Richard Elwes

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

My webpage: https://richardelwes.co.uk/
Twitter: https://twitter.com/richardelwes
Facebook: https://www.facebook.com/587129867966003
Youtube: https://www.youtube.com/watch?v=GJ1S3tFaImo&feature=emb_imp_woyt

Last Notes

2026-04-04 11:46:28 UTC

First media review for Huge Numbers!
Emily Conover in Science News writes: "It’s a delightful survey of the field of googology, the study of large numbers.... It’s a joy to marvel at how boundaries have been broken time and again, thanks to the creative, intrepid explorers of the biggest numbers known."
https://www.sciencenews.org/article/huge-numbers-book-math-googology

2026-03-29 20:24:15 UTC

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Am I right in understanding that you don’t object to your work being formalised, you just don’t want to do it yourself?

2026-02-26 19:38:28 UTC

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Never heard of it but the replies here persuade me I would like it, so thank you!

2026-02-23 19:28:36 UTC

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Yes me, and you’re right - I literally did have to do a second take because I ran out of breath first time through!

2026-02-23 17:08:32 UTC

Just finished another day working on the audiobook of Huge Numbers. This was one of the challenges past Richard threw at me today…
https://media.mathstodon.xyz/media_attachments/files/116/121/041/345/246/050/original/9fe3cac7346f2bcb.png

2026-01-15 11:29:46 UTC

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Thanks - yes you're the second person to suggest this approach, and the answer is quite possibly yes - clearly I should learn my way around regular expressions....

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?

2025-07-31 13:01:25 UTC

Me on Numberphile talking about some of my favourite shapes!
https://youtu.be/BhSlqIe1CRQ?si=yNnlH5-OSK81OaPN

2025-06-21 21:09:42 UTC

Via Viz Magazine. https://shop.viz.co.uk/viz346bs
https://media.mathstodon.xyz/media_attachments/files/114/723/396/655/856/515/original/d9540295e0dd5fbb.png

2025-05-13 17:07:11 UTC

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Ok yes this is very cool! The biggest constructible odd-sided polygon is the product of the known Fermat primes:
3 . 5 . 17 . 257 . 65537
which is 2^32 - 1
which is the largest integer expressible in computational systems which allow integers to have length up 32 bits.

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.]

2025-02-18 20:21:51 UTC

Represent pi in an imaginative way and win a prize!
https://think-maths.co.uk/pi-comp/

2025-02-09 23:59:36 UTC

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I last visited the Louvre 20 years ago and was incredibly depressed by the Mona Lisa experience. I couldn’t see a thing through the field of arms holding phones up in the air (why?).
But the thing that really got me was that in the same room were other renaissance paintings, including a Titian or two, which it was impossible to enjoy because of the ginormous crowd of people bustling around them, paying them no attention at whatsoever.
https://www.contexttravel.com/blog/articles/louvre-artworks-5-underrated-masterpieces?display_currency=USD

2025-01-24 09:36:21 UTC

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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

2025-01-24 00:29:58 UTC

I was very sad to hear of the death of Zoé Chatzidakis, who has been a powerful force in model theory. This is a nice obituary from the Fields Institute.
https://www.fields.utoronto.ca/news/Memoriam-Dr-Zoé-Chatzidakis

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

2024-10-21 19:50:38 UTC

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In question 10, “La” is unambiguously the first word alphabetically in the English language that begins with an “L, so I would have put an “a” in the 1 circle. (I may well have been failed for doing so of course!)