutions? People with high-potential are detected early on and can choose to work in the most prestigious institutions. It's like a pro-athlete. You don't expect Michael Jordan to be playing with a small local team.
- opportune 9y ago
  I think people are psychologically averse to acknowledging this level of "filtering" even though it's mostly true, because it suggests an uncomfortable level of inequality. However I do think that there might be just a little too much focus on contest-math when it comes to identifying the country's best mathematicians. It's easily seen that the best contest mathematicians usually become the best professional mathematicians. In aggregate, though, most contest-math participants come from a very particular demographic (i.e. they live in big cities in wealthy areas, have very supportive/tiger parents (this is the key), go to magnet schools, obviously practice a lot, etc.). These people are still probably much more likely than average to become professionals, but it filters out a lot of bright people from less wealthy families or areas, or in regions where culturally math competitions are barely even a thing.
  - wbl 9y ago
    That's not that true. Plenty of non IMO/Putnam people have won Fields Medals.
    - opportune 9y ago
      I think you may have misinterpreted my comment, because I'm really in agreement with what you just said: placing near the top in prestigious math contests indicates that you'll probably be a good professional mathematician, but not having top contest-math scores does not preclude you from being a good professional mathematician. In general I think placement into top math undergrad/PhD programs (e.g. Harvard) should be less focused on contest math.
- deleted 9y ago
  [deleted]
cybertronic 9y ago
https://www.quantamagazine.org/will-peter-scholze-win-the-fields-medal-in-2018-20160628/ https://www.quantamagazine.org/will-peter-scholze-win-the-fi...
auggierose 9y ago
How about: https://en.wikipedia.org/wiki/Yitang_Zhang https://en.wikipedia.org/wiki/Yitang_Zhang

mianos 9y ago

I am not sure awarding someone a prize 20 years after their work like the Nobel, would achieve the goal of 'encouragement'. It may be ageist due to that goal but that was the intent of Fields.

majos 9y ago
I don't think this article is arguing that the Fields medal should imitate the Nobel prize. Rather, it argues that the Fields medal should return to its early selection criteria: mathematicians who have 1. done good work, 2. look like they will do more good work/positively impact math, and 3. would find the Fields medal's recognition and prestige useful in doing future good work (e.g. in getting them collaborators or funding) The article argues that the <=40 cutoff is a poor proxy for points 2 and 3, and also seems to make a separate point that the habit of awarding mathematicians who are already professors at top institutions means point 3 may not be addressed well either. An example of the kind of person this might help is Yitang Zhang, who made substantial progress on the Twin Primes conjecture in his 50s after a relatively quiet math career as an untenured lecturer beforehand. Granted, his result was big enough to get him a MacArthur and a professorship at his university, so he may not need extra recognition. But perhaps there are similar, less-lauded cases.

Fibo144 9y ago

I think the age limit for the Fields medal reinforces this idea that "mathematics is a young mans game." It's one of many reasons why I got discouraged into entering mathematics when I was young because of this and math competitions. When I was younger , I would visit websites such as AOP , and ask questions and then be treated in a condescending way by students who were my age or younger who would then boast about their scores on Contests such as AMC. This just reinforced me that I probably shouldn't waste time pursuing mathematics as a career because I felt that I was drastically behind them, and I would be competing with them for positions that they could take. It took some time for me to realize that having encouraging parents who are academics/engineers helps significantly in guiding you in a career such as mathematics.

throwaway0255 9y ago
> It took some time to realize that having parents who are academics/engineers helps significantly in guiding you in a career such as mathematics. This is true of every good job. I'm trying to get hired at big 4 tech right now. Every person interviewing me is a rich kid. All of my competition is rich kids. Touring these big tech companies was discouraging. They're all very diverse. Rich white kids. Rich Asian kids. Rich female kids. Rich European kids. Rich Indian kids. I'm not sure there's anything I can ever do to make it past the social/socioeconomic judgment round of these interviews. These interviews make me feel like Red at a parole hearing in Shawshank Redemption.
- ranman 9y ago
  I was in a similar position for a long time but then I found once you make it into one of the circles all of the others open up. It’s dumb. There’s so much untapped talent out there because tech giants are relying on “namebrand” schools or other companies to do their recruiting filters for them.
- gmcballsonface 9y ago
  > Every person interviewing me is a rich kid. All of my competition is rich kids. Touring these big tech companies was discouraging. They're all very diverse. Rich white kids. Rich Asian kids. Rich female kids. Rich European kids. Rich Indian kids. Oh come on -- how could you possibly know this.

javiramos 9y ago

Shocking that 55/56 Fields Medals have been awarded to men. Maryam Mirzakhani has been the only female recipient. [0] [0] https://www.nytimes.com/2017/07/16/us/maryam-mirzakhani-dead.html https://www.nytimes.com/2017/07/16/us/maryam-mirzakhani-dead...

