The text discusses the history of a unique computer built in 1960 by Charles L. Corderman, referred to as a 'PDP-3', 'PDP-2½', or 'CASINO'. It was used to discover the switch engine in 1971, the basis of infinite-growth patterns i...
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The post explores the construction of a 'minimal' infinite threeld, which embeds into every infinite field with this property. It describes an explicit construction of such a field, where every element other than 0 or 1 is transce...
The text discusses the existence of finite phoenix oscillators in Conway's Life, proving that all known finite phoenices have period 2. It also explains the computer-assisted proof of the non-existence of finite phoenices of any p...
The text discusses the discovery of a new aperiodic monotile called Spectre, the omniperiodicity of Conway's Game of Life, and the progress in engineering a 'diehard' in a cellular automaton. It also mentions the plans to build se...
Aperiodic monotile discovered by David Smith, Joseph Myers, Craig Kaplan, and Chaim Goodman-Strauss. The monotile tiles the plane by rotations and reflections but cannot tile the plane periodically. The tiling induced by the monot...
The text describes a prime p and its properties, which are useful for computing number-theoretic transforms over the field. It also discusses the Osmiumlocks prime, a larger cousin of the Goldilocks prime, and its mathematical pro...
The text discusses a recent talk about the project to search for optimal Boolean chains for all equivalence classes of 5-input 1-output and 4-input 2-output functions. The talk was not recorded, but the slides and transcript are i...
The text introduces a new family of axis-aligned n-dimensional polytopes, with vertices identified with ordered partial partitions of {1, …, n}. It describes the polytope's geometric description, combinatorial structure, and highe...
The paper establishes new bounds on the tensor rank of the determinant over various fields. It introduces a new formula for the determinant, provides tighter upper bounds in fields of characteristic p, and presents two independent...
The post discusses various algorithms for 4-by-4 matrix multiplication, including those by DeepMind's AlphaTensor, Winograd, Smirnov, Coppersmith-Winograd, and Virginia Vassilevska Williams. It also highlights the significance of ...