The Mathematician newsletter
📜 History of Mathematics and Its People
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
🎲 Recreational Math, Puzzles, and Math Art
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
🛠️ Applied Math, Computation, and Study Notes
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)
⚛️ Quantum, Complexity, and AI-Assisted Proofs
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
🧠 Pure Math: Groups, Geometry, and Conjectures
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
📚 Academic Research
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