
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 »

Conway’s puzzle M(13) involves the 13 points and 13 lines of $\mathbb{P}^2(\mathbb{F}_3) $. On all but one point numbered counters are placed holding the numbers 1,…,12 and a move involves interchanging one counter and the ‘hole’ (the unique point having no counter) and interchanging the counters on the two other points of the line determined… Read more »

Conway’s puzzle M(13) is a variation on the 15puzzle played with the 13 points in the projective plane $\mathbb{P}^2(\mathbb{F}_3) $. The desired position is given on the left where all the counters are placed at at the points having that label (the point corresponding to the hole in the drawing has label 0). A typical… 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.

The Oscar in the category The Best Rejected Research Proposal in Mathematics (ever) goes to … Alexander Grothendieck for his proposal Esquisse d’un Programme, Grothendieck\’s research program from 1983, written as part of his application for a position at the CNRS, the French equivalent of the NSF. An English translation is available. Here is one… Read more »

2005 was the year that the DaVinci code craze hit Belgium. (I started reading Dan Brown’s Digital Fortress and Angels and Demons a year before on the way back from a Warwick conference and when I read DVC a few months later it was an anticlimax…). Anyway, what better way to end 2005 than with… Read more »

Noam Elkies is one of those persons I seem to bump into (figuratively speaking) wherever my interests take me. At the moment I’m reading (long overdue, I know, I know) the excellent book Notes on Fermat’s Last Theorem by Alf Van der Poorten. On page 48, Elkies figures as an innocent bystander in the 1994… Read more »

Klein’s quartic $X$is the smooth plane projective curve defined by $x^3y+y^3z+z^3x=0$ and is one of the most remarkable mathematical objects around. For example, it is a Hurwitz curve meaning that the finite group of symmetries (when the genus is at least two this group can have at most $84(g1)$ elements) is as large as possible,… Read more »

Noam D. Elkies is a Harvard mathematician whose main research interests have to do with lattices and elliptic curves. He is also a very talented composer of chess problems. The problem to teh left is a proof game in 14 moves. That is, find the UNIQUE legal chess game leading to the given situation after… Read more »
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