
From the Da Vinci code to Galois
In The Da Vinci Code, Dan Brown feels he need to bring in a French cryptologist, Sophie Neveu, to explain the mystery behind this series of numbers: 13 – 3 – 2 – 21 – 1 – 1 – 8 – 5 The Fibonacci sequence, 1123581321345589144… is such that any number in it is the […]

Langlands versus Connes
This is a belated response to a MathOverflow exchange between Thomas Riepe and Chandan Singh Dalawat asking for a possible connection between Connes’ noncommutative geometry approach to the Riemann hypothesis and the Langlands program. Here’s the punchline : a large chunk of the ConnesMarcolli book Noncommutative Geometry, Quantum Fields and Motives can be read as…

Seating the first few thousand Knights
The Knightseating problems asks for a consistent placing of nth Knight at an odd root of unity, compatible with the two different realizations of the algebraic closure of the field with two elements.

big Witt vectors for everyone (1/2)
Next time you visit your mathlibrary, please have a look whether these books are still on the shelves : Michiel Hazewinkel‘s Formal groups and applications, William Fulton’s and Serge Lange’s RiemannRoch algebra and Donald Knutson’s lambdarings and the representation theory of the symmetric group. I wouldn’t be surprised if one or more of these books…

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 unitcircular table. The master of ceremony (that is, you) must give Knights $K_a $ and $K_b $ a place at an odd root of unity, say $\omega_a…

On2 : transfinite number hacking
Surely Georg Cantor’s transfinite ordinal numbers do not have a reallife importance? Well, think again.

best of 2008 (1) : wiskundemeisjes
A feeble attempt to translate the Marcollipost by the ‘wiskundemeisjes’.

Mazur’s knotty dictionary
The algebraic fundamental group of a scheme gives the MazurKapranovReznikov dictionary between primes in number fields and knots in 3manifolds.

Manin’s geometric axis
Manin proposes the idea of projecting spec(Z[x]) not only onto spec(Z), but also to a geometric axis by considering the integers as an algebra over the field with one element.