🏛️ Math History / Culture

Determinism (logarithmichistory​.wordpress​.com). Explores determinism, Laplace, Einstein, Gisin, chaos theory, intuitionist math, and their implications for predictability

Naming the Infinite (realphysics​.blogspot​.com). Explores the infinite in mathematics and philosophy, from Cantor to imaginary numbers, linking modern math to physics and ontology

Reaching the masses (not a Marxist post) (quomodocumque​.wordpress​.com). Six popular math authors discuss talking about math to the public, with notes on precision and dumbing down, plus an Atlantic interview about Marxist art history in math context

Six-decade math puzzle solved by Korean mathematician (koreaherald​.com). Korean mathematician Baek Jin-eon solves the moving sofa problem, confirming Gerver’s upper limit using logic and optimization, amid recognition by Scientific American

Cambridge’s Mathematical Bridge: The Quiet Intelligence of a Bridge (abakcus​.com). Explores Cambridge’s Mathematical Bridge: straight pieces forming an apparent arch, myths about Newton, and lessons in engineering intuition

🎼 Math Music FP

The Tonnetz (johncarlosbaez​.wordpress​.com). Tonnetz-inspired hexagonal grid explores rational/irrational log ratios, tuning commas, and near-periodicity in just intonation

Functors, Applicatives, and Monads: The Scary Words You Already Understand (cekrem​.github​.io). Explains functors, applicatives, and monads using Elm (Maybe, Result, List), Haskell examples, and practical code patterns

An Algebraic Theory of Music (reasonablypolymorphic​.com). Explores an algebraic approach to music using Haskell, denotational design, and functional programming concepts like Voice, Music, and T-based harmony

🧩 Puzzles Combinatorics

BrainTwister #107: Prime products (enigmaticcode​.wordpress​.com). Prime products: explore Euler-like primes with product-plus-one using Python code and prime lists

Sphinx Cryptarithm #13 (enigmaticcode​.wordpress​.com). Puzzle-based cryptarithm solving with prime and square constraints using Python-based approach

Knight’s tour with fewest obtuse angles (johndcook​.com). Knuth-era knight’s tour explores minimal obtuse angles, with a unique solution up to symmetry, by John D. Cook and Knuth

Hunting for extremal Latin squares using MaxSAT solver (yurichev​.com). Hunting extremal Latin squares with MaxSAT, LS repair, and random walk using UWrMaxSat in Python-like workflows

Menger's Horse Enclosure (buttondown​.com/jaffray). Graph theory game analysis: Menger's theorem, vertex cuts, and puzzle design notes in a browser-based horse enclosure

Overlapping rectangle puzzle (leancrew​.com). Overlapping rectangle puzzle analyzed with a per-rectangle intersection code and network-style reasoning, plus a real-world SciAm solution

🧰 Mathy Software Builds

2026 (mathr​.co​.uk). Counting hyperforests on unlabeled nodes with incidence-graph forests using C++23 and 2026 OEIS data

Contours (bit-101​.com). Generating contour lines from height maps using CONREC in Go, with path simplification and per-level styling

Some stories from developing puzlink.js (blog​.cjquines​.com). CJ Quines discusses and experiments with puzlink.js, its utilities, statistics concepts, client-side word relationships, and math ideas in a puzzle-hunt tooling project

Scaling Nektar++ to 65K CPUs on ARCHER2 (nektar​.info). Nektar++ performance on ARCHER2 using VelocityCorrectionScheme, IMEX2, AVX2, HDF5 I/O, and strong scaling from 2k to 65k CPUs

Invertible Bloom antimatroids (11011110​.github​.io). Invertible Bloom antimatroids, ready lists, and peeling sequences on invertible Bloom filters and lookups with constant-time readiness criteria

🤖 ML Theory Lenses

Robustness, interpretability, and scaling of eigenvalue models (alexshtf​.github​.io). Robustness, interpretability, and scaling of eigenvalue models using PyTorch on real data (California Housing), examining spectral bounds and feature importance

Semantic Topological Spaces (lesswrong​.com). Topological thinking on semantic spaces in neural nets; discusses projection, folding, and interpretability across input, latent, and output spaces

The Transformer as Renormalization Group Flow (symmetrybroken​.com). Transformer attention as a Bayesian RG flow: coarse-graining tokens to semantic attractors using neural networks, physics-inspired interpretation

