@thomasfbloom

Royal Society University Research Fellow at the University of Manchester. Mathematician and owner of https://xitter.cf/t.co/SWVqqnq9hn. He/him/his.

Manchester, UK
Joined December 2020
The 'paper map', or dependency graph, tool here makes it a lot easier to navigate the very long papers generated by OpenAI - worth checking out. (I haven't tried the other features it offers yet, so can't comment on how helpful those are.)
We're interested in understanding how to make AI-generated research papers more understandable for relevant research communities. If you're a mathematician reading the recent OpenAI results, check out readable-intelligence.com/. This project aims to make these papers easier to read, through: (1) Readable Versions that rewrite them for clarity and (2) visualization/AI tools to help understand the argument. We'd love feedback from the mathematics community --- please check out the site and reach out to the team!
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Reminds me of the dependency graph provided to help the reader navigate Szemeredi's paper, containing the first (long and intricate) proof of Szemeredi's theorem. (Note that this paper was actually written by Graham and Hajnal, after Szemeredi explained the proof to them)
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A great video that I recommend everyone interested in maths watch (especially those on this site who say "mathematicians are cooked" etc) youtu.be/LKrwhjOI8Nc?is=zejd…
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Ben Green has written a very nice version of the proof that no Siegel zeros exist - only 5 pages, and self-contained elementary arguments: hexagonmath.org/pdf/2610.003…
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This is, it seems, much simpler than the original OpenAI paper (Ben found this by 'vibemathsing' with GPT starting from that original paper).
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(Not entirely self-contained to get no siegel zeros, you need a bit more to go from his sum estimate to a statement about zeros, but this step is completely standard and was well known a long time ago.)
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Thomas Bloom retweeted
A signature feature of academic AI writing is (currently) that it is has bad judgment on what is important and what is not important, even refine.ink. This is one of the most damaging AI "tells", b/c it reflects bad judgment on the part of the author as well. 1/
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Me opening Twitter this morning.
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Thomas Bloom retweeted
The math community deserves its own AI system. Introducing Open Math OS: the infrastructure for Math 2.0. Open models and AI agents. 24/7 cloud compute with 100+ tools. The community controls its data. Compute is free for approved teams. Apply now: openmathmodel.org/
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Many people with relevant expertise think there's a real chance that AI could kill us all in the not too distant future. Others disagree. I've written a post, aimed principally at mathematicians, detailing my struggles to decide what to make of this. gowers.wordpress.com/2026/10…
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I disagree. I think that all AI companies owe a huge amount to mathematicians - just as they do to artists, open source software developers, authors, and so on. They are making a huge amount of money thanks to AI models trained on work made freely available by these groups...
I struggle to fathom this kind of attitude. OpenAI does not owe mathematicians a single cent. That they are donating $5M to a new Simons Foundation initiative to help mathematicians is commendable.
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...which they made available for the benefit of other human beings, little suspecting how they would be used in AI training in the future. Is this an actual enforceable debt? No. But if you are profiting hugely off the work of others, then you owe them a lot.
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Wouter van Doorn and I have written a short paper explaining the 'Egyptian fraction' paper included in the recent OpenAI proofs. Not the most important of the recent proofs, but this is a favourite topic of ours (and of Erdős). erdosproblems.com/static/Uni… Some comments: 1/
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It is this second simpler way we have included in our exposition. (We have not yet read all the details of the more complicated way.) Strangely, the AI did not seem to notice this duplication of effort. 11/
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A good reminder to those looking at the OpenAI papers that a lot of their length may be taken up with entirely redundant detours, and that even a small amount of attention can significantly reduce the length and complexity of the proofs. 12/12
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