Breakdown of the traditional teaching model?

Today may mark a turning point for Oxford mathematics. Because of COVID-19, our teaching will be virtual in the coming term. I had been looking forward to live performances, but no, it has been confirmed today that all our lectures must be prerecorded. In fact, we are encouraged to have them in the can before term begins.

This little development stores up a big question for the future. A year from now, will we be allowed to reuse the lectures we have recorded? It’s hard to see how a “yes” would be tolerable to administrators, who would see their faculty as being paid to do nothing at all. But it’s equally hard to see how a “no” would be tolerable to faculty, who would see themselves as chained to a meaningless make-work scheme.

Perhaps an ingenious resolution will emerge. I look forward to seeing it.

[ 31 July 2020]

Memos to papers to books

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]

Playing the academic game

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]

Chladni lanes

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]