Royal Society University Research Fellow at the University of Manchester. Mathematician and owner of erdosproblems.com. He/him/his.

Joined December 2020
20 Photos and videos
Thomas Bloom retweeted
If you followed the news of the unit-distance Erdős' conjecture disproof by OpenAI, then you might *REALLY* enjoy this great talk by Ravi Ramakrishna (Cornell - my postdoc mentor!) on the algebraic number theory behind the lattice construction. youtu.be/y3QfE2XRK6o
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I have started a collection of essays, blog posts, etc discussing AI in mathematics. I do not agree with everything written, but all are valuable to read - the more different views the better! Please reply with your own suggestions. thomasbloom.org/AIlinks.html

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A great quote from Ellenberg: "It is natural for any community to shift its values over time. But if we do it, I think we should do it on purpose and with our eyes open."
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Mathematics -is- a human endeavour. There is something which maybe you're calling mathematics that has nothing to do with humans, some 'platonic otherworld' of abstract ideas. But what I call mathematics is the human attempt to explore and understand this world.
There are two main points in the Leiden declaration, one good, one bad imho: > Good: science is underfunded, mathematics included. We need more researchers, not less, and with the advent of AGI we will need even more. If AGI is a magical wand, someone still needs to wield it. Researchers are the best prepared for this. > Bad: 'mathematics is a human enterprise it disturbs existing incentive structures'. Mathematics is a not a human endeavor per se. It is definitely so within academia, but science is free for all. If AI can make math progress faster, then it is only for good of mathematics. It definitely does disturb existing incentive structures (grants, who proves what first, peer review), but these are not optimal to begin with and it's a good time to rethink it. Academic mathematicians in the last 50 years have started thinking that mathematics is done solely by university-affiliated academics. This was true for around the last 100 years, but wasn't true before, and it seems won't be true for long. And this is a good change. Good for science, good for mathematics, but perhaps bad for existing academics within their status quo incentives. But they will adapt, and mathematics will only flourish more. In the end the goal should be to expand mathematics (and generally science) as vastly as possible. Abundance of proofs, abundance of explanations, thanks to LLMs, is a great thing for progress.
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But maybe there were other proofs of RH possible. Proofs that better fit our own human intuition and perspective. But maybe the AI prefers another way, and once it is done, the desire to find a human proof for ourselves will fade.
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I am not saying this is inevitable, or even likely or possible. Just that we should try our best, as early as possible, to make sure that AI and humans are aligned on what 'good mathematics' means, both abstractly and in its impact on society.
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I have signed the Leiden declaration, and encourage everyone to read it and reflect. Even if some of the points are impossible to achieve in reality, they are a good set of guidelines to try and do what is best for humanity. leidendeclaration.ai/
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I have written a blog post giving my personal sketch of the recent disproofs of the sum-product and unit distance conjectures. erdosproblems.com/forum/thre…

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Now an interactive version! erdosproblems.com/forum/unit…

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(Having more than two fields, or fields with degree >3, is too much for my website to handle, but I wanted to include two different ones to show how much the field (and its discriminant) affects the density!)
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Thomas Bloom retweeted
“the sun goes down, and every move is the truth” is such a tour de force
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