🏛️ Math History & Culture

Mesopotamian Botanical Motifs May Represent Early Mathematical Thought (archaeology​.org). Halafian pottery depicts floral motifs with petal counts in geometric progressions, suggesting early mathematical thinking

Markov Chain - Russian Math Feud That Now Predicts Your Life (brajeshwar​.com). Markov chains, probability, and next-word prediction traced from Pushkin to Google PageRank and modern NLP tools

Ego in Arcadia (bristoliver​.substack​.com). Explores time-travel, science history, chaos theory, and Archadia's portrayal; discusses Einstein, Lovelace, Shannon, Stoppard, and the role of technology

🎨 Puzzles & Visual Math

Partridge Puzzle (tunbury​.org). Explores OCaml's Combine library (Dlx, Zdd, EMC, tiling) with example code and Advent of Code, Matt Parker, SAT, DLX, and tiling puzzles

New Gozinta Boxes Trick (blog​.tanyakhovanova​.com). Gozinta boxes trick: nested cuboids, rotation, and six possible nesting orders explored by Tanya Khovanova and STEP students

Mathematical Objects: Slice of pizza (aperiodical​.com). A conversation about mathematics inspired by a slice of pizza, featuring Katie Steckles and Peter Rowlett, exploring Gaussian curvature and pizza-related puzzles

Drawing Truchet tiles in SVG (alexwlchan​.net). Drawing Carlson Truchet tiles in SVG using parametric templates and random tiling in JavaScript

🔢 Number Theory Curios

The unreasonable deepness of number theory (lesswrong​.com). Explores Dirichlet primes, Euler’s proof, and how complex analysis reveals deep links to number theory

The Angelakos Prime Spiral: A New Way to Visualize Prime Numbers? (vyruss​.org). Explores prime visualization via a square-spiral using Python/matplotlib to depict prime gaps and monotonic prime sequence

Day 22 – Numerically 2026 Is Unremarkable Yet Happy (raku-advent​.blog). Raku Advent Calendar analyzes 2026 as a semiprime and happy number using Math::NumberTheory, primitive roots, and D3 visualizations in Raku

Multiples with no large digits (johndcook​.com). Curious theorem: for any N not multiple of 10, a multiple of N contains only digits 1–5 in base 10; generalizes to base b with digits 1–b/p

🔐 Crypto, ZK & Quantum

Shipping an L1 zkEVM #2: The Security Foundations (blog​.ethereum​.org). Security foundations for real-time zkEVMs, aiming 128-bit provable security with soundness proofs, milestones, and soundcalc integration

Faster practical modular inversion (purplesyringa​.moe). In Rust, Lemire-inspired Stein-like optimizations for modular inversion, GCD, 64-bit handling, and SWAR techniques with references to Pornin and Yuki

More on whether useful quantum computing is “imminent” (scottaaronson​.blog). Scott Aaronson surveys quantum computing progress, Q2B talks, cryptography urgency, and public commentary dynamics

TBR #300: Quantum Computing (thebitcoinroll​.substack​.com). Quantum computing threats to ECDSA in Bitcoin wallets; P2PKH vulnerability, quantum-resistant DSAs, and compatibility challenges

On Constructing AEs with Leakage and Faults (tosc​.iacr​.org). LEAF: a single-fault-resistant AE construction against leakage and fault attacks using combined secure building blocks

🧑‍💻 Software Craft Notes

An Inequality Union Find Inspired by Atomic Asymmetric Completion (philipzucker​.com). Asymmetric completion, inequality union-find, e-graphs, refinement, and Brunei-style generalized rewriting in Python with LEUF

Property-based testing, adversarial developers, and LLMs (protocols-made-fun​.com). Property-based testing, adversarial developers, LLMs, Hypothesis, Apalache, and Python-based examples in addition, commutativity, and associativity checks

I would still like to write my own constraint programming solver (logicgrimoire​.wordpress​.com). Discusses building a constraint programming solver in Perl (potentially C), with a test suite, Lambda constraints, and graph-search approaches

[Math] Intervals: examples of half-open intervals (yurichev​.com). Half-open intervals across languages (Python, C++, Go, POSIX) with examples of range, random, and STL usage explained

Vibe Coding (davidbau​.com). Vibe coding with LLMs: tests, metaprogramming, and towers of complexity for a Mandelbrot web page

🧮 Numerical Methods

Comparing BDF vs. Tendler vs. Tischer formulas (eklausmeier​.goip​.de). Comparing BDF, Tendler, and Tischer formulas for stiff ODEs using Dahlquist’s test equation with varying Widlund wedge angles and precision tests in double and float complex

You Must Use full_matrices=False with the NumPy SVD function to Compute the Pseudo-Inverse (jamesmccaffreyblog​.com). Using NumPy SVD with full_matrices=False to compute the Moore-Penrose pseudo-inverse in Python

Owen Scrambling in Quantlib (chasethedevil​.github​.io). Owen scrambling in Quantlib with Brent Burley’s hash-based scrambling and QuantLib C++ implementation notes

Trying to fit a logistic curve (johndcook​.com). Fitting a logistic curve from left-tail data with Python's SciPy may fail or be imprecise

Solving Large-Scale Linear Sparse Problems with NVIDIA cuDSS (developer​.nvidia​.com). NVIDIA cuDSS enables scalable sparse solvers on CPU/GPU with hybrid memory, MG mode, and MGMN for large EDA, CFD, and optimization workloads

