The Mathematician: 30th September 2025

The Prehistory of Computing, Part II (oranlooney​.com). Explores Pascaline carry mechanism, Leibniz stepped reckoner, Chebyshev approximations, Difference Engine, Babbage, Ada Lovelace, and polynomial methods in computing history

Book review: If I Am Right And I Know That I Am, by Hanne Strager (carvehername​.org​.uk). Inge Lehmann's life and seismology career, charted against early 20th-century attitudes toward women in mathematics

Monday Morning Math: Kathleen Timpson Ollerenshaw (threesixty360​.wordpress​.com). Kathleen Timpson Ollerenshaw: deaf mathematician, Oxford alumna, Shirley Institute statistician, Rubik’s cube solver, magic squares pioneer, Manchester lord mayor, dame commander

Charles Whitwell – A credit to his master (thonyc​.wordpress​.com). English engraver and instrument maker Charles Whitwell (c.1568–1611), apprentice to Augustine Ryther, contributed maps, sundials, and mathematical instruments used by Dudley and others

Clyde Kruskal talks about his Father Martin on Martin's 100th birthday (blog​.computationalcomplexity​.org). Clyde Kruskal honors his father Martin Kruskal on his 100th birthday, detailing his esoteric and influential contributions in random mappings, chess-playing computer history, Delphi, Kruskal Count, surreal numbers, alpha-beta search, and early public-key cryptography

Cantor Dirac Erdös Fermi Graham Higgs (blobthescientist​.blogspot​.com). Tony Padilla's Fantastic Numbers and Where to Find Them, Cantor's infinity, random data critique, and a cheeky data sanity check

Hobby Hilbert Simplex (nedbatchelder​.com). Explores Hobby curves, Hilbert sorting, and simplex noise for generative swoopy art using Python, Kotlin, and open-source tools

Sparking joy (leancrew​.com). Explores Harshad numbers, Mathematica implementations, and performance of HarshadNumberQ vs. custom code

Strogatz, the NYT, and the Golden Ratio (mrhonner​.com). Explores the golden ratio through Strogatz’s Math, Revealed essays and its connections across algebra, geometry, calculus, and even dentistry

Road Trip (futilitycloset​.com). A Swedish Mathematical Contest problem about road geometry: distances, collinearity, and a right triangle solution

Conway’s pinwheel tiling (johndcook​.com). Conway's right triangle 1:2:√5 is subdivided into five similar triangles to yield an aperiodic pinwheel tiling of the plane

A 3×3 Panmagic Square (futilitycloset​.com). Panmagic 3×3 square by Lee Sallows with corner-tile property and tiling variant details

On brushing up math again (piyushgupta​.xyz). Notebook-warmups in linear algebra and calculus via 3Blue1Brown, Gilbert Strang, Math Academy, MA, and LLMs like Gemini 2.5 Pro

Virtual 1D index for 2D coordinates (ashwiniag​.com). Understanding 1D index mapping to 2D coordinates with division and modulo using a 4x3 grid example

Applied introduction to Categorical treatment of CuTe (veitner​.bearblog​.dev). Explores categorical treatment of CuTe Layouts using morphisms, composition, projections, expansions, and coalesced maps with Python CuTe tooling

GSoC 2025: Bfloat16 in LLVM libc (blog​.llvm​.org). GSoC 2025 explores implementing bfloat16 in LLVM libc with generic, correctly rounded math functions like fabsbf16 and fmaxbf16

Orb: On the Movements of the Earth (2024) (michal​.sapka​.pl). Orb discusses movements of the Earth and related topics with technical insights and historical context

Eulerian Melodies: Graph Algorithms for Music Composition (towardsdatascience​.com). Graph algorithms for music composition using Eulerian paths, de Bruijn graphs, and Python tooling (NetworkX, MIDI, FFmpeg, FluidSynth)

How factoring equality polynomials optimizes sumcheck (blog​.lambdaclass​.com). Optimizing Sumcheck via factoring equality polynomials, block partitioning, SmallValues and precomputed accumulators (BDDT, Gruen)

Proving the Infinitude of Primes in Knuckledragger (philipzucker​.com). Knuckledragger proof sketch of Euclid’s theorem for infinite primes using Z3/KD kernel, primes, divisibility, and factorials

The QMA Singularity (scottaaronson​.blog). Scott Aaronson and Freek Witteveen study black-box amplification limits in QMA with a quantum oracle separation and AI-assisted proof ideas

the Harvard and Brown school of computer science (xianblog​.wordpress​.com). Harvard-Brown school contrasted with LeCun's neural nets, using Bayesian inference and Markov random fields for pattern learning

I gave a talk about machine learning and math (quomodocumque​.wordpress​.com). Talk on machine learning and math, with slides, a CMSA Big Data conference session, and discussion of generating mathematical material using ML

Quoting Scott Aaronson (simonwillison​.net). Freek and I could’ve solved the problem, but AI-assisted iteration helped refine a potential approach

The ATLAS of Finite Groups is sound (thehighergeometer​.wordpress​.com). Breuer–Malle–O’Brien papers confirm ATLAS data sound; Monster subgroup work completed, supporting independent verification of finite group character tables

Dror Bar-Natan and Roland Van der Veen – A Fast, Strong, and Fun knot invariant! (gilkalai​.wordpress​.com). Bar-Natan and Van der Veen present a fast, strong knot invariant with a hexagonal QR-code-like visualization and traffic-rule interpretation

Surjective map from affine space (math​.columbia​.edu). Two examples of surjective, quasi-finite flat morphisms from affine space to projective and affine varieties

The ABC Conjecture Has Probably Not Been Proven (dispatchesfromturtleisland​.blogspot​.com). Mochizuki's IUT critiques and Scholze–Stix debate question the purported abc proof

An inverse problem for the quadratic equation (johndcook​.com). Inverse problem for quadratics: find small integer coefficients given a real root using PSLQ and LLL algorithms

New math revives geometry's oldest problems (quantamagazine​.org). Young algebraic geometry methods and motivic homotopy theory revive enumerative geometry across complex, real, and novel number systems

Semigroup rings and algebraically independent sequences with respect to idempotents in commutative semigroups (arxiv:math). Generalizes d(S,R) for commutative periodic semigroups; bounds and exact results for Clifford, Archimedean, and elementary semigroups; zero-sum invariants in semigroup algebras

Complex Lies, Real Physics: The Role of Algebra Complexification (arxiv:math). Explores complexification of Lie algebras, irreducible representations of the proper Lorentz group, and physical content via (j1,j2) pairs

An upper bound for the size of the ideal class monoid (arxiv:math). Upper bounds for ideal class monoids and class numbers via local orbital integrals and Minkowski bounds

Rings of non-commutative functions and their fields of fractions (arxiv:math). Semifirs from analytic NC functions in noncommuting variables; universal skew fields of fractions; NC meromorphic expressions; domain evaluations in C*-algebras

Infinitely many groups exhibiting intermediate growth in maximal sum-free sets (arxiv:math). Bounds and growth of maximal sum-free sets in finite abelian groups; intermediate growth and container methods

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