Author Archives: Persiflage

BSD and the p-converse (Guest Post: Ashay Burungale)

Posted on October 15, 2026 by Persiflage

(Here is the first of a series of guest blog posts by number theorists on the recent OpenAI results, this one by Ashay Burungale.) Let \(E/\mathbf{Q}\) be an elliptic curve. Its rational points form a finitely generated abelian group. The … Continue reading →

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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 →

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The OpenAI problem dump

Posted on October 6, 2026 by Persiflage

As we await the latest AI-generated results (whether gurgling through the arXiv, appearing on 4chan, or coming straight from the horse’s mouth), I thought I would put on record some interesting open problems from my own field. I don’t mention … Continue reading →

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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 →

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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 →

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Roots of Unity

Posted on September 26, 2026 by Persiflage

This post is a follow-up on a previous post on the abelian house. For an algebraic integer \(\alpha\), the house \(\overline{|\alpha|}\) is the absolute value of the largest conjugate of \(\alpha.\) Raphael Robinson made a number of conjectures concerning cyclotomic … Continue reading →

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Are business schools intellectually bankrupt? (Part Two)

Posted on September 24, 2026 by Persiflage

Nicholas Polson, a professor of Finance at Booth (Chicago’s business school) in the news for authoring 258 papers in 2026. It turns out that I had an interesting interaction with Polson in this past which I never blogged about. Instead, … Continue reading →

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zeta(5) is irrational

Posted on September 24, 2026 by Persiflage

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 →

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Real quadratic fields and finite quantum dilogarithms I

Posted on September 22, 2026 by Persiflage

Danylo Radchenko and Campbell Wheeler have posted an extraordinary new paper in which they prove that Stark units for real quadratic fields are algebraic numbers. (Not yet a Shimura reciprocity law that shows these generate abelian extensions but hey, this … Continue reading →

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An even PSL_2(F_23) Galois extension

Posted on September 20, 2026 by Persiflage

I was wrong! I have said on a number of occasions that my favourite family of groups for the inverse Galois problem is \(G=\mathrm{SL}_2(\mathbf{F}_p)\). This is still true, and the reason is still the same; the fact that \(G\) has … Continue reading →

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