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Weil descent

A classic Andre Weil-tale is his narrow escape from being shot as a Russian spy The war was a disaster for Weil who was a conscientious objector and so wished to avoid military service. He fled to...

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BC stands for Bi-Crystalline graded

Towards the end of the Bost-Connes for ringtheorists post I freaked-out because I realized that the commutation morphisms with the $X_n^* $ were given by non-unital algebra maps. I failed to notice the...

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Farey symbols of sporadic groups

John Conway once wrote : There are almost as many different constructions of $M_{24} $ as there have been mathematicians interested in that most remarkable of all finite groups. In the inguanodon post...

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Looking for F_un

There are only a handful of human activities where one goes to extraordinary lengths to keep a dream alive, in spite of overwhelming evidence : religion, theoretical physics, supporting the Belgian...

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Arnold’s trinities version 2.0

Arnold has written a follow-up to the paper mentioned last time called “Polymathematics : is mathematics a single science or a set of arts?” (or here for a (huge) PDF-conversion). On page 8 of that...

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Andre Weil on the Riemann hypothesis

Don’t be fooled by introductory remarks to the effect that ‘the field with one element was conceived by Jacques Tits half a century ago, etc. etc.’ While this is a historic fact, and, Jacques Tits...

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On2 : Conway’s nim-arithmetics

Last time we did recall Cantor’s addition and multiplication on ordinal numbers. Note that we can identify an ordinal number $\alpha $ with (the order type of) the set of all strictly smaller ordinals,...

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Pollock your own noncommutative space

I really like Matilde Marcolli’s idea to use some of Jackson Pollock’s paintings as metaphors for noncommutative spaces. In her talk she used this painting and refered to it (as did I in my post) as :...

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The odd knights of the round table

Here’s a tiny problem illustrating our limited knowledge of finite fields : “Imagine an infinite queue of Knights ${ K_1,K_2,K_3,\ldots } $, waiting to be seated at the unit-circular table. The master...

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Art and the absolute point

In his paper Cyclotomy and analytic geometry over $\mathbb{F}_1$ Yuri I. Manin sketches and compares four approaches to the definition of a geometry over $\mathbb{F}_1$, the elusive field with one...

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