Richard Elwes

Mathematician & Writer in UK. Latest book: Huge Numbers. Basic Books (April 2026).

Last Notes

2026-09-30 09:52:49 UTC

Numberphile's great output around the Navier-Stokes debacle continues with this excellent interview with the man in the eye of the storm, Tristan Buckmaster.
https://www.youtube.com/watch?v=Mzbtj5nkMXI

2026-04-01 09:06:19 UTC

Me on Numberphile talking about - guess what - big numbers.
"What are the biggest numbers ever contemplated?"
It's an often discussed question (at least by me). But what if someone had asked that question a few hundred years ago, before 20th century techniques?
Very grateful to Brady for the nice book advert at the end!
https://youtu.be/sJqceEImtew?si=6QJYNLmzjHakce5C

2026-02-09 13:59:16 UTC

Here we go! Narrating the audiobook version of Huge Numbers.
Photos by brilliant producer Cathy who is being extremely patient while I stumble over the same sentence for the fifth time…
https://media.mathstodon.xyz/media_attachments/files/116/041/024/171/609/637/original/e2cc744ff3d01488.png
https://media.mathstodon.xyz/media_attachments/files/116/041/026/385/374/848/original/e302615c7767d18f.png

2026-01-18 11:52:51 UTC

- reply

@nprofile…vhdw It’s rigid so solved/unsolved is not terribly meaningful! It is in the state my son decided to reassemble his broken cube.

2026-01-18 09:24:15 UTC

Look carefully at this cube and you’ll see why you couldn’t ever solve it. (More details in alt text.)
https://media.mathstodon.xyz/media_attachments/files/115/915/372/336/568/474/original/f3c2cd4e9d0fc004.png

2026-01-15 10:32:22 UTC

I had the opportunity to use AI to speed up my work yesterday - and I didn't take it.
I am updating some old lecture notes, and needed to replace an obolete typesetting command with a new command. Essentially a search & replace job, but the syntax of the two commands is different enough that the editor's textual search & replace wouldn't work. I used the inbuilt search, but then had to change each occurrence manually.
Or I could have uploaded the file into Copilot and asked it to make all those changes for me. Why didn't I?
Because then my entire module's lecture notes would have passed through a highly complex process I do not understand or trust. I would not feel confident that the AI had only changed the things I asked it to change.
When my notes contain human mistakes - hardly a rare occurrence - I feel fine apologising to the students and making the corrections.
But if my notes contained weird, unexplained, AI-generated errors, I expect I'd feel angry & embarrassed.
I suppose could ask a second AI to compare the output against the original - I didn't actually think of this at the time. I suppose that would provide some reassurance, but would it be enough? Is that the answer to these conundrums?

2025-11-28 14:16:54 UTC

After a talk to sixth formers just now, I invited questions, and someone asked “What’s your least favourite number?’
What would you have said?
I answered 14 as being the first which didn’t strike me at that moment as having anything especially interesting in its favour, but felt it was a fairly feeble answer.

2025-05-12 13:12:04 UTC

Mathematicians! What are the biggest (finite) numbers that have arisen in your research or teaching?
[NB I'm not asking for the biggest numbers you know of, but ones which have arisen in your work.]

2025-01-24 09:36:21 UTC

- reply

@nprofile…fa4k Lots of good stuff around the model theory of fields!
The one I know best is a theorem of hers with Angus Macintyre and Lou Van Den Dries which has been important in the model theory of finite (& pseudofinite) fields. It limits the possible sizes of definable sets. It basically says that given a formula ϕ in the language of fields, for any finite field F and any choice of parameters in F, ϕ will define a set of size approx μ |𝐹|ᵈ for a pair (μ,d) from a finite collection where d is a natural number (the "dimension" of the set).
This generalises the Lang-Weil bound, from absolutely irreducible varieties to arbitrary definable sets.
It also made pseudofinite fields an important example of a a new class of geometrically well-behaved "supersimple" first order theories.
https://people.maths.ox.ac.uk/bays/mtpsf/ChDrMa92.pdf

2024-11-26 22:03:46 UTC

Excited and a bit frightened to make my debut on Numberphile.
Here's me talking about an "unprovable theorem" and some very big numbers.
https://www.youtube.com/watch?v=0Le7NgS-wO0

2024-08-02 21:11:09 UTC

Apparently exciting progress on the Riemann zeta function, in a new preprint by James Maynard and Larry Guth.
(Caveat: the Riemann Hypothesis itself remains a very distant prospect.)
https://www.science.org/content/article/sensational-breakthrough-marks-step-toward-revealing-hidden-structure-prime-numbers