laurentoget 9y ago
putting an age limit of 40 is probably skewing the result as women who want to have children have a biological constraint to have them in their 20s or 30s when their fertility is higher.
wheresmyusern 9y ago
why is it shocking?
- Hasz 9y ago
  If you accept the idea that a penchant for math is randomly distributed among all people, then the odds of 55/56 men winning by chance are very, very, very low.
  - lambdaphagy 9y ago
    If.
  - notzorbo3 9y ago
    > If you accept the idea that a penchant for math is randomly distributed among all people That would seem rather detached from reality.
    - bionsystems 9y ago
      Maybe he meant "Even if" ?
  - cycrutchfield 9y ago
    All it would require is just that the standard deviation for math ability in men (whether by nature or nurture, I am making no judgment either way) is only very slightly higher than for women. Since we are looking at the tail of the distribution, the result would not be surprising.

shem73 9y ago

I think this overlooks the fact that mathematics is very specialised, segmented. Enormous talent in one strain of maths does not mean that anybody, following a slightly different course, would recognise the talent. So, being an arbiter always means disappointing someone. I suggest several micro-Fields medals, each arbitrated by the cross-cut of the nebulously defined experts of this field.

throwaway5752 9y ago

He should institute a Barany medal instead. It's an interesting idea, but the Fields medal is what it is at this point. It would be very slow to change, and even though his article is well researched, it's a bit idealistic and the interpretation of the original intent isn't black & white.

bionsystems 9y ago
> He should institute a Barany medal instead. My thoughts exactly.

tremendulo 9y ago

Credentials and prizes are heading the way of the dodo because we're slowly realising that while neither knowledge nor significance can be measured our opinions can be swayed by prestige and politics.

biohax2015 9y ago
I would say charisma.. that gets people before they think about any of those things

pducks32 9y ago

I recently got to meet a fields medalist who will remain nameless but he mention a really really interesting statistic. No Field’s medalist has ever been the mentor to another Field’s medalist. I (my opinion here not his) think that this glorifies these young mathematicians who never go onto mentor or yield another similarly gifted mathematician. We should be finding great mathematicians who discover great math collaboratively.

jhshah 9y ago
Quibbling about the Fields Medal mentoring claim: Schwartz -> Grothendieck -> Deligne is a counterexample.
- kkylin 9y ago
  Also Avila & Yoccoz: https://en.wikipedia.org/wiki/Artur_Avila https://en.wikipedia.org/wiki/Artur_Avila and https://en.wikipedia.org/wiki/Jean-Christophe_Yoccoz https://en.wikipedia.org/wiki/Jean-Christophe_Yoccoz.
- ocfnash 9y ago
  Also Atiyah supervised Donaldson (albeit jointly with Hitchin), Mirzakhani was supervised by McMullen and others I'm sure.
deleted 9y ago
[deleted]

KKKKkkkk1 9y ago

Committee members started talking about criteria such as age and fields of study, even before suggesting nominees. Most thought that focusing on specific branches of mathematics was inadvisable. They entertained a range of potential age considerations, from an upper limit of 30 to a general principle that nominees should have made their mark in mathematics some time since the previous ICM in 1936. Bohr cryptically suggested that a cut-off of 42 “would be a rather natural limit of age”. By the time the first set of nominees was in, Bohr’s cut-off seemed a lot less arbitrary. It became clear that the leading threat to Bohr’s designs for Schwartz was another French mathematician, André Weil, who turned 43 in May 1949. Everyone, Bohr and Morse included, agreed that Weil was the more accomplished mathematician. But Bohr used the question of age to try to ensure that he didn’t win. Why let the committee argue whether the nuclear reactor needs to be built, when you can get them to argue about the color of the bikeshed. Stuff like that makes you wonder about the true significance of academic accolades.

louithethrid 9y ago
"..overall can not recommend weighting the Vain to be drowned down with golden medalls and recommend the return to a boulder/concrete bucket. How somebody who gives a scrap about the opionion of his fellow men is supossed to archive true greatness - in particular beyond the boundrys of the knowledge of his fellow men escapes my feable mind."
coolgeek 9y ago
This is not an example of bikeshedding. Bikeshedding is fighting over trivial details in order to delay or avoid a decision (perhaps subconsciously) This is an example of gaming the system in order to steer a decision in a particular direction. It is an example of organizational politics - perhaps even of corruption

sumanthvepa 9y ago

I think the equivalent of the Nobel prize for Mathematics is the Abel prize not the Fields Medal. The former rewards lifetime achievement.

kkylin 9y ago
Totally agree, but it should be pointed out that unlike the Fields Medal, the Abel Prize is relatively new, and perhaps intentionally set up in a way to invite comparison to the Nobel (whereas the Fields wasn't).