Tag Archives: Kevin Buzzard

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 →

Posted in Mathematics | Tagged , , , , , , , , , , | 16 Comments

Putting ChatGPT through its paces

Posted on August 11, 2026 by Persiflage

We are all aware of what ChatGPT can do. I think we would be better informed if we also learn what it cannot do (at least right now!). In order to better understand the current capability of the latest publicly … Continue reading →

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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 →

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The Arthurian Legend

Posted on October 18, 2024 by Persiflage

Some time back, Kevin Buzzard (friend of the blog!) gave a series of talks in which he criticized certain aspects of the mathematical culture when it came to accepting proof. In addition to obvious targets like the classification of finite … Continue reading →

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The horizontal Breuil-Mezard conjecture

Posted on October 19, 2023 by Persiflage

Postdoc hiring season will be upon us soon! I have two excellent graduate students who will be applying for academic jobs soon, Chengyang Bao and Andreea Iorga. I have mentioned Chengyang’s first project before here and an introduction to the … Continue reading →

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What the slopes are

Posted on February 25, 2023 by Persiflage

Let \(f\) be a classical modular eigenform of weight \(k\), for example, \(f = \Delta\). The Ramanujan conjecture states that the Hecke eigenvalues \(a_p\) satisfy the bound \(|a_p| \le 2 p^{(k-1)/2}.\) A slightly fancier but cleaner way of saying this … Continue reading →

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The eigencurve is (still) proper

Posted on October 23, 2020 by Persiflage

Although I don’t think about it so much anymore, the eigencurve of Coleman-Mazur was certainly one of my first loves. I can’t quite say I learnt about \(p\)-adic modular forms at my mother’s knee, but I did spend a formative … Continue reading →

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NSF Proposal, Graduate Fellowship Edition

Posted on March 17, 2020 by Persiflage

Note: I feel as a service to the number theory entertainment complex that I should blog more often in these times, even if it means being less coherent than usual. I might even try to get a few guest posts … Continue reading →

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Harris versus Buzzard

Posted on June 12, 2019 by Persiflage

Michael Harris has a new article at quanta. The piece is (uncharacteristically?) coy, referring to the laments of two logicians without divulging either their names or their precise objections, making oblique references to a cabal of 10 mathematicians meeting at … Continue reading →

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Tips for new postdocs

Posted on January 20, 2019 by Persiflage

In my role as junior hiring chair, I’ve been thinking a little bit about how a (R1) institution can best serve its postdocs. Many find the transition from graduate student life to being a postdoc somewhat of a rude shock. … Continue reading →

Posted in Mathematics | Tagged , , , , , , , , , | 4 Comments