Author Archives: apgoucher

Complexity of integer multiplication almost solved

Whilst not quite as close as the proofs of the ternary Goldbach conjecture and bounded gaps between primes, there has been a quick succession of two important and somewhat complementary breakthroughs on the computational complexity of integer multiplication: Afshani, Freksen, … Continue reading

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Fully self-directed replication

A new form of artificial life has been born — and there are no doubts that it directs its own self-replication: So, what exactly is happening? At 0:06, the organism begins to sequentially construct four identical copies of itself. At … Continue reading

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6-colourings of subsets of the plane

There has been further recent activity on the Chromatic Number of the Plane problem, with an eleventh research thread being spawned. Philip Gibbs has been able to 6-colour a large disc (with diameter slightly greater than 4), and Aubrey de … Continue reading

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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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