Author Archives: apgoucher

This last week has been very exciting. On Thursday, I gave a talk in absentia at the 13th Gathering for Gardner on the topic of artificial life (thanks go to Dave Greene and Tom Rokicki for playing the slides and … Continue reading →

Previously, we discussed Homotopy Type Theory, which is an alternative foundation of mathematics with several advantages over ZFC, mainly for computer-assisted proofs. It is based on Martin-Löf’s intuitionistic type theory, but with the idea that types are spaces, terms are … Continue reading →

Tim Hutton recently presented me with a marvellous 3D-printed-graphite set of triakis truncated tetrahedra. These have a natural interpretation as the Voronoi cells of a diamond: the shapes that would form if you gradually enlarged the atoms until they tessellate … Continue reading →

I’ve just realised, with only two minutes to go, that it’s the 136th birthday of the great mathematician Emmy Noether. Naturally, you are probably already aware of many of her contributions to mathematics and theoretical physics, including Noetherian rings and … Continue reading →

Conway and Sloane’s excellent tome, Sphere Packings, Lattices and Groups, is now due a fourth edition. Maryna Viakovska’s proofs of optimality of the E8 and Leech lattices should go in the fourth edition as well…

Over the last couple of months, I have been experimenting with the use of SAT solvers. This research recently came to fruition, with Tomas Rokicki and me announcing a new discovery with the intention of writing up the methodology in … Continue reading →

I’d like to open with congratulations to the talented students who made the leaderboard in the second round of the British Mathematical Olympiad. Some highlights worth mentioning: Three of the four team members for the European Girls’ Mathematical Olympiad made … Continue reading →

You are probably familiar with the Riemann hypothesis. This concerns the behaviour of the Riemann zeta function, which is defined on the complex plane by analytic continuation of the following series: The behaviour of the zeroes of the function outside … Continue reading →

Something amazing has happened. A couple of years ago, we closely followed the progress of AlphaGo, the distributed DeepMind algorithm which defeated Lee Sedol in four out of five games of the ancient board game Go. This has since been … Continue reading →

In the last post, we discussed Voevodsky’s homotopy type theory. One of the important notions is whether a space is contractible, this being the base case for the inductive definition of homotopy levels. It turns out that the algorithmic undecidability … Continue reading →