The Mathematician 18-11-2025
🧩 Puzzles & Problem Solving
A Puzzle With Sums and Factorials (cantorsparadise.com). Explores a puzzle with sums and factorials, using stars and bars, e, and differentiations to derive a general formula
My favorite math problem (bytesauna.com). Explains a mutilated chessboard problem and connects existence proofs to AI and formalization via type systems
Foresight (blog.evanchen.cc). Foresight as predicting future moves in problem solving, using lines in Hanabi and mathematical proofs to guide strategy
Tantalizer 84: Ficts and Facts (enigmaticcode.wordpress.com). A New Scientist puzzle about Muggleton players, truth-tellers and liars with a loop-logic puzzle and Python code
The Geometry Problem That Could Have Protected the French Royal Jewels (politicalcalculations.blogspot.com). Explains the art gallery problem, its 360-degree camera strategy, Fisk’s 1978 three-coloring proof, and applications to Louvre security
Midy’s Theorem (futilitycloset.com). Midy’s Theorem: even-length repeating decimals for primes yield 9s upon splitting and summing halves
📘 Expository Math & Science
mathematics (oh4.co). Prime-based foundations of natural numbers, FTA, edge cases 0 and 1, and the role of primes in arithmetic
to the early Universe and back (xianblog.wordpress.com). Observations at IAP Paris on Florent Leclercq's habilitation; cosmostatistics, forward modelling, SELFI, Simbelmynë, BOLFI, and Bayesian likelihood-free inference in cosmology
Adding an imaginary unit to a finite field (johndcook.com). Explains forming finite field extensions by adjoining i, with examples in Fp and p^2, plus Ethereum alt_bn128 using i and Python code
Monday Morning Math: Bernoulli (threesixty360.wordpress.com). Quick primer on Bernoulli generations and family tree references, with notes on naming and sources
Optimal scaling for magic state distillation in quantum computing achieved (phys.org). Phys.org reports constant-overhead magic state distillation for qubits using algebraic geometry codes, led by Adam Wills (MIT) and colleagues, Nature Physics 2025
📜 History & Biographies
From τὰ φυσικά (ta physika) to physics – LIV (thonyc.wordpress.com). Huygens’ optics work, wave theory of light, and historical debate with Newton, Pardies, and Hooke; from telescope design to the Traité de la Lumière
New Proofs Probe Soap-Film Singularities (quantamagazine.org). Mathematicians prove generic regularity for area-minimizing surfaces in dimensions up to 11, revealing when singularities can be perturbed away
Aristocratic Tutoring Cannot Explain von Neumann’s Success (greyenlightenment.com). Aristocratic tutoring, nature vs nurture, von Neumann, Manhattan Project, explosive lenses, EDVAC, and debates over genius
Meet The Shape That Cannot Pass Through Itself (hackaday.com). Rupert’s Property explored; Noperthedron, convex polyhedra limits, and 3D-printed demos with shapes passing through themselves
🧰 Computational Math Tools
Emmy, the Algebra System: Classical Mechanics Prologue (clojurecivitas.github.io). Functional differential geometry, Lagrangian mechanics, Lisp/Scheme, and programmatic reasoning in Emmy by MAK and Sam Ritchie
Simuler une planète sur GPU : Partie 1 (patrickcelentano.com). GPU compute shaders, SPH, and a C++/SDL2/Vulkan path to simulate planetary tectonics and plate dynamics
Curl of Curl. Tensor and GA expansion, and GA equivalent identity. (peeterjoot.com). Geometric algebra and tensor methods derive curl of curl identity with Levi-Civita tensors in 3D space
AI: Hyperbolic (markbernstein.org). Hyperbolic geometry in code: refactoring Tinderbox maps with DiskPoint/ScreenPoint, Claude/Gemini AI help, and Poincaré disk concepts
Experiments with THRML (madebynathan.com). Experiments with THRML: exploring THRML library, AI-assisted maze solving, DFS variants, and playful simulations using GPU prototypes
Approximating arbitrary complex-valued continuous functions (lesswrong.com). Complex-valued function approximation via uniform algebras, density operators, and tensor construction in functional analysis
💻 Theoretical CS & Algorithms
Cameron Seth is breaking down the world’s hardest CS problem piece by piece (uwaterloo.ca). Cameron Seth breaks down P vs NP using graph algorithms, sublinear-time, and approximation methods in Cheriton School of Computer Science
