Tag Archives: AI

A Brief Digest of Some New OpenAI Results

Posted on October 8, 2026 by Persiflage

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 , , , , , , , , , , , , , , , , , | 14 Comments

Journals

Posted on October 5, 2026 by Persiflage

In my recent post, I listed four broad topics which I think our profession should urgently try to address. Here I want to say something about journals. Whenever I have tried to write one of these posts, I always get … Continue reading →

Posted in Mathematics | Tagged , , , , | 15 Comments

AI disclosures done right

Posted on September 27, 2026 by Persiflage

Another shiny new AI proof, this time a proof by Constantin Kogler of the Odlyzko–Poonen conjecture which says that a polynomial with coefficients chosen randomly from \(\{0,1\}\) is irreducible. What I want to emphasize on this occasion is the exemplary … Continue reading →

Posted in Mathematics | Tagged , , , | 9 Comments

Ways to improve Mathematics (an introduction)

Posted on September 17, 2026 by Persiflage

The goal of this continuing sequence of posts is to recognize the reality in how our subject is changing and how we should adapt. Even in a hypothetical world where AI was infallible, essentially omniscient, benevolent, a wonderful expositor, and … Continue reading →

Posted in Mathematics | Tagged , , , , , , , | 9 Comments

Look, Mom, I pressed a button!

Posted on September 5, 2026 by Persiflage

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 , , , , , , , | 11 Comments

Xena on Counterexamples

Posted on July 22, 2026 by Persiflage

There is an interesting post here on Xena’s blog. I don’t centre “proof” in mathematics to anywhere near the extent that Kevin does, but I think emphasizing that distinction obscures the fact that our opinions about mathematics, mathematicians, and, I … Continue reading →

Posted in Mathematics | Tagged , , , , , , , , , , | 3 Comments

It wasn’t me!

Posted on March 13, 2025 by Persiflage

I have a gentleman’s bet with another number theorist that I will be able to write a nonsense paper and get it published in respectable journal. To be honest, I barely have enough time to write actual papers let alone … Continue reading →

Posted in Mathematics, Rant | Tagged , , | 1 Comment

SL_n versus GL_n

Posted on July 18, 2024 by Persiflage

I recently wrote a paper (with Toby Gee and George Boxer, see also here) on constructing regular algebraic automorphic representations \(\pi\) of (cohomological) weight zero and level one, and therefore also cuspidal cohomology classes in the cohomology of \(\mathrm{GL}_n(\mathbf{Z})\) for … Continue reading →

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