Is There a Curse of the Fields Medal? [pdf] | Hacker News Reader

Is There a Curse of the Fields Medal? [pdf]

web.math.princeton.edu

44 pointspaulpauper24 comments

Destroying one career is not the same as destroying a field. Mathematicians like to believe the likely apocryphal tale that Nobel didn't endow a prize for math because the likely first winner was sleeping with his wife. Nevertheless, the Fields medal distorts math far less than Nobel prizes distort the sciences.

Mathematicians pursue math in defiance of the far greater rewards of other paths. I know at least nine Fields medalists and many near misses. Unlike the Nobel prize, neither the quest nor the realization of the Fields medal turned anyone into an ashpile.

> Mathematicians like to believe the likely apocryphal tale that Nobel didn't endow a prize for math because the likely first winner was sleeping with his wife

It’s certainly apocryphal. Alfred Nobel never married.

That you know of -- it's possible he was secretly married, and his secret wife was sleeping with the likely first winner of a Nobel prize in mathematics.

Unlikely, yes, but the tale is not certainly apocryphal ;)

Google gives the following definition of apocryphal:

> (of a story or statement) of doubtful authenticity, although widely circulated as being true.

So it seems to be certainly apocryphal.

He had no secret wife, but 3 non-secret official affairs. The last one with Sophie Hess lasting for 18 years, in which she had a second lover. https://oe1.orf.at/programm/20190122/540398/Die-geheimen-Lie...

The rumor is that his first love interest in Russia Anna Desry preferred the mathematician Franz Lemarges.

https://simanaitissays.com/2018/08/23/on-alfred-nobel-and-go... and https://simanaitissays.com/2018/08/24/on-alfred-nobel-and-go... is possibly a better reference here.

In that case, the likely first winner was sleeping with all of his wives.

Hey Syzygies. Can you please reach out to me at my HN bio? I am conducting an analysis of mathematicians and Fields medalists’ proclivity to remain within pure mathematics terrain vs context switch to some worldly contribution, particularly in light of some of the pressing problems of modernity. You seem to have insight in this subject. If you have the few minutes of time, I would appreciate you reaching out. I can compensate for survey time as well. Thank you in advance!

Very surprised to see no attempt at discussing regression to the mean other than the quickest possible throw away on pg2, when it is so pervasive and must be operating to at least some degree in any result of the form 'after filtering on extreme event Y, variable X decreased/increased!' Most of the data seems pretty silent on this. (Yes, yes, the two groups look pretty similar temporally in raw # of papers before Fields, but you don't get a Fields for simply publishing a lot - by definition the Fields medalists' papers were different from and better than the non-medalists, and that's why they won.)

Regression to the mean is ruled out by comparing against strong contemporaries, whose number of papers produced kept growing on average. This group of strong contemporaries was not selected by looking at the number of papers, but instead by looking at the pool of strong mathematicians selected for other prizes.

You are right, but it is not ruled out entirely because they used Wolf and Abel prize in the contenders group, which are awarded for a lifetime of work in mathematics and therefore biasing the contender groups.

And, as I already pointed out, the non-award-winners must by definition be different from award-winners and cannot control for unobserved baseline differences. Even more so if those prizes are, as is only sane, intended to reward different things than what the most prestigious prize in the field already rewards...

Figure 2 shows increased “cognitive mobility” after receiving the Fields medal.

This suggests that the story in the number of papers and the citation counts is not regression to the mean but switching to a new area where the medalist is less experienced.

How worried should you be that getting a Fields medal might destroy your research career?

So, not what I feared the title suggested and one graphic suggests Fields medalists live on average longer than mere contenders.

RIP Maryam Mirzakhani, who died like 3 years after becoming the first woman and first Iranian Fields medalist. Happily, this does not appear to be a trend.

https://news.stanford.edu/2017/07/15/maryam-mirzakhani-stanf...

Great essays, shows that Fields Medal is doing its desired effects [personal opinion after reading].

For those that didn't read until the end, recipient of Fields Medal had a far greater "Cognitive Mobility" in which they opened new fields of research.

Those fields may as well be dead end, and even if they aren't their production in terms of papers are probably slow to ramp up. But those are the research we need as compared to certain fields, where the amount of papers being churned out arguably have a negative effect.

The article uses "new field" as a relative term -- a field that the researcher is not an expert in.

> A question [BD14] had to address in this connection is: what constitutes a brand-new direction? Again MathSciNet guides the answer. For each pair of the 73 Mathematics Subject Classification numbers, the authors worked out the likelihood that a paper in one area is referred to by a paper in another area. Thus, for instance, they see that 35 (Partial Differential Equations) is closest to 58 (Global Analysis)and 76 (Fluid Mechanics) but furthest from 08 (General Algebraic Systems) and 19 (K-theory). Borjas and Doran deem a topic brand-new if it is not among the 15 closest to the researcher’s original area. This is a conservative choice and probably underestimates the cognitive mobility

Or maybe, after receiving the Best Mathematician of the Year (Under 40 category) award, since your desire for social recognition of your supreme genius and success is now undeniably fulfilled, you start to realize that you can adopt a new healthy focus on some other aspects of life too, so your late career publications and fame burn less intensely than your supernova early career?

Reviewing the Fields paper at https://scholar.harvard.edu/gborjas/_publications (2015) (wrong link in the review)

https://scholar.harvard.edu/files/gborjas/files/jhr2015.pdf

Number of Fields medalists at each award year (Award years occurring every four years):

2,2,2,2,2,4,4,2,4,3,3,4,4,4,2,4,4,4,4,4

- The total sum is 64. An even number and a power of 2

- The only two odd numbers are equally distanced from the beginning and end of the sequence

- Until the first odd number sequence A279401

- From second odd number sequence A321319

Mathematicians don't like odd numbers? :-)

...recipients feel the “weight of expectations” and so publish only papers that they consider “worthy of a Fields medalist”...

This sentence is probably not only anecdotal but could well be the premise that explains the phenomenon discussed in this article.

I am missing error bars here. The analysis is looking at 64 individuals and a unknown number of contenders. For such small samples I would expect the uncertainty to be quite high.

> With one exception, only people with a Ph.D. in mathematics have received Fields medal

Who was the exception?

Ed Witten, Ph.D. in physics, 1976

Thanks!

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