The Mathematician newsletter
đ History and Philosophy of Mathematics & Science
John von Neumann: Computer Wizard and AI Visionary (thatsmathsâ.com) . John von Neumannâs foundational work on computer architecture, quantum foundations, and early AI foresight highlighted alongside the ENIAC and weather forecasting
From Ïᜰ ÏÏ ÏÎčÎșÎŹ (ta physika) to physics â LII (thonycâ.wordpressâ.com) . Descartes' physics and cosmology: corpuscular mechanics, motion laws, vortices, and comparisons with Beeckman, Huygens, Newton
Galileo's Children (realphysicsâ.blogspotâ.com) . Bellarmine's caution on heliocentrism; Galileo's math vs natural philosophy; critiques of scientific certainty and later proofs like Foucault's pendulum
Sir Harold Jeffreys Graces the Cover of âDe Psycholoogâ (bayesianspectaclesâ.org) . Jeffreys' odd-even number hypothesis linked to masculinity and femininity, presented via Bayesian inference context in De Psycholoog cover
Bertrand Russell to Oswald Mosley (1962) (lettersofnoteâ.com) . Bertrand Russell rejects Oswald Mosley with moral opposition to fascism and bigotry
đŹ Applied Math in Science and Engineering
Seminar on Mathematical General Relativity â 2025â2026 (philippeleflochâ.org) . Geometric boundary conditions for asymptotically Anti-de Sitter spaces and stability results for Einstein-Maxwell-scalar-Vlasov systems
Global epistasis emerges from a generic model of a complex trait (or: random walks on a hypercube with reweighting) (quomodocumqueâ.wordpressâ.com) . A simple model of evolution using 2^n genotypes on a hypercube with fitness polynomial and reweighting dynamics
Discovering new solutions to century-old problems in fluid dynamics (deepmindâ.google) . New AI-assisted method using Physics-Informed Neural Networks to discover unstable singularities in IPM and Boussinesq fluid equations
New AI Technique Unravels Quantum Atomic Vibrations in Materials (caltechâ.edu) . Caltech AI method speeds up phonon interaction calculations for thermal transport by compressing high-order tensors via CANDECOMP/PARAFAC decomposition
đ Geometry, Projections, and Recreational Math
Strogatz, the NYT, and Taxicab Geometry (mrhonnerâ.com) . Strogatzâs Taxicab geometry explored for teaching, including pi=4, Manhattan metric, and classroom prompts
A Tetrahedron That Always Lands on the Same Side (politicalcalculationsâ.blogspotâ.com) . Explains a monostable tetrahedron that always lands on a chosen face and references Matt Parker and Quanta Magazine coverage
Mollweide map projection and Newtonâs method (johndcookâ.com) . Explains Mollweide equal-area projection, solving theta(phi) with Newtonâs method, its convergence issues near phi = pi/2, and a proposed improvement approach
Mental math posts (johndcookâ.com) . Mental math collection covers divisibility, day-of-week rules, logarithms (base 2, e, 10) and their inverses, trig functions, roots, and the gamma function with approximate methods
đ§ Formal Methods, Proof Assistants, and Research Practice
Who (or what) could have written a better book? (noncommutativeanalysisâ.wordpressâ.com) . Technion graduate course FA textbook The Analyst's Gambit; author Orr Shalit discusses motivation, publishing, and AI obsolescence concerns
Isabelle/HOL rule musings (blueberrywrenâ.dev) . Explores Isabelle/HOL rule tactics: rule, erule, drule, frule, and _tac variants with examples and meta-forall handling
Everything you know is wrong (lawrencecpaulsonâ.githubâ.io) . Historical overview of AI's evolution: symbolic AI, PROLOG/ML, DPLL/resolution, expert systems, and higher-order logic verification
Proof Certificates (acornproverâ.org) . Proof certificates for Acorn 0.1 explain step-by-step proofs as minimal JSONL, enabling fast validation and future AI experimentation
What is "PhD-Level Intelligence"? (blogâ.computationalcomplexityâ.org) . Discussion of what constitutes PhD-level intelligence for LLMs, focusing on understanding research papers and oral exams as benchmarks
We can find more papers on the web than we used to. Are we reading them? (blogâ.computationalcomplexityâ.org) . Explores how researchers find and read mathematical papers online, vs. older library methods, and outlines a personal workflow
System Instruction Fixed Point (funcallâ.blogspotâ.com) . Explores fixed-point iterations on system instructions to self-improve prompts, via iterative refinement, on a Lisp analysis prompt
𧟠Computational Linear Algebra & Numerical Methods
GaussâSeidel visually explained (wordsandbuttonsâ.online) . Gauss-Seidel visualized: iteration geometry, convergence conditions, and impact of row swapping on solving linear systems
Think Linear Algebra (allendowneyâ.com) . Think Linear Algebra explores code-first approaches to linear algebra, with chapters on PageRank, 2D graphics transforms, LU decomposition, null space, and truss analysis
Notes on Solving Math Equations in Python with SymPy and Todayâs LLMs (wasi0013â.com) . Using SymPy for symbolic solving, inequalities, ODEs, and systems, augmented by todayâs LLMs for explanation and code generation
Rayleigh quotient (aarnphmâ.xyz) . Rayleigh quotient for Hermitian matrices, eigenvalue bounds, eigenvectors, and Lagrangian formulation with extensions to covariance, generalized and two-sided forms
𧩠Pure Mathematics: Theorems and Number Theory
The Malgrange preparation theorem (alanrendallâ.wordpressâ.com) . Malgrange preparation theorem for smooth functions: division, polynomial form, and relation to Mather division; Fourier approach and local holonomic structure
Two Number Theory Items (and Woody Allen) (mathâ.columbiaâ.edu) . Two number theory items and reflections on Mochizuki, IUT, and â-loops in a post by Peter Woit
Polynomial Bounds for Chowlaâs Cosine Problem (gilkalaiâ.wordpressâ.com) . Polynomial bounds for Chowlaâs cosine problem via spectral graph theory and Hadamard products
Grokking Fermat's last theorem (srikuâ.org) . Grokking Fermat's last theorem with a hand-wavy digit-count intuition and a nod to n=3 case
đ Academic Research
Split Lemma and First Isomorphism Theorem for groupoids (arxiv:math) . Split Lemma, First Isomorphism Theorem, and crossed products in groupoids; universal kernels and semidirect products
Matchings in Matroids over Abelian Groups, III (arxiv:math) . Matroid theory meets group matchings: base matchings, paving matroids, hyperplane-nullity, and additive structure in abelian groups
Mayer--Vietoris sequences for complexes of tori (arxiv:math) . MayerâVietoris sequences for complexes of tori in patching, with crossed modules, six- to nine-term exact sequences
Invariant Rings of $ \mathbb{G}_{a} $-Representations are not always Finitely Generated in Positive Characteristic (arxiv:math) . Weitzenböck conjecture in positive characteristic; Mukai-style counterexample using six-dimensional G(a)-representation and Cox ring
Zero-cycles on varieties over a $\mathfrak{B}_s$-field (arxiv:math) . Divisibility of Chow groups on varieties over B_s-fields; Milnor K-theory, Milnor K_s^M, and Kato homology applications