Today for the first time ever, because of the coronavirus pandemic, Balliol’s Governing Body meeting was held online. We didn’t do this in 1348 (Black Death) or 1665 (Great Plague).

[16 March 2020]

A colleague tells me that among students and faculty in economics these days, it’s hard to find people who are genuinely interested in how economies work. Instead they are wrapped up in the technicalities of the mathematical models they have been trained to analyze. Give the students an exam question that requires thought about fundamentals, he tells me, and rather little comes back.

It’s the same in mathematics! It may sound paradoxical, but here, too, students and researchers are distracted, and excessively impressed, by mathematical technicalities. Give the students an exam question that requires thought about what the point of a mathematical construction is and — I speak from long experience — they will hurry off in search of more technical questions, where they can turn the crank.

One might have thought that mathematics would be the one field immune to the problem of being dazzled by mathematics. But in fact, it’s just as bad here as elsewhere, maybe worse, since camouflaged.

[11 March 2020]

Often physicists do something new, and mathematicians later make it rigorous. Generally the physicists couldn’t care less, and as for the mathematicians, they quickly forget the physicists’ part in the story.

Here’s an example in the beloved book by Körner on Fourier series. In 1909 the physicist Jean Perrin, building on Einstein’s paper of 1905, realized that Brownian motion trajectories are continuous but nowhere differentiable. This was made mathematically rigorous in the 1920s by Norbert Wiener and Paul Levy. Körner summarizes Wiener’s construction with the words, “In accordance with Perrin’s prophetic remarks [the Brownian paths] turned out to be continuous and nowhere differentiable”.

Prophetic remarks! Once again, it would seem, a physicist had struck it lucky.

[8 March 2020]

The outstanding mathematician Louis Nirenberg died January 26. I knew him from my own times at NYU, and I liked him very much. Nirenberg was a mensch.

But how exasperating to read the obituary in Nature describing him as “skating above emerging distinctions between pure and applied mathematics”. What nonsense! Nirenberg was the quintessential pure mathematician. He was no more an applied mathematician than Einstein was an electrical engineer.

This imperialist point of view is all too familiar, and it drives me crazy. Pure mathematicians like to think mathematics is one, and as some kind of a corollary, it follows that the great pure mathematicians encompass the applied side too. For a few, like von Neumann, this may be true. For most, it’s preposterous.

[5 March 2020]