A comment on the sowa versus Gowers affair

by Orr Shalit

I wanted to write about something else this weekend, but I got distracted and ended up writing this post. O well…

This is post is reply to (part of) a post by Scott Aaronson. I got kind of heated up by his unfair portrayal of the blog “Stop Timothy Gowers!!!“, and started writing a reply which got to be ridiculously long, so I moved it here.

Dear Scott,

I think that, as others remarked in the comments, you unfairly portray sowa’s blog. It is much more than just a rant against Gowers, and contains some “positive” contributions (agreed, the “positive” ones are mostly historical/philosophical/other and not Gowers-style exposition, so what?). But even if it was true that that blog just had “negative” comments, I think it has a place. Here are some points to consider.

(Before the points, this is written in defense of sowa, and not in damnation of Gowers. I have never met either, I didn’t read their papers, I don’t agree with everything sowa said about Gowers, and I am willing to bet that Gowers is a very nice guy and a gentleman.)

 

1) “Lack of exposition” I. You wonder why doesn’t sowa for once take a break from discussing (say) the epochal greatness of Grothendiek, and “walk us through examples”. Well, he uses his blog to write about things he cares about. For serious mathematics he has others outlets. He wants to discuss the politics of mathematics, and he wants to oppose the what he sees as the current trends and power structure. There are politics in mathematics and there are power structures, fads, trends, celebrities, etc. These things affect the development of mathematics, where people go, where the money goes. These are totally legitimate issues to address.

 

2) “Lack of exposition” II. The kind of blogging that tries to teach some mathematics, expose it in a simplified way that non-experts can understand, is very difficult to do. I try to do it on my own blog, and honestly, I sometimes wonder whether the piece I wrote has any value at all. It happens (to me, and maybe also to you) that by the time you reach the beef, you run of breath, or out of time, or you realize that you cannot do this technical part any better than original paper or book that you linked to. And as a reader, when reading expositions on certain blogs or expository journals (or colloquium talks) I sometimes say to myself: the author really tried to walk me through this piece of mathematics/science or through their thought process, but unfortunately was unsuccessful in conveying any substantial information. So I can totally understand a blogger who feels that writing these friendly expository pieces is not useful, and spend no time on that.

3) Symmetry. You mention that there is asymmetry between them: Gowers writes about math, and sowa writes about Gowers. Well, you are right, there really isn’t symmetry: Gowers is at the center, and sowa is peripheral. Gowers has power and influence, and sowa thinks that Gowers has too much. So it is ridiculous to point out that sowa is just complaining and not talking math, and that Gowers isn’t wasting time complaining about politics. When it comes to the power structure in mathematics, Gowers doesn’t have much to complain about (although, being human, he does actually complain and rant on his blog, when the issues are not the ones where he happens to be up).

I want to emphasize a fallacy you have made: You point to the asymmetry as an answer to a question you raise: “How could a neutral observer possibly decide who was right?” (You mean, if the neutral observer didn’t care to weigh the actual statements made?) Interesting question, but your answer seems all wrong to me. The person complaining might have a strong point – that’s why he is so upset! – and the person not complaining might be comfortable enough.

4) The three cultures in this discussion. Scott, you are an American, watching from the side an exchange between an (apparently) Eastern European raised mathematician and an English mathematician. To you, it might seem like the first is shouting, and the second is being the most polite and maybe even gallant person ever. These differences in culture can distract from the actual points made. So the best thing to do would be to concentrate on the points themselves, and not on the volume.

5) The point of the matter I. As pointed out by eminent mathematicians, there is a certain periodic movement in the mainstream culture of mathematics, between the abstract and theoretical developments, on the one hand, and more concrete, problem-driven work, on the other. Very roughly speaking, Sowa on his blog advocated a certain style of mathematics, or a certain way of doing mathematics, which he felt was the best one. His point of view on what is good mathematics can be summarized in one word: “Grothendiek”. He very often used Gowers as an example of bad trends in mathematics, giving arguments against points-of-view publicized by Gowers. But in the beginning that blog did not look like a crusade against Gowers, and had the pleasant name: “Notes of an owl”. Sowa was just another force affecting the perpetual periodic motion in mathematical philosophy.

If I get the story, sowa really lost his top when it became known that Gowers would be presenting the work of Abel prize winner Pierre Deligne (and as his blog says, that’s when he changed the title of his blog to the current one). He stated his opinion that Gowers is unqualified to speak about Deligne’s work. Is it unacceptable to raise such a point? I think that it is (though I am in no way competent to answer the question of what Gowers is capable of). He also made a point that it was the third time in a row that Gowers was chosen to present the life work of an Abel prize winner. This is an even more valid point to make.

I know that everybody says that Gowers is a brilliant expositor. Well, I also saw a video of the lecture “The importance of mathematics” by Gowers and it was, indeed, a wonderful talk. I recall thinking that it is one of the best lectures I saw in my life (and for sure the best one that I saw on video). So I am convinced that he has the capability of expositoring exquisitely. But nobody is perfect, and no-one irreplaceable.

I stopped reading Gowers’s Blog some time ago, but there was a time that I tried to read a lot. I know what people are talking about when they speak of his posts as an intellectually honest journey, where he takes you by the hand and leads you through his thought process; I know what they are talking about, but I interpret this “leads you through his thought process” as lazy writing. Reading some of his old posts I got the notion that he hasn’t thought it all out before writing, and that his “delete” button is broken. Now, I don’t want to go and search for the old posts that I read and did not like (as Gowers once said: “I don’t have the information at the tip of my fingers”…), I am not out to prove that Gowers is a bad expositor, of course he isn’t; my point is just that different people might find different styles of expositoring appealing or useful. So the question, whether it is correct to have the same person present the prize three times in a row is, seems to me to be right on. And maybe, if you liked the style of the guy who did it the first time, then you wouldn’t have raised that question “is he the right person”, when he was chosen for the third time in a row. But once the question is raised, you cannot ignore it just because it is kind of rude to ask it.

6) The point of the matter II. Another harsh criticism of sowa on Gowers (too harsh, I think, but basically right) is on the matter of publishing in mathematics. It is ironic that one of the good things that you (Scott) have to say about Gowers is that “He’s also been a leader in the fight to free academia from predatory publishers”. Google “predatory publishers”, I don’t think it means what you think it does. Indeed he played a creditable role as a leader in the boycott against Elsevier (about which I had doubts, I won’t go into that). But Gowers, in my opinion, abused his reputation and played a very dangerous role in actually vindicating predatory publishers, when he helped to set up Gold Open Access journals (see also this). In his defense, he seems to be very thoughtful and careful about these matters, is aware of the dangers, and has also later set up an arXiv overlay journal. Sowa has a lot to say on this matter, and here too, and I agree with some of the points he makes.