I often wonder what on earth motivates the discussions on Peter Woit’s blog, which this week has a bizarre exchange concerning the increasing lack of rigour that plagued algebraic geometry in the first half of the 20th century. I have something of a personal or family interest in this, since my father did a PhD in algebraic geometry in the 1950s, supervised by one of the surviving members of the dying “Italian school”. The main item of decoration in the living-room when I was growing up was an illustration of the associative law of addition on a cubic curve in general position, executed in marquetry.

When I became a mathematical adult, we occasionally tried to discuss mathematics: I would try to explain what my PhD was about, and he would try to explain what his PhD was about. Neither aim was successful. But there were some points of contact: we both understood, in our different ways, the group of the 27 lines on a cubic surface, and the group of 28 bitangents of a quartic curve. And I think I gained something by seeing them in a more geometric light than the purely algebraic context I had been used to.

The context of the discussion on Peter Woit’s blog seems to be a comparison of various types of lack of rigour, and perhaps a cautionary tale that lack of mathematical rigour in theoretical physics may lead to the same kind of collapse that attended the “Italian school of algebraic geometry”, and for the same reason. But algebraic geometry was rescued by mathematicians, who were appalled by the increasing number of results that were claimed, but false, and worked hard to build a solid foundation and rigorous methods for a reliable mathematical theory. The same is not happening in theoretical physics.

Why not? Because nobody in theoretical physics listens to mathematicians. Those of us mathematicians who have made a serious study of the foundations of theoretical physics can point out in gory detail exactly where all the mistakes are. Well, maybe not all of them, but enough to be going on with. Physicists are only interested in mistakes when they are actually contradicted by experiment. Mathematicians can point out mistakes at a much earlier stage, and save billions of pounds in unnecessary experiments. Just read the last 100 or so posts on this blog – I may have repeated myself once or twice, but this seems to be necessary in order to get the message across.

Why does Peter Woit, and all the people he allows to comment on his blog, think it is OK for theoretical physicists to try things at random and hope they get something consistent with experiment? Why do they not start by ruling out everything that is mathematically inconsistent? Oh, I know why – because *everything* they try is mathematically inconsistent. Please, people, listen to the mathematicians, and take rigour seriously. If you don’t, you are condemned to another century of nonsensical theory, and failure to obtain a consistent unified picture of the universe we live in.