The Mathematician 12-11-2025
new math puzzles, historical mathematical insights, computational projects
𧩠Puzzles & Recreational Math
Tantalizer 83: Arcadia (enigmaticcodeâ.wordpressâ.com). Arcadia map puzzle: intersecting circles and parity colouring; 2-colour solution; discussion of boundaries, 4-colour theorem relatives, on plane and torus; mentions New Scientist 1969 and Platoan politics
BrainTwister #98: Sâ P numbers (enigmaticcodeâ.wordpressâ.com). Explore Sâ P numbers where digits are nonzero, summing and multiplying to equal the number, with Python examples and puzzle variants
Inquiries-Week 5: Triangles Emerge (fractalkittyâ.com). Explore triangle-free edge limits on small graphs using node connections, with even/odd n, and conjectures in a hands-on planning tool
Hanoi graphs redrawn (11011110â.githubâ.io). Center-of-mass layout for Hanoi graphs reveals disk-move relations and Hamiltonian paths across multiple pegs
Mesmerizing Marble Runs from Procedural Generation (hackadayâ.com). Procedurally generated marble runs using Python, OpenSCAD, and a motorized screw for return, by Will Morrison
đ History & Biographies
Netzâs false claims about Kuhn (intellectualmathematicsâ.com). Critiques Netzâs claims on Kuhn and KoyrĂ©, comparing asserted errors with actual quotations and context in Copernican Revolution
I reviewed a book about the math foundations crisis for the New York Times (quomodocumqueâ.wordpressâ.com). Review of a math foundations book for the New York Times; critique of prose, clarity, and Cantorâs continuum concepts
The most beautiful wrong equation in history (1841) (skullsinthestarsâ.com). Explores Mayer's 1841 ideas on conservation of energy, his âmost beautiful wrong equation,â and the historical context with Joule, Poggendorff, and Tyndall
Monday Morning Math: Happy Birthday dy/dx! (threesixty360â.wordpressâ.com). 350th birthday of the dy/dx notation; Leibniz in Paris, derivatives, product and quotient rules investigation
The last of the magicians (logarithmichistoryâ.wordpressâ.com). Debunks Newtonian humility quotes, frames Newton as last of magicians; discusses heliocentrism origins, Hermes Trismegistus, and rise of modern science
The Manuscripts of Edsger W. Dijkstra (csâ.utexasâ.edu). Overview of E. W. Dijkstra Archive, EWD manuscripts, indexing, translations, and related events and memorials
đ» Computational Projects
TomoSphero (githubâ.com). PyTorch raytracer in spherical coordinates; demonstrates 3D/4D volume raytracing with examples and memory usage analysis
RotMG map seeds (redblobgamesâ.com). RotMG map seeds explored using Voronoi-based generation; Rust reconstruction, Flash-to-Rust reimplementation, and seed matching
Bit counting and geometric series (veitnerâ.bearblogâ.dev). Bit counting using x & (x-1) and popcnt; C, inline assembly, and GCC builtins discussed
The shadows lurking in the equations (godsâ.art). FuzzyGraph visualizes equations in non-binary mode, revealing shadows, black holes, and near-solutions ignored by conventional graphs
DubHacks 2025 (byronsharmanâ.com). Seatt le DubHacks 2025: a Dynamicland-inspired tabletop Desmos, ArUco markers, Typst PDFs, real-time graphing, and judge-led demos
đ€ AI & Formalization
The (near) Future of AI in Math (blogâ.georgeshakanâ.com). AI, Lean formalization, tooling, and software engineering shape future mathematical research
Mathematical exploration and discovery at scale (terrytaoâ.wordpressâ.com). Terence Tao and collaborators use AlphaEvolve (Google DeepMind) to evolve code for solving high-dimensional math problems in analysis, combinatorics, geometry, with Python, Lean proofs, and insights on conjectures
Implementing E Unification using SMT (philipzuckerâ.com). Explores E-unification with SMT solvers (Z3), propagation, anti-unification, and miniKanren style ideas in Python
