
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…

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 : Jackson Pollock “Untitled N.3”. Before someone writes a post ‘The Pollock noncommutative space hoax’ (similar to my own…

On2 : Conway’s nimarithmetics
Conway’s nimarithmetic on ordinal numbers leads to many surprising identities, for example who would have thought that the third power of the first infinite ordinal equals 2…

Arnold’s trinities version 2.0
Arnold has written a followup to the paper mentioned last time called “Polymathematics : is mathematics a single science or a set of arts?” (or here for a (huge) PDFconversion). On page 8 of that paper is a nice summary of his 25 trinities : I learned of this newer paper from a comment by…

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 football team and … mathematics. In recent years several people spend a lot of energy looking for properties of an elusive object : the…

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 Ive added yet another construction of the Mathieu groups $M_{12} $ and $M_{24} $ starting from (half of) the Farey sequences and…

BC stands for BiCrystalline graded
Towards the end of the BostConnes for ringtheorists post I freakedout because I realized that the commutation morphisms with the $X_n^* $ were given by nonunital algebra maps. I failed to notice the obvious, that algebras such as $\mathbb{Q}[\mathbb{Q}/\mathbb{Z}] $ have plenty of idempotents and that this mysterious ‘nonunital’ morphism was nothing else but multiplication…

Weil descent
A classic Andre Weiltale 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 Finland, to visit Rolf Nevanlinna, as soon as war was declared. This was an attempt to avoid being…