Sampling Permutations is Hard (emanueleviola.wordpress.com). Discusses a sampling lower bound for permutations and new techniques in sampling complexity from a collaboration including Alekseev, Göös, Myasnikov, Riazanov, and Sokolov
Toy decompiler (yurichev.com). Toy decompiler in Python demonstrates rewriting addk chains into multiplies, showing manual decompilation of Microblaze-like code
🔐 Crypto & Coding Theory
Supporting abstract algebra in MPC for threshold cryptography (techblog.rosemanlabs.com). Explores MPC for threshold cryptography using abstract algebra, class groups, xgcd, MPyC, and ZKPs
(2025-11) All Polynomial Generators Preserve Distance with Mutual Correlated Agreement (cronokirby.com). Polynomial generators preserve distance with mutual correlated agreement across linear codes and Reed–Solomon codes
(2025-11) On Reed–Solomon Proximity Gaps Conjectures (cronokirby.com). Disproves range of Reed-Solomon proximity conjectures and links correlated agreement to list decoding in cryptographic SNARKs and proof systems
🔎 Formal Proofs & Logic
Variants of Fitch Cheney’s Trick (possiblywrong.wordpress.com). Explores Fitch Cheney’s trick variants, counting arguments, bi-regular graphs, and practical schemes in math and computation
The elementary theory of surreal arithmetic is bi-interpretable with set theory, Notre Dame Logic Seminar, November 2025 (jdh.hamkins.org). Bi-interpretability between surreal arithmetic and set theory (ZFC) in a Notre Dame Logic Seminar talk
Follow up to Hintikka on the analytic/synthetic distinction - some thoughts on proof depth, logical omniscience and tractability (mynamelowercase.com). Explores Hintikka’s analytic/synthetic distinction, proof depth, and tractability via depth-bounded natural deduction and connections to computational complexity
Jaakko Hintikka on the analytic/synthetic distinction in logic and arithmetic (mynamelowercase.com). Explores analytic vs synthetic judgments in Kant, Frege, Hintikka; includes proof-theoretic approach, existential instantiation, and imagination in arithmetic reasoning
AlphaProof Paper (julian.ac). AlphaProof uses Lean, RL, and tree search to formalize IMO solutions; discusses Lean proofs, AlphaCode-inspired training, and Nature paper
🧮 Pure Math Research
Matrices map between biproducts (unstableontology.com). Biproducts in semiadditive categories explain matrices as decomposed morphisms for finite-dimensional vector spaces
Graphs defined on algebras (cameroncounts.wordpress.com). Graphs defined on algebras generalize group graphs; explores directed power, enhanced power, and related graph properties in general algebras
New Nikodym set constructions over finite fields (terrytao.wordpress.com). Terence Tao uploads arXiv paper on Nikodym sets over finite fields using AlphaEvolve, DeepThink; discusses constructions, probabilistic methods, and surface removals
Linkage (11011110.github.io). Overview of lattice path matroids, with notes on accessibility, origami, and related mathematical topics and figures
Updated paper: Moduli spaces of semiorthogonal decompositions in families (pbelmans.ncag.info). Update on moduli spaces of semiorthogonal decompositions in families; smoothing assumptions and étale descent in a smooth, proper setting
📚 Academic Research
Eigenvalues of Brownian Motions on $\mathrm{GL}(N,\mathbb{C})$ (arxiv:math). Resolves Biane's conjecture: empirical eigenvalue law of Brownian motion on GL(N,C) converges to a deterministic free-probabilistic measure. Major advance in random matrix theory
A number-theoretic conjecture implying faster algorithms for polynomial factorization and integer factorization (arxiv:math). Proposes a number-theoretic conjecture enabling distinct-degree polynomial and integer factoring algorithms faster than n^3/2, potentially n^4/3. Huge implications for computational number theory
Connecting conformal dimension and Poincaré profiles (arxiv:math). Links Ahlfors-regular conformal dimension to Poincaré profile exponents, proving equality for product and Heintze cases. Provides new embedding obstructions in geometric group theory
On a generalisation of Cameron's base size conjecture (arxiv:math). Completes proof generalizing Cameron's base-size conjecture: almost simple groups have regular orbits for ≥7 core-free non-standard maximal subgroups (≥6 with one exception). Powerful group-theoretic result