📜 History & Math Philosophy

What is the Essence of Mathematics? (themathdoctors​.org). Explores multiple views on the essence of mathematics, including abstraction, theorem derivation, structure, rigor, and the science-vs-art debate

Cédric, le retour ? (xianblog​.wordpress​.com). Cédric Villani interviews on politics and public mathematics work, with notes on Leçons de mathématique joyeuse and Poincaré

Note on Quote: Knuth on Theory vs Practice via CAUSEweb (joshbeckman​.org). Knuth on theory vs practice; program proving; TL; TLA+; CAUSEweb quote

Sylvester and Clifford on Curved Space (johncarlosbaez​.wordpress​.com). Sylvester and Clifford on curved space; historical context, 19th-century ideas, and early tests of space curvature influencing relativity

🤖 AI & Mathematical Insights

Small Steps Towards Proving Stochastic → Deterministic Natural Latent (lesswrong​.com). Dovetail project explores Natural Latents, stochastic vs deterministic, Jensen-Shannon, and counterexamples with Python/Mathematica proofs

Teaching a Neural Network the Mandelbrot Set (towardsdatascience​.com). Explores neural networks learning the Mandelbrot set, using Gaussian Fourier Features to overcome spectral bias in an MLP

“Erdos problem #728 was solved more or less autonomously by AI” (mathstodon​.xyz). AI tools solve Erdos problem #728 with autonomous-like reconstruction and rapid exposition writing

What Does the Linear Representation Hypothesis Even Mean? (alok​.github​.io). Explores what a 'linear representation' means in AI, comparing word analogies, logistic probes, and steering vectors

How LLMs Really Do Arithmetic (data-processing​.club). LLMs like Llama3-8B reveal arithmetic via coarse heuristic neurons and logit boosts, not exact calculation, analyzed with logit lens methods

🧾 Proof Assistants & Verification

I asked ChatGPT to look at a proof, here's what happened... (karagila​.org). Set theory discussion on ChatGPT analysis of a proof about least inaccessible and least measurable cardinals, with reflections on GenAI reliability

Pulling a New Proof from Knuth’s Fixed-Point Printer (research​.swtch​.com). Russ Cox discusses Knuth’s fixed-point printer, transforms P2 into a simpler proof, and explores correctness via digit-walking, pre-multiplication, and refactoring in Ivy-like pseudocode

Axiom (lagomor​.ph). Axiom offers client-side Fitch-style proof checking in TypeScript, supporting propositional and first-order logic with SCORM-ready Web Components

Mathematics for Computer Science (2018) [pdf] (courses​.csail​.mit​.edu). MIT 6.042 Mathematics for Computer Science (2018) notes cover graphs, sets, logic, probability, and combinatorics with formal proofs and examples

The Evolution of a Lean Programmer (unnamed​.website). Lean programming explorations: insertion sort proofs and implementations in Lean using Mathlib and various styles

Quick Take: Bridging Compile-Time and Runtime Performance in Lean 4 (alok​.github​.io). LeanBench now correlates compilation metrics with runtime data from profilers, supporting CPU, GPU, memory, and FFI timings

📐 Linear Algebra & Arrays

Computing Moore-Penrose Pseudo-Inverse Using Three Techniques: Standard Inverse, SVD Decomposition, QR Decomposition (jamesmccaffreyblog​.com). Python demo computes Moore-Penrose pseudo-inverse using three techniques: standard inverse, SVD, and QR in NumPy

“Kernel Ridge Regression with Cholesky Inverse Training Using JavaScript” in Visual Studio Magazine (jamesmccaffreyblog​.com). Kernel ridge regression with JavaScript and Cholesky inverse training using RBF kernel in Visual Studio Magazine

Gaussian-Based Spectral Upsampling (colour-science​.org). Gaussian-based spectral upsampling in Colour: Python-based reflectance recovery using clamped Gaussian basis spectra and Smits 1999 decomposition

Cumulative Sums as Matrix Multiplication (austinrochford​.com). Cumulative sums as matrix multiplication using Python/NumPy; explores U and U^λ for decayed sums and Hypothesis testing

🕸️ Graphs & Discrete Algorithms

JLMS centenary (cameroncounts​.wordpress​.com). JLMS centenary: Cameron highlights ten open-access papers from a centennial issue and Hall’s Marriage Theorem among notable works

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

Graph layout (macwright​.com). Explores graph layout, d3-force, orthogonal drawing, HOLA and PRALINE; mentions Mapbox earcut; discusses researchers and papers in graph visualization

