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.
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