Tag Archives: Grothendieck

The paramodular conjecture is false for trivial reasons

(This is part of a series of occasional posts discussing results and observations in my joint paper with Boxer, Gee, and Pilloni mentioned here.) Brumer and Kramer made a conjecture positing a bijection between isogeny classes of abelian surfaces over … Continue reading

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The ABC conjecture has (still) not been proved

The ABC conjecture has (still) not been proved. Five years ago, Cathy O’Neil laid out a perfectly cogent case for why the (at that point recent) claims by Shinichi Mochizuki should not (yet) be regarded as constituting a proof of … Continue reading

Posted in Mathematics, Politics, Rant | Tagged , , | 33 Comments

The decline and fall of Publications Mathématiques de l’lHÉS

I want to discuss the decline of a once great journal. How did IHES go from this: and this: to this: It is a sad state of affairs. To be clear, I am talking about the typesetting here. The old … Continue reading

Posted in Mathematics, Waffle | Tagged , , , , , | 5 Comments

Effective Motives

This is a brief follow up concerning a question asked by Felipe. Suppose we assume the standard conjectures. Let be a pure motive, and consider the following problems: Problem A: (“effectivity”) Suppose that has non-negative Hodge-Tate weights. Then is effective? … Continue reading

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The Two Cultures of Mathematics: A Rebuttal

Gowers writes thoughtfully about combinatorics here, in an essay which references Snow’s famous lectures (or famous amongst mathematicians – I’ve never met anyone else who has ever heard of them). The trouble, however, starts (as it often does) with the … Continue reading

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