Previous post: The Politics of Timothy Gowers. 2.
The preparations of Gowers to the elimination of mathematics are not limited to the elevation of the status of the most amenable to the computerization part of mathematics. T. Gowers uses other means also. His web page "Mathematical discussions” aims at developing some “more natural” ways to discover key mathematical ideas. By “more natural” Gowers apparently means “not requiring a sudden insight”. Some titles of his mini-articles are very telling. A good example is “How to solve basic analysis exercises without thinking.” To do mathematics without thinking is exactly what is needed for replacing mathematicians by computers. I consider this project as a failed one: no real way to discover key ideas without insight, not to say without thinking, is even hinted at in these notes. One of approaches used by Gowers is to reverse the history and shows how to use more recent ideas to discover the older ones, like in his note about the zeta-function. Euler’s and Riemann’s work on the zeta-function stimulated a lot of developments in analysis, and to use these developments to rediscover the main result of Euler looks like cheating. In other cases, like in his note about cubic equations, Gowers more or less rediscovers the original approaches. His approach to the cubic equations is very close to the one presented in every book about Galois theory paying some attention to the history.
My favorite part of this page is entitled "Topology”. It consists of only one phrase: "Watch this space”. This did not change at least since April 18, 2001 (according to the web archive). So, I am watching this space for more than a decade. Topology is the quintessential “first culture” mainstream mathematics, mathematics of Serre and Milnor. Completely missing, even without such a phrase, is algebraic geometry. It seems that the two most important developments in the twenties century mathematics are not amenable even to an attempt to eliminate or at least reduce the roles of insights and thinking.
The posts under the tag ‘Demystifying proofs’ in Gowers blog have the same goal and overlap with his “Mathematical discussions”.
Another project Gowers is actively promoting is called the “Polymath”. See posts in his blog under tags like “polymath”, “polymath1”, etc. Perhaps, the best place to start is the posts “Is massively collaborative mathematics possible?” and “Background to a polymath project”. The idea is, apparently, to prove theorems not by the usual process of an individual discovery or close interaction of few mathematicians, but by a massively parallel working of many mathematicians interacting on a special web site. This immediately brings to the memory famous computer “Deep Blue”, who won (at the second attempt) a chess match with Garry Kasparov, perhaps the best chess player of all times. “Deep Blue” relied on massively parallel computation, combined with the chess players’ insights (it turned out that without substantial help from human chess players the computer cannot beat Kasparov). Gowers attempt to arrange something similar but using only humans. This is, clearly, could be a good step toward replacing human mathematicians by computers, if successful.
To the best of my knowledge, the first attempt was somewhat successful, in the sense that it resulted in a published paper. But the result proved was not surprising at all, and the main contributions to the proof were made by very few mathematicians (perhaps, no more than three). The result was certainly accessible to a good mathematician working alone.
Much more can be found at “The polymath blog” and the Polymath1wiki (a Wiki-like site). Amazingly, 1/3 of the described there nine “Polymath projects” are devoted to solving specific problems from International Mathematical Olympiads. As is well known, a sufficiently bright and trained high school student can solve such problem in one-two hours.
So, it seems that the idea failed.
(It is worth to note that the domain name michaelnielsen.org, a subdomain of which is the Polymath1wiki, belongs to Michael Nielsen, who presents himself as “a writer, scientist, and programmer”. Perhaps, he is neither a writer, nor a scientist, nor a programmer, if these notions are understood in a sufficiently narrow sense. But we are not living at the times of André Weil, and nowadays he is definitely all of the above. The point is that even nowadays he is not classified as a mathematician.)
I think that all this gives a good idea of what I understand by the politics of Gowers.
He is also actively involved in a battle with big publishers over the prices of scientific journals. In this case his goals are quite close to my heart (in contrast with the already discussed activities), and I even signed an inspired by Gowers declaration of non-collaboration with the infamous publisher Reed-Elsevier. Still, I believe that his approach is misguided. Elsevier may be the most evil scientific publisher, but not the only one evil, and even the university presses and learned societies act in an evil manner more often than one may expect. From my point of view, the root of the problem is in the scientific community itself, and the solution can be found also only within this community. Everything depends on the transfer of the copyright from authors to publishers. Scientists need to refuse to transfer the copyright. But this is another topic.
Next post: T. Gowers about replacing mathematicians by computers. 1
While the content of this blog is ridiculous and does not deserve any comments, one remark would be in place - I don't know if anyone reads these posts, but the absolute minimum of decency requires that you do not post unfounded accusations and hearsay (like in your post about the "politics" behind Abel Prize) anonymously. Regardless of what you think about Gowers and other people you should write under your own real name.
ReplyDeleteDear MK,
ReplyDeleteI believe that people should behave and write consistently at the very least. You do know if anyone reads these posts. For example, you did. If you demand from others to use real names (and what else do you need, home address, place of work, Social Security Number?), you should sign your writings by your real name.
I have no idea what do you mean by "accusations". Till now, this blog is devoted to my commentary to some publicly available information. I never referred to a hearsay, I believe (please, correct me if I did). Of course, this commentary is influenced by my opinions about mathematics and many things. It is not a news report, it is a commentary supplemented by some general discussion. The fact that the politics in the sense I explained is involved in the selection of winners of various prizes, is a common knowledge in the mathematical community. In fact, if one only observes from a distance how this system works, this would be obvious. Still, I explained why I think that in some cases, in particular in the case of this year Abel Prize, politics was used more heavily than usual.