🎲 Ranking & Bayesian

Elo rating systems via Markov Chains (xianblog​.wordpress​.com). Explores Elo ratings via Markov Chains, Bradley–Terry–Luce models, spectral gap optimization, SGD updates, and Bayesian ranking discussions

a (sunny, crisp) day at ICSDS 2025 (xianblog​.wordpress​.com). Bayesian learning sessions at ICSDS 2025 in Xi’an; proper prior minimaxity, variational inference, DIC, AI priors, martingale prediction, and urn-based math discussed by George, Margossian, Christensen, Rockova, Ng, Cappello, Ghiglietti

Kelly Criterion in Practice (vertoxquant​.com). Explains Kelly criterion, fractional Kelly, continuous-time models, Bayesian updates, and multi-asset sizing with Python-like pseudocode

🤖 ML Theory & Symmetry

The shape of mathematics to come (hoyleanalytics​.org). Explores AI in formal and non-formal mathematics, Kontorovich’s Shape of Math To Come, Lean, MathLib, AlphaProof, and implications for data science

Experiments to understand Singular Learning Theory's Free Energy & Local Learning Coefficient (LLC) (lesswrong​.com). Explores Singular Learning Theory's free energy and LLC through SGLD-MCMC experiments, grokking, polynomials, and low-rank nets, with Python/Numpy-style analysis

NeuroIPS Spotlight 6: Equivariant Neural Networks for General Linear Symmetries on Lie Algebras (quantumformalism​.substack​.com). Equivariant Neural Networks on Lie algebras for general linear symmetries; GitHub implementation; Lie groups, manifolds, and tangent spaces discussed

How PyTorch Generates Random Numbers in Parallel on the GPU (blog​.codingconfessions​.com). Parallel RNGs on GPUs with Philox: counter-based randomness, 4x32 outputs, 10 rounds, CUDA/C++ templates, reproducible seeds in PyTorch

Construcción de intervalos de confianza para gráficos de calibración vía "bootstrap" y algunos asuntos más (datanalytics​.com). Calibración de gráficos con bootstrap, intervalos de confianza y temas relacionados en estadística y ML usando R y Python

Voting as a way to surface the hidden reasons (cjauvin​.github​.io). Explores voting to reveal hidden motives behind majority preferences using aggregation by LLMs to surface underlying reasons

🧾 Proofs & Formal Methods

Understanding Vibe Proving (towardsdatascience​.com). Explores verifiable Vibe Proving for LLMs, building a symbolic proof DSL and a checker to verify step-by-step math reasoning

Formal Scientific Modeling (johncarlosbaez​.wordpress​.com). Category theory for modeling in epidemiology; formal scientific modeling; collaboration insights with Nate Osgood, Xiaoyan Li, Kris Brown, Evan Patterson; software for epidemiology modeling

The good places to submit your papers (jesper​.sikanda​.be). Open-access publishing in type theory and interactive theorem proving; critiques of ACM policy; lists journals and conferences like ETAPS and Schloss Dagstuhl

The absoluteness of consistency (umsu​.de). Pluralism about consistency faces worries about logic and meaning in arithmetic and English terms

🧠 Pure Math Research

The maximal length of the Erdős–Herzog–Piranian lemniscate in high degree (terrytao​.wordpress​.com). Terence Tao explores maximal lemniscate length for high-degree polynomials using Fryntov-Nazarov methods, stochastic tools, and Stokes’ theorem; includes AlphaEvolve visualizations

Beta/Gamma/Normal and Jacobi/Laguerre/Hermite (djalil​.chafai​.net). Beta/Gamma/Normal and Jacobi/Laguerre/Hermite: links between distributions and orthogonal polynomials, with Askey scheme and spectral operators

Combinatorial Species (unnamed​.website). Introduction to combinatorial species, Lagrange inversion, Cayley’s formula, and proof ideas with functional perspectives

Uniformly Random High-Degree Regular Graphs are Asymptotically Almost Surely Link-Irregular (jix​.one). High-degree regular graphs; distance sequences; unlink/link-irregularity; Bollobás distance identifications;, Béla Bollobás

Counting rectangles in a staircase polyomino (ckrao​.wordpress​.com). Counting rectangles in a staircase polyomino using combinatorics and binomial identities

📚 Academic Research

Abelian structure in approximate groups and Alon's conjecture on Ramsey Cayley graphs (arxiv:math). Shows large abelian structure inside approximate groups of solvable groups, yielding stronger bounds. Applies to Alon’s Ramsey Cayley graph conjecture and nonabelian Roth-type results too

Hyperbolicity and fundamental groups of complex quasi-projective varieties (II): via non-abelian Hodge theories (arxiv:math). Using non-abelian Hodge theory, proves generalized Green–Griffiths–Lang for quasi-projective varieties with big reductive π1-representations. Identifies special loci, advancing hyperbolicity classification in complex geometry and number-theory

An inverse theorem for all finite abelian groups via nilmanifolds (arxiv:math). Establishes an inverse theorem for Gowers norms on all finite abelian groups using only nilmanifolds. Links compact finite-rank nilspaces to nilmanifold factors, impacting dynamics broadly

Equidistribution of polynomial sequences in function fields: resolution of a conjecture (arxiv:math). Resolves a conjecture on equidistribution of polynomial sequences over function fields, giving sharp irrationality conditions. Extends analytic number theory methods to positive characteristic settings decisively

Seed-Prover 1.5: Mastering Undergraduate-Level Theorem Proving via Learning from Experience (arxiv:cs). ByteDance’s Seed-Prover 1.5 trains a Lean agent with large-scale reinforcement learning and lemma caching. Achieves state-of-the-art PutnamBench and FATE performance, narrowing formalization gaps for mathematicians