The Physics of mHC: Why Deep Learning Needs Energy Conservation (toooold​.com). Conservation-inspired mHC uses doubly stochastic matrices and Sinkhorn iterations to build energy-conservative neural layers in Python-like reasoning

Human embeddings (trfetzer​.com). Explores human embeddings for team design using 1024D vector space, open-source embeddings, GPT-OSS, and clustering to form diverse groups

📐 Analysis Mechanics

Linkage (11011110​.github​.io). Overview of computational geometry, symplectic integrators, and graph theory topics and tools mentioned

log2(3) and log2(5) (johndcook​.com). Explores rational approximations of log2(3) and log2(5) via continued fractions and precision limits

Fourier Polynomials (pgadey​.ca). Explores Fourier Polynomials and related concepts, with notes on implementation and tools used in mathematical programming

Modelling a Spring System in Hamiltonian Mechanics (ritog​.github​.io). Model a spring system in Python using Hamiltonian mechanics, Euler and semi-implicit Euler integration, and visualize phase space trajectories

✅ Proofs Verification

Is hallucination-free AI code possible? (kucharski​.substack​.com). Explores how to verify AI-generated code using Lean proofs, code checks, and qualitative validations across gravity models and beyond

Seemingly impossible programs in Lean (joachim-breitner​.de). Lean, Cantor sequences, modulus predicates, and Escardo-inspired find in Lean with termination tricks

Proving liveness with TLA (roscidus​.com). Proving liveness with TLAPS and TLA+ Toolbox; modeling a vchan channel in Xen, using TLC, PTL, and temporal logic concepts

Comment prouver que j'ai vu la fin de la série sans te spoiler ? (newsletter​.lescryptosdecaro​.com). Zero-knowledge proofs explained via spoiler-free analogy, covering ZK-Rollups, private transactions, DID, and anonymous DAO voting

AI and Research Papers (blog​.computationalcomplexity​.org). AI disruption in academia rethinks writing, review, verification, collaboration, and LaTeX generation for research papers

🧠 Abstract Structures

The Axiom Engine: A Phenomenology of Abstract Structures (cafebedouin​.org). Phenomenology of abstract structures exploring topology, number theory, statistics, set theory, dynamics, group theory, dynamics and game theory through narrative metaphors

Coxeter and Dynkin Diagrams (golem​.ph​.utexas​.edu). Coxeter and Dynkin diagrams overview, with ADE classifications and connections to Lie theory, quivers and representation theory

Axiom J in Homotopy Type Theory (HoTT) (blueberrywren​.dev). HoTT axiom J explained via cubical type theory, using P, Sigma types, and contractibility to justify path induction in J

Polynomial towers and inverse Gowers theory for bounded-exponent groups (terrytao​.wordpress​.com). Tao, Jamneshan, and Shalom present a polynomial-tower inverse Gowers theory for bounded-exponent finite abelian groups

Anthropomorphizing the Russell paradox (infinitelymore​.xyz). Cantor’s diagonalization and Russell paradox explored via anthropomorphized proofs with Hamkins and Lex Fridman

📚 Academic Research

The least prime with a given cycle type (arxiv:math). Gives zero-free, character-theoretic bounds for the smallest unramified prime with specified Frobenius cycle type. Delivers uniform exponential-in-n exponents for S_n, sharpening Chebotarev-type results across groups

Averages of Arithmetic Functions over Conductors of Function Fields (arxiv:math). Counts regular Galois extensions of F_q(t) with fixed group and one ramified place, advancing Boston–Markin. Uses braid-group homology and braided vector spaces to compute averages

Configuration Spaces of Finite Representation Type Algebras (arxiv:math). Associates an irreducible, rationally parametrized affine variety to any finite representation type algebra. Links string integrals, Jasso reduction, and new Rogers dilogarithm identities beyond Dynkin

LeanCat: A Benchmark Suite for Formal Category Theory in Lean (Part I: 1-Categories) (arxiv:cs). LeanCat provides 100 formal category-theory tasks in Lean to measure abstraction and library reasoning. Baselines reveal large gaps; retrieval aids modestly, guiding next-generation theorem-proving systems

EternalMath: A Living Benchmark of Frontier Mathematics that Evolves with Human Discovery (arxiv:cs). EternalMath automatically converts recent research papers into executable, verifiable math problems, creating a living benchmark. Shows frontier reasoning remains unsolved for LLMs, and constantly updates