Category Archives: Uncategorized

Atiyah’s problem

Posted on September 21, 2018 by apgoucher

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

Posted on July 14, 2018 by apgoucher

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

Posted on June 1, 2018 by apgoucher

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

Posted on May 19, 2018 by apgoucher

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

Posted on April 15, 2018 by 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 →

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Cubical Type Theory

Posted on April 9, 2018 by apgoucher

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

Posted on April 9, 2018 by apgoucher

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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Happy Noethday

Posted on March 24, 2018 by apgoucher

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 →

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Serge Vlăduţ : Lattices with exponentially large kissing numbers

Posted on March 12, 2018 by apgoucher

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…

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A rather satisfying winter

Posted on March 11, 2018 by apgoucher

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 →

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