Author Archives: apgoucher

Atiyah’s problem

At the Heidelberg Laureate Forum three years ago, I took lots of selfies with Fields medallists, Abel prizewinners and Turing laureates. This included having a dinner in a castle with Leonard Adleman, pioneer of asymmetric cryptography: …and Endre Szemeredi of … Continue reading

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Sorting networks

Important note: whenever log is mentioned in this particular post, it is referring to the ceiling of the base-2 (binary) logarithm. (Elsewhere on cp4space, when there isn’t this disclaimer, it refers to the base-e (natural) logarithm.) For reasons that shall soon become … Continue reading

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Eurozone’s Lemma

David Davis has proposed two geopolitical ideas: For Northern Ireland to have dual EU/UK status; For there to be a 10-mile ‘trade buffer zone’ between Northern Ireland and the Republic of Ireland. The second is more interesting from a mathematical … Continue reading

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Royal Wedding and Polymath16

Congratulations to Meghan Markle and Prince Harry on what is undoubtedly the most energetic Royal Wedding! In other news, following on from Aubrey de Grey’s 5-chromatic unit-distance graph, there has been an effort to study the algebraic structure of the … Continue reading

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Assorted news

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

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Cubical Type Theory

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

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Diamonds

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

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