Previous post: What is combinatorics and what this blog is about according to Igor Pak.
There is a new thread of comments to the post "What is mathematics?" started by Sandro Magi. The post is dated April 3; this thread started on May 31. The thread is concerned with only one claim in that post: proofs are not needed at all for applications of mathematics.
Unfortunately, the very first phrase of Sandro Magi set the tone for the rest of the discussion: "This is blatantly false". I do not like to discuss things in such a manner: with a total lack of cooperation. The combinatorialists at Gowers's blog are much more friendly even after a direct attack on their field. But, I believe that the reason is not any kind of malice of either party. This dialog is a good illustration of the near impossiblity of people thinking linearly and verbally to understand people thinking visually. In this case the dialog of a mathematician (every mathematician thinks at least partially visually) and a software engineer turned out to be impossible. I encountered the same sort of difficulties while discussing essentially any other subject, from the movies to the current affairs. I see also this lack of understanding of visual and "the big picture" issues in the design and functionality of almost all the software.
Still, it seems to me that there are some important ideas in that discussion. Of course, it would be better to give a coherent exposition. But an attempt to write it would take a lot of time, and who knows when it would be ready.
If somebody wants to comment on any issue there, I suggest to post comments here; this will result in a more clear structure of comments. As an additional benefit for the next 30 days the comments here are not moderated; they are moderated at that post. This rule is subject to change without notice. :-) I would like to ask Sandro Magi to continue our discussion in comments to "What is mathematics?" and not here (of course, he is under not obligation to continue); then the whole discussion will be at the same place.
Next post: 2014 Fields medalists?.
I am interested in your opinion, Sowa, about possible Fields medal candidates in this online poll?
ReplyDeletehttps://sites.google.com/site/fieldsmedal2014poll/
Dear Tamas Gabal,
DeleteGood question. I cannot satisfactory answer right now. In particular, I took only a quick glance at the list in the poll. It contains some of my favorite candidates, contains some mathematician who should not be considered at all by anybody as a candidate, and that the list is a little bit short. From the fairly old proceedings of congresses, one may see (usually directly stated by the presenter) that the "short list" in the past consisted of 35-40 candidates. One may expect that a "community poll list" would be longer.
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. I 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, his was a fairly nontraditional at the time (or so it looked). I cannot do anything like this now without knowing the composition of the committee. Recent choices look more or less random, with some obvious exceptions (like Grisha Perelman).
I will try to write a separate post about this. But since some of my personal friends were involved in the selection process in the past and may be involved in it now, my hands are somewhat tied.
Thank you, Sowa! I look forward to your post about this. I understand that your hands are somewhat tied but at least discussing your favorite candidates should be appropriate.
DeleteUnfortunately, not only the composition of the committee is a secret but the entire selection process is a secret and it would be interesting to learn about basic underlying procedures. For example, in my answer to a question here
http://gowers.wordpress.com/2010/08/22/icm2010-villani-laudatio/#comment-41931
I am guessing (based on the interviews with Fields medalists) that the candidates know they are being considered. Apart from exceptional cases, such as Perelman, does the Committee consider candidates whose best work has not been published yet or accepted for publication? Harald Helfgott's proof of the ternary Goldbach conjecture could be a good example. Do you have any comments about Harvey Friedman's proposal for a different selection process:
http://www.cs.nyu.edu/pipermail/fom/1998-September/002135.html
Thanks!
DeleteAnd thanks for the links. By the way, Google does not automatically transform an URL to a link, but this can be done by hand in the standard manner: (a href="URL needed")whatever you want to be the title, for example the URL itself(/a); ( , ) should be replaced by the corresponding angle brackets. Then you get, say http://www.cs.nyu.edu/pipermail/fom/1998-September/002135.html.
Yes, everything is secret. Harvey Friedman suggestion seems to be reasonable. But, up to and including the 1986 medals everything was working, as H. Friedman admits himself (without giving an exact date) with the same or even a little bit higher level of secrecy as now. So, I am not very hopeful about a very open process outlined by H. Friedman. In fact, this is a mute question: nothing like this will be implemented by the current mathematical community. Most of mathematicians just plain hate any open discussions. The American Mathematical Society avoids discussions almost completely. Occasionally, once in few years, they publish a Letter to the Editor (of the Notices of the American Society) on a controversial issue, a short reply to it, and, often but not always, as a response from the original author, a few lines in the next issue.
Theoretically, it is possible to open the process by a decree of the International Mathematical Union. But nobody will participate in open discussions. If discussion would be required by the rules, everything will be agreed upon behind the closed doors in advance, a play (web-play) will be written, and then performed on the web. Intruders will be ignored in the same manner as T. Gowers ignored almost all of my comments and arguments in my comments in his blog.
The real issue is not how to distribute prizes, but why do we need them at all? I believe that the prizes are inherently evil in any creative (and not only) field. May be I will give examples, illustrating this, later. Some supporting arguments are mentioned by H. Friedman.
Tim Gowers is a great politician. Seemingly, he expresses his opinions about many things and he does it openly but somehow I always feel that he does not say what he really thinks. Is his blog just an advertising platform? On the other hand, it was so refreshing to read your blog even when I did not agree with you. I understand that we can not do this openly but I wish more people would speak their mind, even anonymously.
ReplyDeleteI also have to agree with you that prizes do more damage than good, especially, at such a level as the Fields medal. Probably, the damage is even higher when the area is in the early stages of development. Somebody wins the Fields medal and half of young people in that area (good ones!) jump to the same topic. Meanwhile, other important directions remain unexplored. Results and ideas are not judged on their own merits. The balance of natural selection is completely disrupted. What makes the problem even worse is that mathematicians are human too - a fact that comes with all its usual consequences.
Of course, his blog is an advertizing platform. He himself demonstrated what his does not writes frankly. I was very sympathetic to his crusade against Elsevier in early 2012. But the choice of Elsevier as the only target was fairly strange: Elsevier newer was a big player in mathematical publishing, and by 2010 it was hardly a significant one. Its main strength is in biomedical fields. But after it turned out in early July 2012 that Gowers has his own ambitious plan amounting to more or less complete control of all mathematical publishing, my sympathy evaporated. Later on, new information surfaced. Namely, Gowers nearly completed (or completed) negotiations about his own system of journals with Cambridge University Press (one of three main publishers in mathematics now, the other two being Springer and AMS) by time of his posts about Elsevier. So, his indignation about Elsevier was nothing more than a smoke screen.
ReplyDeleteWhile initially I considered my semi-anonymity on the web as hardly significant, now things look quite differently. It is extremely important to have the option to be anonymous on the web. For this issue the right place to start is the Electronic Frontier Foundation. Nowadays, everyone wants to know my real life identity: Google, Facebook, Yahoo, government agencies for sure want to know everything about everyone. This alone forces me to defend my right to be just Owl as long as I will be able to do this.
I think that the negative influence of prizes is much more extensive and complicated than the mechanism you outlined (which is present, for sure). 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.
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.
ReplyDeleteBy the way, some of these unpredictable winners lately were pleasant surprises (at least for me), for example, Stas Smirnov.
My reply is too long for a comment. I posted it as the next post 2014 Fields medalists?.
Delete