Timothy Gowers
@wtgowers.bsky.social
Mathematics professor at Collège de France and fellow of Trinity College Cambridge.
(That "you" is of course a "one" and isn't referring to you.)
December 19, 2025 at 9:43 AM
(That "you" is of course a "one" and isn't referring to you.)
If you think "edging down" is getting better, rather than continuing to get worse at a slightly slower rate.
December 19, 2025 at 9:42 AM
If you think "edging down" is getting better, rather than continuing to get worse at a slightly slower rate.
British news a bit more coy about it for some reason.
December 14, 2025 at 5:42 PM
British news a bit more coy about it for some reason.
Sorry, I should have explained in more detail. But instead of doing that, I'll give you a direct link to the most recently published article of the journal: arxiv.org/pdf/2307.15822
arxiv.org
December 12, 2025 at 2:26 PM
Sorry, I should have explained in more detail. But instead of doing that, I'll give you a direct link to the most recently published article of the journal: arxiv.org/pdf/2307.15822
Maybe he's secretly trying to do something about climate change.
December 8, 2025 at 9:15 PM
Maybe he's secretly trying to do something about climate change.
I can't decide whether it's that or just appalling tactics -- making huge compromises in order to win a second term, which in practice have had the effect that he almost certainly won't win a second term (unless he's very lucky and Reform self-destructs).
December 8, 2025 at 8:26 AM
I can't decide whether it's that or just appalling tactics -- making huge compromises in order to win a second term, which in practice have had the effect that he almost certainly won't win a second term (unless he's very lucky and Reform self-destructs).
Have you watched the Liz Truss Show? After five minutes of that I think you might be forced to admit that Starmer is the lesser of two evils.
December 7, 2025 at 9:47 AM
Have you watched the Liz Truss Show? After five minutes of that I think you might be forced to admit that Starmer is the lesser of two evils.
Even if she does give two shits, she would probably be far too afraid of the inevitable reaction that the right-wing press would have to such a measure.
December 2, 2025 at 2:03 PM
Even if she does give two shits, she would probably be far too afraid of the inevitable reaction that the right-wing press would have to such a measure.
which for now I regard as something that just happens to be the case. Likewise, if somebody were to find a human-scale argument for the Pythagorean-triples problem then I would be delighted. But I very much doubt that such an argument exists, and that doesn't bother me. 9/9
November 11, 2025 at 9:30 AM
which for now I regard as something that just happens to be the case. Likewise, if somebody were to find a human-scale argument for the Pythagorean-triples problem then I would be delighted. But I very much doubt that such an argument exists, and that doesn't bother me. 9/9
That said, if someone were to find a proof of the four-colour theorem (for example) that didn't require a huge case analysis, I'd celebrate that and regard it as an advance in understanding, since it would explain why the case analysis had worked out, 8/
November 11, 2025 at 9:30 AM
That said, if someone were to find a proof of the four-colour theorem (for example) that didn't require a huge case analysis, I'd celebrate that and regard it as an advance in understanding, since it would explain why the case analysis had worked out, 8/
There appear to be some problems that cannot realistically be solved except by this kind of approach, in which case I see no reason not to use it, and I'm happy with the resulting level of understanding. 7/
November 11, 2025 at 9:30 AM
There appear to be some problems that cannot realistically be solved except by this kind of approach, in which case I see no reason not to use it, and I'm happy with the resulting level of understanding. 7/
But of course a proof of this kind is not designed to be read in the conventional way, and has its own kind of appeal. Personally, I'm fine with the idea of using nice arguments to reduce a proof to a massive computation and then doing the computation. 6/
November 11, 2025 at 9:30 AM
But of course a proof of this kind is not designed to be read in the conventional way, and has its own kind of appeal. Personally, I'm fine with the idea of using nice arguments to reduce a proof to a massive computation and then doing the computation. 6/
But I'm pretty sure it was meant humorously and not (as suggested in the Quanta article) as any kind of criticism, since I think now, and thought then, that these kinds of results are pretty cool. 4/
November 11, 2025 at 9:30 AM
But I'm pretty sure it was meant humorously and not (as suggested in the Quanta article) as any kind of criticism, since I think now, and thought then, that these kinds of results are pretty cool. 4/
I am quoted in this Quanta article as describing the proof as "the most disgusting proof ever". Unfortunately, the quote is from a comment made on a post by someone else on the now defunct Google Plus, so I can't look at the context of whatever it was I said. 3/
To Have Machines Make Math Proofs, Turn Them Into a Puzzle | Quanta Magazine
Marijn Heule turns mathematical statements into something like Sudoku puzzles, then has computers go to work on them. His proofs have been called “disgusting,” but they go beyond what any human can do...
www.quantamagazine.org
November 11, 2025 at 9:30 AM
I am quoted in this Quanta article as describing the proof as "the most disgusting proof ever". Unfortunately, the quote is from a comment made on a post by someone else on the now defunct Google Plus, so I can't look at the context of whatever it was I said. 3/
This solved an old problem of Ron Graham. The proof was a massive brute-force argument. Not pure brute force, since that would have been utterly infeasible, but a clever brute-force computation using a SAT solver. 2/
November 11, 2025 at 9:30 AM
This solved an old problem of Ron Graham. The proof was a massive brute-force argument. Not pure brute force, since that would have been utterly infeasible, but a clever brute-force computation using a SAT solver. 2/
County football -- that would be something.
November 8, 2025 at 11:43 PM
County football -- that would be something.
Was her middle name Mabel?
November 5, 2025 at 9:26 PM
Was her middle name Mabel?
I clearly missed a trick there — I actually knew Ron Graham.
November 3, 2025 at 9:57 PM
I clearly missed a trick there — I actually knew Ron Graham.
I take it your use of the word “amount” here was a deliberate wind-up.
November 3, 2025 at 9:56 PM
I take it your use of the word “amount” here was a deliberate wind-up.
Another point is that I think the result, or something very similar, is pretty likely to be known, so it it is likely that the slightly clever reduction to the lemma was something it had seen before rather than something it came up with by itself.
November 1, 2025 at 11:29 AM
Another point is that I think the result, or something very similar, is pretty likely to be known, so it it is likely that the slightly clever reduction to the lemma was something it had seen before rather than something it came up with by itself.
Not all that much, but there was something slightly indirect about going via the lemma, so I'm not sure how long it would have taken me to think of formulating it. Once it was formulated, I could have asked GPT5 whether it was known and it would have told me.
November 1, 2025 at 11:27 AM
Not all that much, but there was something slightly indirect about going via the lemma, so I'm not sure how long it would have taken me to think of formulating it. Once it was formulated, I could have asked GPT5 whether it was known and it would have told me.