🃏 Shuffles, Entropy & Sampling

Combining in-shuffles and out-shuffles (johndcook​.com). Explores how in-shuffles and out-shuffles generate a subgroup of permutations for 52 cards and its size via Diaconis, Graham, Kantor results

Time's arrow (bristoliver​.substack​.com). A look at probability, entropy, and the uniform distribution via supermarket prices and card shuffles

Owen Scrambling a la Burley (chasethedevil​.github​.io). Owen scrambling compared with Algorithm 823 for Sobol’ sequences in quantitative finance using Burley’s hashing approach

🔐 Number Theory & Cryptography

Primecoin primality test (johndcook​.com). Primecoin uses a probabilistic primality test combining Fermat base 2 with Euler-Lagrange-Lifchitz criteria to verify prime chains linked to block headers

Residue Number System (mathr​.co​.uk). Overview of Residue Number System (RNS) arithmetic, conversions, and mixed-radix methods with CRT, including key researchers and references

Mastering Zcash (maxdesalle​.com). Explores Zcash privacy via zk-SNARKs, shielded notes, UTXO concepts, and Zerocash origins with references to Chaum, cypherpunks, and Zcash founders

💹 Econometrics & Decision Theory

General Equilibrium (deeshaa​.org). General Equilibrium explored through Walras, Arrow-Debreu, OLG, CGE and DSGE models with quotes and reflections

Time Series with Konrad: episode 1 (konradb​.substack​.com). Practical time series fundamentals: decomposition, stationarity, ACF/PACF, differencing, and transformations using Python-based examples

Whose benefit of the doubt? (emilkirkegaard​.com). Explores costs of biased decision-making using game theory, selection methods, and utility analysis with examples like landlords and tenants

📡 Transforms & Quantum Phases

Fast-Fourier Transform (FTT) and Number-Theoretic Transform (NTT) - FFT, NTT and LBC (godspowereze​.com). Explores FFT, NTT, root of unity concepts, and lattice-based cryptography with Python examples

Understanding complex conjugates in quantum mechanics (lesswrong​.com). Explores complex conjugates, phase translation, and O(2) groupoid representations in quantum mechanics with groupoid theory insights

The unreasonable effectiveness of the Fourier transform (joshuawise​.com). Teardown 2025 talk on Fourier transform fundamentals, OFDM insights, Python demos, and practical signal processing lessons

🌊 Fluids & Numerical Simulation

Using AI, Mathematicians Find Hidden Glitches in Fluid Equations (quantamagazine​.org). AI-driven PINNs reveal unstable and stable singularities in Euler and related fluid equations, exploring potential blowups with DeepMind collaboration

Comparing BDF vs. Tendler vs. Tischer formulas, #2 (eklausmeier​.goip​.de). Runge test equation comparisons of BDF, Tendler, and Tischer methods using Runge's function in double and quadruple precision with Bash scripts

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

🧠 Foundations & Complexity

A02 MCQ: Possible definitions of the naturals (pgadey​.ca). Explores possible definitions of the naturals in a programming and mathematical context, via notes and blog discussion

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

Computational Depth (blog​.computationalcomplexity​.org). Overview of computational depth, Kolmogorov complexity, shallow sets, and connections to average-case complexity and SAT witnesses

📚 Academic Research

Compact quotients of homogeneous spaces and homotopy theory of sphere bundles (arxiv:math). Proves compact quotients of reductive homogeneous spaces force fiber-homotopically trivial sphere bundles, ruling out many examples and settling Kobayashi conjectures; new constraints for pseudo-hyperbolic spaces

Weight filtration of Hurwitz spaces and quantum shuffle algebras (arxiv:math). Links weight filtrations on Hurwitz-space cohomology to new ‘algebraic weight filtration’ on quantum shuffle algebras, enabling explicit weight bounds over ℂ and 𝔽_p in practice

Agentic Proof Automation: A Case Study (arxiv:cs). Case study shows LLM agents can mechanize complex Lean 4 proofs: 14k-line System Capless development, 87% task success, major productivity boost and releases interaction logs

A Poincaré-Bendixson theorem for Bebutov shifts and applications to switched systems (arxiv:math). Extends Poincaré–Bendixson theory to Bebutov shifts, yielding criteria for periodic orbits and proving stability equivalences for 3D switched systems, resolving open conjectures in control theory

Galois theory, automorphism groups of prime models, and the Picard-Vessiot closure (arxiv:math). Generalizes Galois correspondence inside prime models of totally transcendental theories, applying to Picard–Vessiot closures of differential fields and proalgebraic exact sequences, clarifying gaps in Magid