The Mathematician 04-11-2025
reflections on math history, AI methodologies, computational projects, discrete math
📜 Math History, Biography and Reviews
Monday Morning Math: The Scottish Book (threesixty360.wordpress.com). Scottish Book's 90-year math lore from Lwów Café, Banach, Mazur, Enflo, Tao, and Ulam to modern puzzles and accolades
Rodney Baxter (1940-2025): Mathematical Physicist (condensedconcepts.blogspot.com). Rodney Baxter (1940-2025) renowned for exact solutions of 2D lattice models; connections to BKT, Yang-Baxter, and knots
Did Euclid exist? Is it okay to quote people that did not exist? (blog.computationalcomplexity.org). Explores Euclid's existence, attribution of the quote, and historical evidence via Proclus and other sources, with ChatGPT role in verification
The Man from the Future: The Visionary Ideas of John von Neumann (olshansky.info). Brief critique of a Von Neumann biography, highlighting strong early chapters and a tedious Manhattan Project timeline
Robert Hooke's "Cyberpunk” Letter to Gottfried Leibniz (mynamelowercase.com). Hooke and Leibniz, cybernetics precursors, explore a universal language for science and a hacker ethos in 17th century natural philosophy
🧠 AI, Methodology & Tools
I have met the LLMs, and they are us (pandoricity.com). Explores intuition in math, parallels with LLM outputs, memory, time, and considering humanity vs. AI in a reflective blog
Marshall on the use of mathematics in economics (larspsyll.wordpress.com). Marshall endorses mathematics as a shorthand tool for economics, warns against overreliance, and advocates translating math into English with real-life examples
scenario discovery (studium.dev). Scenario discovery, uncertainty theory, and high-dimensional data insights with links to slides and theory sources
Live Conversational Threads: Not an AI Notetaker (lesswrong.com). Explores Live Conversational Threads (LCT) for marking and porting insights into contextual formalisms; discusses live theory, post-rigorous thinking, and AI-assisted tooling
🛠️ Computational Projects
Other wavy paths (leancrew.com). Sinusoidal and circular wavy paths along roads; numerical integration and Mathematica code to compute path lengths for a 5 km race
Building a Rules Engine from First Principles (towardsdatascience.com). Lightweight rules engine using sparse truth-table representation and state algebra with t-objects, vector-logic library, and transitivity proofs
Procedural storytelling (blog.kenperlin.com). Procedural storytelling uses live interactive demos to teach computer graphics concepts and algorithms through a narrative-driven magic-show style
🧮 Discrete Math & Combinatorics
Graph Paper Lindenmeyer Systems (blog.giovanh.com). Graph Paper Lindenmeyer Systems use Chebyshev geometry to generate hand-drawn L-systems on grid paper with a custom, recursive JavaScript implementation
Depth-first Unary Degree Sequence (bruceediger.com). Explores DFUDS (Depth-first Unary Degree Sequence) for representing higher-degree trees, ordinal vs cardinal, with Lisp-like encodings and related Dyck words
A Laser-Cut Tromino Puzzle (divisbyzero.com). Induction puzzle on tiling a 2n x 2n grid with trominoes; Dave Richeson explores laser-cut puzzle experiments and proofs
Character Study (futilitycloset.com). Tic-tac-toe impossibility puzzle; exploration of move counts and win conditions from Paul Hoffman’s puzzle in Science Digest
Presentations of avoiding transversal (q-)matroids (matroidunion.org). Discusses avoiding transversal (q-)matroids, presents minimal/maximal presentations via cyclic core, with examples and Saaltink conjecture proof
📐 Geometry & Topology
What Is a Manifold? (quantamagazine.org). Manifolds reshape geometry and physics, explaining how shapes look flat locally and form the backbone of relativity, topology, and data analysis
topology (aarnphm.xyz). Evergreen topology study anchored on Munkres and MIT 18.901, linking π1 and H1 concepts to Perelman’s Poincaré roadmap
Tetrahedral analog of the Pythagorean theorem (johndcook.com). Tetrahedral De Gua theorem illustrated with Python, NumPy code, and higher-dimensional generalizations by John D. Cook
An ancient generalization of the Pythagorean theorem (johndcook.com). Apollonius's theorem generalizes Pythagoras for any triangle using midpoints and the median, with m and h defined as AD and CD respectively
⚛️ Mathematical Physics
Second Quantization and the Kepler Problem (golem.ph.utexas.edu). Explores Kepler problem, hydrogen atom via Einstein universe, SO(4) symmetry, L2(S3), and second quantization with spin-½ particles
A fun application of Green’s functions and geometric algebra: Residue calculus (peeterjoot.com). Green’s functions for the 2D gradient and geometric algebra yield a Cauchy integral form using complex-number-like even multivectors
potts model (studium.dev). A concise overview of Potts model insights with links to Wikipedia, including notes on changes and authorship
🧩 Proofs, Logic & Formalization
"Why don't you use dependent types?" (lawrencecpaulson.github.io). Reflections on dependent types, AUTOMATH, Martin-Löf type theory, Isabelle, Lean, and the practical trade-offs in proof engineering
Another way of doing big O notation (alok.github.io). Explains Big O via nonstandard analysis: checking infinitesimal/unlimited ratios with hypernaturals and transfer
Isabelle/ML starting tips (edoput.it). Isabelle/ML tips for productive extension of Isabelle: navigation, incremental debugging, and exploring HOL/ML code
What is your number? Logic puzzles for mathematicians – 2025 DePrima Memorial Lecture, Caltech (jdh.hamkins.org). Caltech talk by Joel David Hamkins on logic puzzles, infinity, and computational themes in mathematics
📚 Academic Research
The Skolem Problem in rings of positive characteristic (arxiv:math). Decides the Skolem problem for linear recurrences over finitely generated commutative rings of positive characteristic. Gives algorithms and zero-set structure, impacting arithmetic dynamics and computation
A Deep Learning Framework for Multi-Operator Learning: Architectures and Approximation Theory (arxiv:math). Introduces architectures and theory for neural learning of families of operators. Proves universal approximation and scaling laws, validated on parametric PDEs for efficient computation workflows
The Oka principle for tame families of Stein manifolds (arxiv:math). Establishes an Oka principle for continuous families of Stein manifolds under tameness. Gives Oka–Weil results and nontame counterexamples, advancing complex geometry and deformations of structures
Wiener-Pitt sets for compact Abelian groups (arxiv:math). Proves strongly continuous measures with rapidly decaying Fourier spectra avoid Wiener–Pitt pathology on compact Abelian groups. Convolution becomes absolutely continuous, strengthening harmonic analysis foundations significantly
Rigidity and flexibility results for groups with a common cocompact envelope (arxiv:math). Studies property transfer between finitely generated groups with a common cocompact envelope. Proves rigidity for solvable finite-rank cases and surprising flexibility, influencing quasi-isometry classifications theory
✨ Before you go...
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Thanks a million, and have a great week! Alastair.