I mentioned in a comment in a blog that a substantial part of activity of Timothy Gowers in recent ten or more years is politics. It seems that this claim needs to be clarified. I will start with the definitions of the word “politics” in Merriam-Webster online. There are several meanings, of which the following (3a, 5a, 5b) are the most relevant.

3

a :

*political affairs or business; especially : competition between competing interest groups or individuals for power and leadership (as in a government).*

5

a :

*the total complex of relations between people living in society*

b :

*relations or conduct in a particular area of experience especially as seen or dealt with from a political point of view*.

It seems that the interpretation of T. Gowers himself is based only on the most objectionable meaning, namely:

3

c :

*political activities characterized by artful and often dishonest practices*.

I am not in the position to judge how artful the politics of Gowers is; its results suggest that it is highly artful. But I have no reason to suspect any dishonest practices.

With only one exception, I was (and I am) observing Gowers activities only online (this includes preprints and publications, of course). I easily admit that in this way I may get a distorted picture. But this online-visible part does exist, and this part is mostly politics of mathematics, not mathematics itself.

I do classify as politics things like

*“The Princeton Companion to Mathematics”*, which do not look as such at the first sight. This particular book gives a fairly distorted and at some places an incorrect picture of mathematics, and this is why I consider it as politics – it is an attempt to influence both the wide mathematical public and the mathematicians in power.

I was shocked by Gowers reply to the anonym2’s comment to his post “ICM2010 — Villani laudatio” in his blog. The Gowers blog at the time of 2010 Congress clearly showed that he has almost no idea about the work of mathematicians awarded Fields medals that year. But Gowers was a member of the committee selecting the medalists.

*“How it could be?”*asked anonym2. The reply was very short:

*“No comment”*. This lack of a response (or should I say

*“this very telling response”*?) and the following it explanations of T. Tao clearly showed that the work of the Fields medals committee is now a pure politics, contrary to Tao’s assertion of the opposite. If the members of the committee do not understand the work of laureates, they were not able to base their choices on the substance of the works considered, and only the politics is left. In fact, nowadays it is rather easy to guess which member of the committee was a sponsor for which medalist. This was not the case in the past, and the predictions of the mathematical community were very close to the outcome. I myself, being only a second year graduate student, not even suspecting that there is any politics involved, was able to compile a list of 10 potential Fields medalist for that year, and all four actual medalists were on the list. The question of anonym2

*"How could the mathematical community be so wrong in their predictions?"*could not even arise at these times.

Next post: Part 2.

Dear Owl,

ReplyDeleteCan you please elaborate on "'The Princeton Companion to Mathematics' [...] gives a fairly distorted and at some places an incorrect picture of mathematics"?

Dear Anonymous,

DeleteI hope that it is clear that a detailed review of a more than 1,000 pages long and very fragmented book is hardly possible here. So, I will limit myself by few remarks.

First of all, the alphabetical arrangement of material in most of the parts does an immense disservice to the readers and to mathematics. It completely hides the architecture of mathematics, the logic which leads from one topic to another.

The choice of topics is very bizarre. For example, in Part III on the same level we see "Braid groups" and "Categories", with a little bit more space given to categories. In fact, the theory of categories is one of the main organizing tools for the whole mathematics, and also a very powerful tool for proving new results. Braid groups is a nice curiosity, useful in a very narrow class of questions. In the same part "Knots" got more space than "K-theory". Again, K-theory is one of central ideas, and knots is a hardly important topic by itself (it is popular now only because some physical ideas can be applied to them). But braids (forming the braid groups) and knots are essentially combinatorial objects, and a typical knot lacks of any structure, resembling an arbitrary graph. So, Gowers put forward subjects closer to his tastes. One may go on and on with such pairs. In Part V we see the immensely important Atiyah-Singer theorem and the Four-color "theorem". The latter has had no influence on the mathematics at all (except that people stopped working on the four-color conjecture), but all (one or two - it is not clear if the original proof is correct, or, more precisely, can be corrected) available proofs are computer-assisted and cannot be understood by humans. Again, Gowers promotes his ideology.

In Part VII, "The influence of Mathematics", there is no section about physics!!!

I hope you got the idea. It is a nice bedtime book for browsing by a mature mathematician, if he or she is tolerant enough to ignore all these disbalances.

And there is an unfogivable omission: the authors of the articles are not listed in the table of contents. This makes fairly hard even to find a suitable bedtime reading in the book.