Previous post: The Politics of Timothy Gowers. 3.

Starting with his “GAFA Visions” essay, T. Gowers promotes the idea that it is possible and desirable to design computers capable of proving theorems at a very high level, although he will be satisfied if such computers still will be not able to perform at the level of the very best mathematician, for example, at the level of Serre or Milnor. I attempted to discuss this topic with him in the comments to his post about this year Abel prize.

I had no plans for such a discussion, and the topic wasn’t selected by me. I made a spontaneous comment in another blog, which was a reaction to a reaction to a post about E. Szemerédi being awarded this year Abel prize. But I stated my position with many details in Gowers’s blog. T. Gowers replied to only three of my comments, and only partially. It seems that for many people it is hard to believe that a mathematician of the stature of T. Gowers may be interested in eliminating mathematics as a human activity, and this is why my comments in that blog made their way to Gowers’s one (one can find links in the latter).

For Gowers, the goal of designing computers capable of replacing mathematicians is fascinating by itself. Adding some details to his motivation, he claims that such computers cannot be designed without deep understanding of how humans prove theorems. He will not consider his goal achieved if the theorem-proving computer will operate in the manner of “Deep Blue” chess-playing computer, namely, by a huge and a massively parallel (like “Deep Blue”) search. Without any explanation, even after directly asked about this, he claims that in fact a computer operating in the manner of “Deep Blue” cannot be successful in proving theorems. In his opinion, such a computer should closely imitate humans (whence we will learn something about humans by designing such a computer), and that it is much simpler to imitate humans doing mathematics than other tasks.

In addition, Gowers holds the opinion that elimination of mathematics would be not a big loss, comparing it to losing many old professions to the technology.

Gowers’s position contradicts to the all the experience of the humanity. None of successful technologies imitates the way the humans act. No means of transportation imitates walking or running, for example. On the other end and closer to mathematics, no computer playing chess imitates human chess players.

Note that parallel processing (on which “Deep Blue” had heavily relied) is exactly that Gowers attempts to do with mathematics in his Polymath project. It seems that this project approaches the problem from the other end: it is an attempt to make humans to act like computers. This will definitely simplify the goal of imitating them by computers. Will they be humans after this?

Gowers’s position is a position of a scientist interested in learning how something functions and not caring about the cost; in his case not caring about the very survival of mathematics. In my opinion, this means that he is not a mathematician anymore. Of course, he proves theorems, relies on his mathematical experience in his destructive project, but these facts are uninteresting trivialities. I expect from mathematician affection toward mathematics and a desire of its continuing flourishing. (How many nominal mathematicians such a requirement will disqualify?)

Next post: T. Gowers about replacing mathematicians by computers. 2.

## About the title

**About the title**

I changed the title of the blog on March 20, 2013 (it used to have the title “Notes of an owl”). This was my immediate reaction to the news the T. Gowers was presenting to the public the works of P. Deligne on the occasion of the award of the Abel prize to Deligne in 2013 (by his own admission, T. Gowers is not qualified to do this).

The issue at hand is not just the lack of qualification; the real issue is that the award to P. Deligne is, unfortunately, the best compensation to the mathematical community for the 2012 award of Abel prize to Szemerédi. I predicted Deligne before the announcement on these grounds alone. I would prefer if the prize to P. Deligne would be awarded out of pure appreciation of his work.I believe that mathematicians urgently need to stop the growth of Gowers's influence, and, first of all, his initiatives in mathematical publishing. I wrote extensively about the first one; now there is another: to take over the arXiv overlay electronic journals. The same arguments apply.

Now it looks like this title is very good, contrary to my initial opinion. And there is no way back.

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