
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… Read more »

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,… Read more »

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… Read more »

For the better part of the 30ties, Ernst Witt (1) did hang out with the rest of the ‘Noetherknaben’, the group of young mathematicians around Emmy Noether (3) in Gottingen. In 1934 Witt became Helmut Hasse‘s assistent in Gottingen, where he qualified as a university lecturer in 1936. By 1938 he has made enough of… Read more »

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.

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… Read more »

To mark the end of 2009 and 6 years of blogging, two musical compositions with a mathematical touch to them. I wish you all a better 2010! Remember from last time that we identified Olivier Messiaen as the ‘Monsieur Modulo’ playing the musical organ at the Bourbaki wedding. This was based on the fact that… Read more »

Over the weekend I read The artist and the mathematician (subtitle : The story of Nicolas Bourbaki, the genius mathematician who never existed) by Amir D. Aczel. Whereas the central character of the book should be Bourbaki, it focusses more on two of Bourbaki’s most colorful members, André Weil and Alexander Grothendieck, and the many… Read more »

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…

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

A few recollections and a very quick number game by Hendrik Lenstra.

About a year ago I did a series of posts on games associated to the Mathieu sporadic group $M_{12} $, starting with a post on Conway’s puzzle M(13), and, continuing with a discussion of mathematical blackjack. The idea at the time was to write a book for a general audience, as discussed at the start… Read more »

Most chess programs are able to give a numerical evaluation of a position. For example, the position below is considered to be worth +8.7 with white to move, and, 0.7 with black to move (by a certain program). But, if one applies combinatorial game theory as in John Conway’s ONAG and the BerlekampConwayGuy masterpiece Winning… Read more »

Ever tried a chess problem like : White to move, mate in two! Of course you have, and these are pretty easy to solve : you only have to work through the finite list of white first moves and decide whether or not black has a move left preventing mate on the next white move…. Read more »

Terry Tao is reworking some of his better blogposts into a book, to be published by the AMS (here’s a preliminary version of the book “What’s New?”) After some thought, I decided not to transcribe all of my posts from last year (there are 93 of them!), but instead to restrict attention to those articles… Read more »

The Archimedes codex is a good read, especially when you are (like me) a failed archeologist. The palimpsest (Greek for ‘scraped again’) is the worlds first Kyotoapproved ‘sustainable writing’. Isn’t it great to realize that one of the few surviving texts by Archimedes only made it because some monks recycled an old medieval parchment by… Read more »

I’ve reinstalled the Google analytics plugin on december 22nd, so it is harvesting data for three weeks only. Still, it is an interesting tool to gain insight in the social networking aspect of mathblogging, something I’m still very bad at… Below the list of all blogs referring at least 10 times over this last three… Read more »

Interactive Fiction (IF) describes software simulating environments in which players use text commands to control characters and influence the environment. Works in this form can be understood as literary narratives and as computer games. In common usage, the word refers to text adventures, a type of adventure game with textbased input and output. As the… Read more »

A first yearfirst semester course on group theory has its hilarious moments. Whereas they can relate the two other pure math courses (linear algebra and analysis) _somewhat_ to what they’ve learned before, with group theory they appear to enter an entirely new and strange world. So, it is best to give them concrete examples :… Read more »

(continued from part one). Take twelve cards and give them values 0,1,2,…,11 (for example, take the jack to have value 11 and the queen to have value 0). The hexads are 6tuples of cards having the following properties. When we star their values by the scheme on the left below and write a 0 below… Read more »

In the series “Mathieu games” we describe some mathematical games and puzzles connected to simple groups. We will encounter Conway’s M(13)puzzle, the classic Loyd’s 15puzzle and mathematical blackjack based on Mathieu’s sporadic simple group M(12).

Here a list of pdffiles of NeverEndingBooksposts on games, in reverse chronological order.

This morning, Esther Beneish arxived the paper The center of the generic algebra of degree p that may contain the most significant advance in my favourite problem for over 15 years! In it she claims to prove that the center of the generic division algebra of degree p is stably rational for all prime values… Read more »

In another post we introduced Minkowski’s questionmark function, aka the devil’s straircase and related it to Conways game of _contorted fractions_. Side remark : over at Good Math, Bad Math Mark ChuCarroll is running a miniseries on numbers&games, so far there is a post on surreal numbers, surreal arithmetic and the connection with games but… Read more »

Who was the first mathematician to give a slide show talk? I don’t have the definite answer to this question, but would like to offer a strong candidate : Hermann Minkowski gave the talk “Zur Geometrie der Zahlen” (On the geometry of numbers) before the third ICM in 1904 in Heidelberg and even the title… Read more »
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