
eBook ‘geometry and the absolute point’ v0.1
In preparing for next year’s ‘seminar noncommutative geometry’ I’ve converted about 30 posts to LaTeX, centering loosely around the topics students have asked me to cover : noncommutative geometry, the absolute point (aka the field with one element), and their relation to the Riemann hypothesis. The idea being to edit these posts thoroughly, add much […]

mathblogging and pollresults
Mathblogging.org is a recent initiative and may well become the default starting place to check on the status of the mathematical blogosphere. Handy, if you want to (re)populate your RSSaggregator with interesting mathematical blogs, is their graphical presentation of (nearly) all mathblogs ordered by type : group blogs, individual researchers, teachers and educators, journalistic writers,…

How to play Nimbers?
Nimbers is a 2person game, winnable only if you understand the arithmetic of the finite fields $\mathbb{F}_{2^{2^n}} $ associated to Fermat 2powers. It is played on a rectangular array (say a portion of a Goboard, for practical purposes) having a finite number of stones at distinct intersections. Here’s a typical position The players alternate making…

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.

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 : 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…

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