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Meta
Tag Archives: Irrationality
A Brief Digest of Some New OpenAI Results
I thought it might be worth discussing some of the recent OpenAI results in my field, or at least in algebraic number theory. For each of them, I’d like to offer a few thoughts, if I have any, on what … Continue reading
Posted in Mathematics, Uncategorized
Tagged AI, Ana Caraiani, Artin Conjecture, BSD, Catalan's Constant, Fontaine-Mazur Conjecture, GRH, Hardy, Hilbert's 10th problem, Hooley, Irrationality, James Newton, OpenAI, Ramanujan Conjecture, Rankin, Rankin-Selberg, Riemann Hypothesis, Roth's Theorem
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zeta(5) is irrational
So one day after an amazing result by humans, the computers have struck back! This time, a proof that \(\zeta(5)\) is irrational. The paper I saw gives me the impression of being almost entirely AI generated (if so, it then … Continue reading
Posted in Mathematics
Tagged \zeta(5), Francis Brown, Irrationality, Marc Prévost, Tanguy Rivoal, Wadim Zudilin
4 Comments
Look, Mom, I pressed a button!
I have recently heard a few extraordinary opinions about how mathematicians should use AI. One I would paraphrase as “professional mathematicians should never use AI for any problem not in their narrowly defined (by whom?) research program”, which seems ridiculous … Continue reading
Posted in AI, Mathematics
Tagged AI, ChatGPT, Irrationality, Johannes Sprang, Li Lai, Vesselin Dimitrov, Wadim Zudilin, Yunqing Tang
11 Comments
Arbeitsgemeinschaft 2026
The April 2026 Oberwolfach Arbeitsgemeinschaft will be on Arithmetic Holonomy Bounds and Applications to Irrationality, and in particular will discuss some of the results of this paper. For those who don’t know, the Arbeitsgemeinschaft (“study group”) is different from usual … Continue reading
Posted in Mathematics
Tagged Arbeitsgemeinschaft, Irrationality, Oberwolfach, Vesselin Dimitrov, Yunqing Tang
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A talk on my new work with Vesselin Dimitrov and Yunqing Tang on irrationality
Here is a video of my talk from the recent 70th birthday conference of Peter Sarnak. During a talk one always forgets to say certain things, so I realized that my blog could be a good place to give some … Continue reading
Posted in Mathematics
Tagged Alf van der Poorten, Apéry, Ball, François Charles, Hermite, Irrationality, Jen-Benoît Bost, Lambert, Lindemann, Occam, Peter Sarnak, pi, Tanguy Rivoal, Vesselin Dimitrov, Wadim Zudilin, Yunqing Tang
4 Comments