To Have Machines Make Math Proofs, Turn Them Into a Puzzle (quantamagazineâ.org). Marijn Heule uses SAT solvers and LLM-guided encodings to turn math problems into puzzles, enabling automated reasoning and Lean-verified proofs
Building an AI Mathematician with Carina Hong - #754 (twimlaiâ.com). Carina Hong discusses building an AI Mathematician using Lean, LLMs, and code generation for autoformalization and self-improvement
An ARENA 6.0 Capstone: Model Organism of Encoded Reasoning (lesswrongâ.com). ARENA 6.0 capstone using RL on Qwen-3-4B to study encoded reasoning in GSM8K math CoTs with judge models, toxicity signals, and RL challenges
đŹ Logic, Theory & Complexity
Tree-eval, catalytic computation, simulating time with square-root space (emanueleviolaâ.wordpressâ.com). Tree evaluation and catalytic computation show how to simulate time on multi-tape machines using square-root space and circuit transformations by CM24, Wil25, Sha25
The Inverse Cube Force Law (johncarlosbaezâ.wordpressâ.com). Explores Newtonâs inverse cube force, centrifugal effects, Cotes spirals, and quantum scaling phenomena in classical and quantum contexts
November: The leisurely tour of SIST continues (errorstatisticsâ.com). Leisurely tour of SIST explores N-P and Fisherian tests within Severe Testing framework (SIST) and includes LSE seminars, slides, and video
Comparing Payor & Löb (lesswrongâ.com). Löbâs theorem vs Payorâs lemma explored for trust, belief, and reliability in logic-based decision procedures
đ Pure Math Deep Dives
The determinant of transvections (freedommathdanceâ.blogspotâ.com). Transvections over rings: determinants, proofs via fractions and generic cases in linear algebra
Circular Sorting (anuragbishnoiâ.wordpressâ.com). Explores circular sorting on a circle, affine permutations, strong complete mappings, and counterexamples via quadratic orthomorphisms with primes and wreath-product constructions
Japanese polygon theorem (johndcookâ.com). Explores Japanese cyclic polygon theorem with Python illustrations of incircles in triangulations
Analog of Heronâs formula on a sphere (johndcookâ.com). Spherical triangle area from side lengths using LâHuilierâs formula, with small-triangle sanity checks on a unit sphere
Umbral Calculus (hedonisticlearningâ.com). Umbral calculus overview: formal power series, Sheffer sequences, APPell families, and Bernoulli polynomials in a math-focused exposition
đ Academic Research
Ideals, Gröbner Bases, and PCPs (arxiv:cs). Introduces a Gröbner-basis PCP framework yielding the first one-step proof of the PCP theorem. It simplifies constructions, links algebraic geometry to complexity, reshaping approximation hardness
Complexity of counting points on curves and the factor $P_1(T)$ of the zeta function of surfaces (arxiv:math). Certifies curve point-counts and surface P1 zeta factors in AM â© coAM, with poly(log q)-time for fixed-degree surfaces. Bridges algebraic geometry with complexity theory deeply
On the gradient of the coefficient of the characteristic polynomial (arxiv:math). Proves a bivariate CayleyâHamilton theorem generalizing the classical result and deriving gradient identities. Produces smaller ABPs for determinant, significantly advancing algebraic complexity theory
Infinitely many primes of basic reduction for some abelian fourfolds (arxiv:math). Extends Elkies' supersingular-primes result to a DeligneâMostow genusâ4 family, proving infinitely many primes of basic reduction for associated Jacobians. Uses Shimura curves, CM cycles, equidistribution
There is no universal separable Banach algebra (arxiv:math). Shows no separable (commutative) Banach algebra is universal for embeddings, resolving a natural universality question. Employs tensor-product linearizations and JohnsonâSzankowski embedding theorem