It would be much more productive if you would counter my arguments by yours. As it stands now, it is you who are making unfounded accusations.
Finally, about anonymity. The value of online anonymity is recognized by the internet community. Most of online social networking places do recognize its value and protect it. I all cases I observed over the years, a person demanded to disclose the real life identity only when he or she had no substantive arguments, and hoped to dismiss the opponent position on irrelevant grounds.
In any case, the validity of my arguments and opinions does not depend on my real life identity. I would like them to be discussed based on their merits, not on who I am. In fact, you have no way to know even if these posts are all authored by the same person. The same applies to everybody. The validity of T. Gowers ideas does not depend on his stature in the mathematical community or in the scientific community. Even the correctness of his proofs does not depend on the prizes he got for them. If some kid in China will discover a gap and post his or her findings anonymously to the web, the proof will be not considered as a correct one anymore.
My real life identity is only moderately protected. If you cannot guess who the author of this blog is, then my name will tell you nothing.
I have to add that I neither confirm, nor reject any conjectures about my real life identity. Would you be friendlier, you would have much higher chances to be told by me (privately) who writes this blog.
Have a nice day.
I find your posts interesting and informative, and it is good that somebody is finally highlighting these issues. However, I do not think that your apocalyptic way of talking about Gowers as wanting to "eliminate mathematics" as we know it is very helpful. I am not saying that your analysis is incorrect, but I do not think this is the most relevant issue (replacing mathematicians by computers is going to remain science fiction for a while still) and that kind of rethoric is just going to alienate people from the really important discussion of power and influence in the mathematics community.
ReplyDeleteIn my view this is what the discussion should be about: the open and critical analysis of very influential individuals or groups in the mathematics research community. As a mathematician I feel worried that there is currently no such discussion at all, even though there is one in many other professions (including basic research). After having spent most of my professional life in the academic mathematics community I can only conclude that most mathematicians are rather poor at critically examining large scale practical issues and acting on them in a realistic and politically efficient way. Typically a few influential individuals, like Gowers, are good at this and the rest of the community falls into a herd mentality and follows the leaders. In my opinion, this is to a large extent what happened in the Elsevier boycott.
The political influence of Gowers and his circle is very strong and growing, and you have illustrated this several times. There is nothing inherently bad about influential groups, and one might argue that Gowers is only trying to restore some balance to a community long dominated by geometry, topology, arithmetic geometry, etc. There are similarly influential individuals representing these latter areas, and there is no other way it could be, that is, we have to accept that different people want to do different types of mathematics and this is not always going to be of the abstract "conceptual" kind. There is no problem with this situation unless one political force becomes too dominant. The only way to prevent this is to get the whole community engaged in a discussion and to counteract one political force with another so that we may achieve an approximate balance representing the wishes and tastes of the research community at large.
The reply turned out to be very long, so I posted it as a new post "Reply to a comment".
Delete"Amazingly, 1/3 of the described there nine “Polymath projects” are devoted to solving specific problems from International Mathematical Olympiads. As is well known, a sufficiently bright and trained high school student can solve such problem in one-two hours."
ReplyDeletecan you further document this? do not know details but afaik the problems are challenging and not any from high school challenge problems.
you seem to devalue the difficulty of truly hard problems. what problems one pursues is truly a matter of taste, but your rejecting truly difficult problems as trivial is immature and childish. children look at big things and say, "that is not hard".
Hi!
DeleteThe first thing I did was to allow your comment to be published.
The "Polymath project" is extensively discussed in Gowers's blog, with references to a wiki-like page of the project itself, where all particular problems done are listed, as also some proposed problems. They were done by humans, but in a highly collaborative manner similar to the highly parallel processing. Nothing like this is done in the mathematics properly, be it combinatorics of any kind or algebraic geometry or whatever.
Gowers himself done almost all of his work alone. One of his early papers is a joint paper with another mathematician, but this is because they simultaneously and independently discovered the same result. This is a sound approach: not to publish two similar papers, but only one joint paper. His recent papers are joint papers with 3-4 mathematicians; this is a common way to continue to publish when a mathematician ages and lose at least a part of his technical power. The latter is inevitable; the mathematics is a young persons game. I can go as far as to suggest a mandatory retirement at 40 (not forbidding doing mathematics, but not paying for this either beyond the pension based on what was done before 40).
Well, this was a digression to give you some perspective. I believe that you will be able to easily find the references. I am a lazy person, despite that you apparently think, and I am not inclined to search Gowers’s blog or to use Google for you. The project page explicitly states what problems are actual problems from the International Mathematical Olympiad. It is not like I believe that they are of this type and level, they actually were Olympiad problems. The claim “1/3” is, of course, relates to the day that was written. I do not follow this. Probably, I should also say that these problems are not easy, most of successful mathematicians, I believe, will be not able to solve any of them quickly (this was even tested). The kids who compete at the International Mathematical Olympiads are very bright and specially trained to solve that kind of problem. But T. Tao and T. Gowers, who are the main contributors to the solutions, were in the past such kids.
You are wrong; I do not reject difficult problems. A lot of problems the solutions of which I admire are very difficult. In particular, the one almost solved by Grothendieck, with P. Deligne completing the solution, was the most difficult problem (and the most important, in my opinion) solved in the previous century. But I do not like the problems which attract attention only because they are difficult. I do not consider them as “big things”.