You write that the text of the Laudationes (using Fausto Di Biase’s linguistic remark above) will be eventually available. Do you know roughly when? I am quite surprised that this is still not the case (unless I am doing something stupid when I check the website, which I cannot exclude). What is the customary amount of time that passes through the cerimony and the public release of the texts of the Laudationes.

I am honestly very curious to read those two neighboring my area and it would be convenient to get a sense of “when to look for them”, instead of trying out every week.

Thank you in advance in case you can provide this Info.

]]>Good point. It’s amazing how pervasive, and old, these schemes are. I think they are the ultimate over-fitting schemes: winning the game becomes the goal as opposed to being experiences that help advance the discipline, be that discipline mathematics or any other. As I mentioned elsewhere, whether keeping the 40 year limit in the Fields Medal is good for the medals will only become clear 20 to 30 years from now given that now there are alternative ways to honor great mathematicians that do not have the 40 year old limit.

]]>” the examination necessarily degenerates into a kind of game, and instruction for it into initiation into a series of stunts and tricks.”

Hardy’s comments seem somewhat appropriate to the IMO as well, for what it’s worth.

]]>Happy to see that there is some common ground. When it comes to the Abel Prize, I think we will need another 20 or 30 years of data (say by 2050) to see how things turn out, but neither of the winners starting in 2014 has won a Fields Medal (even though they would have been eligible under the Fields Medal rules):

– Yakov Sinai

– John Nash

– Louis Nirenberg

– Andrew Wiles

– Yves Meyer

– Robert Langlands

I don’t know if this was a deliberative decision by the Abel Committee but it is hard not to notice.the pattern.

Of these, I am most familiar with Yves Meyer’s work. He started the work he was given the Abel Prize for -the development of wavelet theory- when he was in his mid 40s. Wavelets are now pervasively used in applied mathematics. Did the different Fields committees miss Yves’ potential or is it just that indeed the Fields Medals rules should be relaxed lest they -the medals- become irrelevant in 50 years?

]]>With the Abel prize, it always seems to me that the winner is one of the “usual suspects”, one of the older leaders in math who surprises no one when he wins. I tend to pay little attention to it since its purpose seems to just confirm what everyone already believes.

]]>I had never heard about it, but I found a copy here http://www-history.mcs.st-and.ac.uk/Extras/Hardy_Tripos.html . I find this paragraph particularly interesting,

“It has often been said that Tripos mathematics was a collection of elaborate futilities, and the accusation is broadly true. My own opinion is that this is the inevitable result, in a mathematical examination, of high standards and traditions. The examiner is not allowed to content himself with testing the competence and the knowledge of the candidates; his instructions are to provide a test of more than that, of initiative, imagination, and even of some sort of originality. And as there is only one test of originality in mathematics, namely the accomplishment of original work, and as it is useless to ask a youth of twenty-two to perform original research under examination conditions, the examination necessarily degenerates into a kind of game, and instruction for it into initiation into a series of stunts and tricks. It was in any case certainly true, at the time of which I am speaking, that an undergraduate might study mathematics diligently throughout the whole of his career, and attain the very highest honours in the examination, without having acquired, and indeed without having encountered, any knowledge at all of any of the ideas which dominate modern mathematical thought. His ignorance of analysis would have been practically complete.”

In my experience, a lot of undergraduate and some graduate classes fit precisely this paradigm at America’s most prestigious universities (I know less the rest of the world). It’s only at the PhD level that people make the transition to doing actual original mathematical work.

Coming back to the Fields Medal/Nevanlinna Prize age limit. Suppose that somebody, somehow were to come up with a definite answer to either the Riemann hypothesis or the P vs NP question and that somebody is 50. The current age limit is signaling the world that such thing cannot happen provided that the Fields Medal/Nevanlinna Prize prize remain the most prestigious awards in mathematics/computer science. If that were to happen, then the idea of these awards being the most prestigious awards would have been falsified. In a way, keeping the age limit is setting up some sort of demonic scenario in mathematics. The only guy who has solved one of the Millennium problems was also eligible for a Fields Medal but there is no guarantee that this will continue to be the case in the future.

I think that keeping the age limit has more to do with the current winners seeking to keep the value of their award up than anything else. It’s like the kind of laws that restrict new construction developments in areas with high priced real estate. They have nothing to do with their alleged goals (such as environmental concerns) but are really proxies to keeping the value of existing real estate high. This might work in the short term, but in the long run, I doubt it will because people will find creative ways to overcome the limit, such as was the case for Yitang Zhang. I do not know enough about advanced number theory to judge whether his theorem was a breakthrough of the first order, but given the awards he collected as a result, it would seem so.

]]>This reminds Hardy’s influence to modify the Tripos (in particular, in his 1926 presidential address to the Mathematical Association on “The case against the Mathematical Tripos”).

]]>[This is a reply to Terry’s comment]

Ah, I was wondering about this committee and the result. I didn’t realise it had concluded two years ago! Here was me still telling people this year that the IMU was looking into the age limit…

]]>Thank you for the detailed clarifications that this issue was discussed in the past.

I don’t find the arguments in favor of keeping the age limit very compelling though. Yes the IMU cannot compete financially with the Breakthrough or Abel prizes, but it can compete in being the premier mathematical body and keeping the Fields medal as the premier mathematical award given its past.

Keeping the age limit risks, in the long run, diminishing the significance of the Fields medal particularly if prizes like the Abel Prize continue to be awarded to people like Andrew Wiles or Robert Langlands. Take the latter. The so called “Langlands program” is not my area of expertise and I understand little of it. It would seem to me that when history of mathematics is written 100 years from now, the guy who built the theory will be given more credit than the several winners of Fields Medals that worked on proving some of his conjectures. For example, it’s Einstein who gets the credit for coming up with General Relativity, not the different Nobel Prize winners who have worked in verifying experimentally the predictions of the theory as important as this verification work was.

If the list of Abel Prize continues to be as impressive, we could see in 100 years two tracks of honors in Mathematics: one track honoring the best mathematics humans do before they reach the age of 40. The second honoring the best mathematics humans can do in a lifetime. Something tells me that the second track is likely to be the most impressive of the two, even though I am also sure that the intersection between the two tracks won’t be an empty set.

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