About the title

About the title

I changed the title of the blog on March 20, 2013 (it used to have the title “Notes of an owl”). This was my immediate reaction to the news the T. Gowers was presenting to the public the works of P. Deligne on the occasion of the award of the Abel prize to Deligne in 2013 (by his own admission, T. Gowers is not qualified to do this).

The issue at hand is not just the lack of qualification; the real issue is that the award to P. Deligne is, unfortunately, the best compensation to the mathematical community for the 2012 award of Abel prize to Szemer├ędi. I predicted Deligne before the announcement on these grounds alone. I would prefer if the prize to P. Deligne would be awarded out of pure appreciation of his work.

I believe that mathematicians urgently need to stop the growth of Gowers's influence, and, first of all, his initiatives in mathematical publishing. I wrote extensively about the first one; now there is another: to take over the arXiv overlay electronic journals. The same arguments apply.

Now it looks like this title is very good, contrary to my initial opinion. And there is no way back.

Sunday, July 28, 2013

2014 Fields medalists?

Previous post: New comments to the post "What is mathematics?"

I was asked by Tamas Gabal about possible 2014 Fields medalists listed in an online poll. I am neither ready to systematically write down my thoughts about the prizes in general and Fields medals in particular, nor to predict who will get 2014 medals. I am sure that the world would be better without any prizes, especially without Fields medals. Also, in my opinion, no more than two persons deserve 2014 Fields medals. Instead of trying to argue these points, I will quote my reply to Tamas Gabal (slightly edited).

Would I know who the members of the Fields medal committee are, I would be able to predict medalists with 99% confidence. But the composition of the committee is a secret. In the past, the situation was rather different. The composition of the committee wasn't important. When I was just a second year graduate student, I compiled a list of 10 candidates, among whom I considered 5 to have significantly higher chances (I never wrote down this partition, and the original list is lost for all practical purposes). All 4 winners were on the list. I was especially proud of predicting one of them; he was a fairly nontraditional at the time (or so I thought). I cannot do anything like this now without knowing the composition of the committee. Recent choices appear to be more or less random, with some obvious exceptions (like Grisha Perelman).

Somewhat later I wrote:

In the meantime I looked at the current results of that poll. Look like the preferences of the public are determined by the same mechanism as the preferences for movie actors and actresses: the name recognition.

Tamas Gabal replied:

Sowa, when you were a graduate student and made that list of possible winners, did you not rely on name recognition at least partially? Were you familiar with their work? That would be pretty impressive for a graduate student, since T. Gowers basically admitted that he was not really familiar with the work of Fields medalists in 2010, while he was a member of the committee. I wonder if anyone can honestly compare the depth of the work of all these candidates? The committee will seek an opinion of senior people in each area (again, based on name recognition, positions, etc.) and will be influenced by whoever makes the best case... It's not an easy job for sure.

Here is my reply.

Good question. In order to put a name on a list, one has to know this name, i.e. recognize it. But I knew much more than 10 names. Actually, this is one of the topics I wanted to write about sometime in details. The whole atmosphere at that time was completely different from what I see around now. May be the place also played some role, but I doubt that its role was decisive. Most of the people around me liked to talk about mathematics, and not only about what they were doing. When some guy in Japan claimed that he proved the Riemann hypothesis, I knew about this the same week. Note that the internet was still in the future, as were e-mails. I had a feeling that I know about everything important going on in mathematics. I always had a little bit more curiosity than others, so I knew also about fields fairly remote from own work.

I do not remember all 10 names on my list (I remember about 7), but 4 winners were included. It was quite easy to guess 3 of them. Everybody would agree that they were the main contenders. I am really proud about guessing the 4th one. Nobody around was talking about him or even mentioned him, and his field is quite far from my own interests. To what extent I understood their work? I studied some work of one winner, knew the statements and had some idea about their proof for another one (later the work of both of them influenced a lot my own work, but mostly indirectly), and very well knew what are the achievements of the third one, why they are important, etc. I knew more or less just the statements of two main results of the 4th one, the one who was difficult to guess – for me. I was able to explain why this or that guy got the medal even to a theoretical physicist (actually did on one occasion). But I wasn’t able to teach a topic course about works of any of the 4.

At the time I never heard any complaints that a medal went to a wrong person. The same about all older awards. There was always a consensus in the mathematical community than all the people who got the medal deserved it. May be somebody else also deserved it too, but there are only 3 or 4 of them each time.

