In recent years I’ve settled into the habit of writing numbered research memos. A typical one might be four pages long and include half a dozen computational experiments and plots along with theorems and references. The time scale of a memo is a matter of days, so they are excellent for day-to-day motivation, unlike papers (months) and books (years). These mathematical memos are the main way I communicate during an ongoing project with my coauthors and my increasingly forgetful self.
The current series, on rational functions, is up to Rat124, and 8 journal articles have come out of these. That’s 15 memos per paper. One level up in this verbal food chain, I note that all together in my career, I have published around 140 papers and 7 books. That’s 20 papers per book.
So my career to date has the heft of around 2100 memos. Actually, I wasn’t always so memo-happy; the true number is more like 400 — plus a few hundred Chebfun Examples, which are psychologically similar.
[27 July 2020]
Academic papers keep getting longer, to the point where these days, we rarely read a paper as opposed to leafing through it for highlights. Here’s an extreme example that has caught my eye today. There’s a trio of numerical analysts who have published 39 papers together since 2003, with these statistics at Google Scholar:
Average number of pages: 40.9, Total pages: 1594.
Average number of citations: 27.8, Total citations: 1084.
These are good people employed at good universities, and the papers are in the top journals. Yet I regard these numbers with horror. In my career, I’ve published five papers longer than 30 pages. These guys have 29 of them! When I look at the latest, with its 278 lines of displayed equations, my eyes glaze over.
I am certain that the mountain of long technical papers out there is bad for communication. The disturbing question is, is it good for careers? I hope no, but I fear yes. I have tried to push back against the trend in conversations with colleagues, as a referee and journal editor, in a letter printed in SIAM News, and indeed as SIAM President, but I don’t recall encountering anybody who agrees with me that this is something we should be exercised about.
[27 July 2020]
Cycling country lanes in Somerset this week, I notice how the sand accumulates in the middle. The two side tracks are clear, but stay away from the middle, where your tires will skid.
It’s almost the same principle as the celebrated Chladni patterns. On Chladni’s plates, the sand accumulates along nodal lines because elsewhere it gets bounced away. In the lanes of Somerset, much the same.
[18 July 2020]
Emma and Jacob each share half my DNA. After that, it is strange how little kin I’ve got. Third-closest is Cousin Nancy, whose mother and my grandmother were sisters and whose father and my grandfather were (I think) first cousins. So Nancy and I share 5/64 of a genome. Just a neck behind her are Ted, Ron, and Bruce Harrington, whose father was my father’s half-brother. That’s 1/16 of a genome each. After them, I think everybody is at the 1/32 level or below. My overlap with John Trefethen, Chairman of Trefethen Vineyards and my sixth cousin, is unfortunately just 1/8192.
[28 May 2020]
For the past two months I have sat at my desk doing mathematics, while on the lawn out the window, a blackbird has been hopping about finding worms. He’s there in the morning and he’s there at noon and he’s there in the evening. He hops, he stops, he hops again. All day long.
I remarked to Kate, what an empty and meaningless life he leads! She countered that the blackbird probably thinks my life is meaningless too.
So I have refined my view, appreciating my good fortune to be sharing this confinement with such an agreeable colleague.
[25 May 2020]
I updated my profile on italki, including date of birth, and I ticked the box “Allow people to view my age.” Why not?
Then I checked how my profile appeared online and I was horrified. My age was showing as 65! Why, I’m only 64, not 65, and I won’t be 65 until August! What a blunder of programming! How deeply they had got me wrong!
I immediately went back and unticked the box.
[11 April 2020]
The pandemic so consumes us that everything exists in reference to the big story. As I chopped an onion for dinner, my eyes started burning. Instantly I realized this was a model of how virus particles can undetected reach our face.
[11 April 2020]
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]