A friend sent me an email with “regretfully” where he should have put “regrettably”. No big deal. He’s not a native English speaker, and these fine points are tricky.

It did, however, get me thinking of the old debate about “hopefully”. All this trouble, I realized, has been caused simply by the absence in English of the word “hopeably”!

But now we live in an AI world. So I checked and found that regrettably, my neologism is not new. Another index card nipped in the bud. Will any of these notes have value in the end?

[29 June 2026]

Harvard recently hosted an Undergraduate Math Modernization Summit on the challenge of reinventing undergraduate mathematics education for the AI era. How to move past a curriculum still rooted in the 1950s and 1960s? In an article in the Harvard Gazette, Harvard’s Director of Introductory Math says “Math educators must demonstrate that quantitative reasoning is an essential skill for many disciplines”.

I am happy with those words “quantitative reasoning”, but I am not sure all mathematicians would be. Mathematics, after all, is not just about numbers. Mathematicians like to speak of our subject more grandly as the search for patterns or structures. Quantitative reasoning? Isn’t that something from another era?

[11 June 2026]