
At the moment I’m rereading Siobhan Roberts’ biography of John Horton Conway, Genius at play – the curious mind of John Horton Conway. In fact, I’m also rereading Alexander Masters’ biography of Simon Norton, The genius in my basement – the biography of a happy man. [full_width_image] [/full_width_image] If you’re in for a suggestion, try… Read more »

Soon, we will be teaching computational geometry courses to football commentators. If a player is going to be substituted we’ll hear sentences like: “no surprise he’s being replaced, his Voronoi cell has been shrinking since the beginning of the second half!” David Sumpter, the author of Soccermatics: Mathematical Adventures in the Beautiful Game, wrote a… Read more »

It was fun following the second game last night in real time. Carlsen got a winning endgame with two bishops against a rook, but blundered with 62. Bg4?? (winning was Kf7), resulting in stalemate. There was this hilarious message around move 60: “The computer has just announced that white mates in 31 moves. Of course,… Read more »

Last time we introduced the game of transfinite Nimbers and asked a winning move for the transfinite game with stones a at position $~(2,2) $, b at $~(4,\omega) $, c at $~(\omega+2,\omega+3) $ and d at position $~(\omega+4,\omega+1) $. Above is the unique winning move : we remove stone d and by the rectanglerule add… Read more »

Today, we will expand the game of Nimbers to higher dimensions and do some transfinite Nimber hacking. In our identification between $\mathbb{F}_{16}^* $ and 15th roots of unity, the number 8 corresponds to $\mu^6 $, whence $\sqrt{8}=\mu^3=14 $. So, if we add a stone at the diagonal position (14,14) to the Nimbersposition of last time… 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 »

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.

Can one base a grouptheory 101 course on the notion of groupoids?

Hendrik Lenstra found an effective procedure to compute the mysterious elements alpha(p) needed to do actual calculations with infinite nimarithmetic.

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.

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 »
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