Mathematics is a human activity. This is one of the facts that T. Gowers prefers to ignore. Nobody verifies proofs line by line. Initially, you trust your guts feelings. If you need to use a theorem, you will be forced to study the proof and understand its main ideas. The same is true about the deepness of a result. You do not need to know all the proofs in order to write down a list like my list of 10 most likely winners (next time my list consisted of no more than 5 or 6, all winner were included). It seems that I knew the work of all guessed winners better than Gowers knew the work of 2010 medalists. But even if not, there is a huge difference between a graduate student trying to guess the current year winners, and a Fellow of the London Royal Society, a Fields medalist himself, who is deciding who will get 2010 medals. He should know more.

The job is surely not an easy one now, when it is all about politics. Otherwise it would be very pleasant.

Next post: Guessing who will get Fields medals - Some history and 2014.


  1. Sowa, thank you for your answer.

    I want to add that, in my opinion, it is normal that T. Gowers did not know about the work of 2010 Fields medalists before, but I was disappointed that after serving on the selection committee he was not able to talk about their work at least at the same level as his presentation of Deligne's Abel prize.

    Also, your answer raises more questions. For example, why do you think the world would be better without any prizes? You mentioned that you had some good examples in mind...

    The first time I paid attention to the Fields medals was in 2006, so my opinions on the subject are based more on common sense than experience. After reading your answer I still don't understand what happened after 1986. What your wrote, it seems like before 1986 Fields medalists were also chosen based on name recognition, and the depth of their work was evaluated on the basis of intuition, since no one could possibly know the work of all the candidates fairly well. Maybe, you were trying to say that the selection process was just as bad as now, but the outcome was somehow more agreeable?

    Finally, I must respectfully disagree with you. I think there's more than enough good candidates who deserve the Fields medal in 2014 (accepting the fact that it will be awarded).

  2. Dear Tamas Gabal,

    I agree that there is no big deal that T. Gowers or any other member of any prize awarding committee wasn't familiar with the work of some or even all winners before the deliberations started. In the past, the short list consisted of 35-40 names. I do not expect anybody to be familiar with the works of 40 leading mathematicians, all working in different areas. But I expect that members of the committee make themselves familiar with the work of at least winners, and also with work of non-winners. Every member of the committee should be able to say at least a couple of phrases about WHY somebody did not got the medal. In the past, the typical answer was that he is young enough to have a second chance, or even a third one. It seems that actually almost nobody got the medal in the next round. The exceptions (up to 1986) are all related to extreme difficulty of verification of his proofs. The first example is H. Hironaka: it took about 6-8 years to digest his (published in Annals of Mathematics) papers on resolution of singularities sufficiently to believe that they are correct. It seems that in a deeper sense almost nobody understands them even now, 50 years later. But such an excuse is available only rarely.

    I said that I am not ready to explain why the world would be better without prizes. I thought about this, discussed this with other mathematicians. So, I have a worked out theory, the problem is to write it down in a moderately coherent manner. I will try to do this later. One of the reasons is contained directly in your first question in this blog. That poll is only one step from placing bets on candidates, like on race horses. I do not see such a perspective as a decent one, and even a small chance of this scares me.

    Right now I have to go, so I will comment on your next paragraph later.

    As of the last one, could you tell me who deserves 2014 medals and why (in a couple of words: I presume that you are not a member of the committee). In return, I will tell about my choice, and try to explain, if such a question will arise, why others are not (I reserve the right to change my opinion after a more detailed study of the suggested list). That remark was made to be an anchor for a discussion.

  3. Dear Sowa, unfortunately, I must admit that my opinion about these candidates is based solely on what I heard in seminar talks and in discussions with other people. For what it's worth, my list would look like this: Avila, Bhargava, Lurie, Sheffield.

  4. Dear Tamas Gabal,

    There is nothing unfortunate, nothing to “admit”. This is quite natural. If you are interested, it is not very difficult to get at least a general idea of what these four mathematicians are doing, and what are their achievment, assuming that you have some general background (I assume that you do, otherwise you would not ask me questions like you are asking). To learn the proofs is a completely different matter.

    Amazingly, my list is part of yours: Lurie and Bhargava. I have some reservations about them too. I decided to write down some of my thoughts and post them as the next post Guessing who will get Fields medals - Some history and 2014.