🔒 Complexity & Cryptographic Protocols

Universal Denial of Service (starkeblog​.com). Explores computronium, DoS concepts, TREE(3), and JavaScript/Python demos for a universe-scale denial-of-service scenario

Speeding up sumcheck: an in-depth walkthrough of our implementation (blog​.lambdaclass​.com). Speeding up sumcheck using SVO and Eq-Poly optimizations in Rust, with BDDT-inspired folding for Whirlp3/PCS workflows

Zero knowlege proof of compositeness (johndcook​.com). Zero knowledge proof of compositeness explores Fermat’s little theorem as a ZKP and discusses primality, Carmichael numbers, and practical verification in Python

🛠️ Applied Math Projects

Combinations and permutations and locks, oh my! (blog​.alexbeals​.com). Explores how push-button locks work, clarifies permutation vs combination, and uses math and CAD renders to visualize lock mechanisms

Calculating Pi (relaycomputer​.co​.uk). Relay Computer calculates Pi to 20 digits, using assembly, hardware division, and a high-level .NET prototype

Solving the Partridge Packing Problem using MiniZinc (zayenz​.se). Using MiniZinc to solve Partridge Packing with OR-Tools CP-SAT, exploring base and improved models

Tiny-TPU : comprendre et construire un TPU quand on est débutant·e (tinytpu​.com). Novices recreate a TPU-like accelerator using Verilog basics, systolic arrays, and LeakyReLU in a 2x2 XOR toy model

Matrix Moore-Penrose Pseudo-Inverse Via SVD Using C# (jamesmccaffreyblog​.com). Moore-Penrose pseudo-inverse via SVD (Jacobi) implemented in C# with MatDecompSVD and helper matrix operations

🧾 Math Notation & Publishing

Eri Pazos: interop and mathml core (conflor​.es). Interoperability in MathML Core across Chromium, Firefox, and WebKit; RTL mirroring, math-shift, font choices, and CSS-based depth features

Linkage (11011110​.github​.io). Explores how readers chunk complex math formulas into meaningful units, with examples from random graphs, graph theory concepts, and Wikipedia practices

Manifesto (cameroncounts​.wordpress​.com). Open-access advocacy in mathematics; arXiv and diamond journals; Peter Cameron's stance on publishing

📊 Analysis & Probability

Discrete Calculus (jiha-kim​.github​.io). Discrete math, falling powers, generating functions, Stirling numbers, and umbral calculus in a programming-leaning exploration

Diffeomorphic deformations of Markov diffusions (djalil​.chafai​.net). Diffeomorphic deformation of Markov diffusions: Itô calculus, semigroups, generators, and flattening via diffusion-diffeomorphism tricks

Equal things that don’t look equal (johndcook​.com). Five expressions for the Poincaré hyperbolic metric in the upper half-plane, with Python checks and Möbius-invariance

Learning Feynman's Trick for Integrals (zackyzz​.github​.io). Explores Feynman's trick (differentiation under the integral sign) with heuristics, examples, and variants, using calculus, integrals, and parameterisation

📜 Mathematical Lives & History

Chapter 8: An Elliptical Universe (analog-antiquarian​.net). Kepler’s ellipse-based cosmos, Tycho’s data, Copernican shift, Galileo’s telescope, and the nascent unity of physics in Prague

Fantastic Women Series: Ada Lovelace First Computer Programmer (360onhistory​.com). Ada Lovelace, first computer programmer, notes on the Analytical Engine, Babbage, Bernoulli numbers, and early concepts of universal computing

Mihai Pătrașcu Best Paper Award: Guest post from Seth Pettie (scottaaronson​.blog). SOSA Best Paper Award renamed for Mihai Pătrașcu; Pettie discusses Mihai’s impact on data structures, geometry, and lower bounds

The renaissance theory that you could build anything out of just 6 kinds of simple machine (mynamelowercase​.com). Explores six simple machines, Reuleaux, Leibniz, Euclid, and the idea of a universal language for invention and computation

I wrote about John von Neumann for the Free Press (quomodocumque​.wordpress​.com). John von Neumann’s humanity and impact explored beyond space alien myths, linking math, history, and technology in a candid immigrant portrait

🎨 Rendering & Distance Fields

Generalized Worley Noise (ianthehenry​.com). Explores generalized Worley noise, signed distance functions, and Bauble for 3D procedural textures and distortion

Periodic Spaces (ianthehenry​.com). Explores signed distance fields, domain repetition, and 2D/3D ray marching tricks in SDFs

Jackknife Transmittance and MIS Weight Estimation (momentsingraphics​.de). Jackknife transmittance, MIS weight estimation, UMVU exp(-τ) with two ray-marched τ estimates, variance-aware IS, SIGGRAPH Asia 2025 work by Christoph Peters

📚 Deep Algebra & Structures

The Sixteen Faces of Logic: All Possible Boolean Functions with Two Inputs (kaue​.me). Explore the 16 two-input Boolean functions, NAND/NOR universality, and their role in digital design across logic categories

The determinant of transvections (an update) (freedommathdance​.blogspot​.com). Explores determinants of transvections over rings, proving det(I+f⊗v)=1+f(v) with cases by field, domain, and general ring construction

Why transformation monoids are harder than permutation groups (cameroncounts​.wordpress​.com). Transformation monoids vs permutation groups: orbitals, partial preorders, and coherent configurations open research paths

Sphere packing, cap set, and the Turán problem are all the same thing (quomodocumque​.wordpress​.com). Overview of unifying themes in sphere packing, cap sets, and Turán problems via group actions and FI-set families

🧮 Formal Proofs & Verification

‘Reverse Mathematics’ Illuminates Why Hard Problems Are Hard (quantamagazine​.org). Reverse mathematics links theorems in complexity to the pigeonhole principle, revealing equivalences and limits of PV1 using metamathematical methods

Making a computer solve your math problems (thetech​.com). Automated theorem prover Canonical built on Lean, exploring transformations to solve math problems via AI-assisted state transitions

Can We Secure AI With Formal Methods? November-December 2025 (lesswrong​.com). AI security via formal methods, verification benchmarks, and Lean 4 proofs; mentions LLMs, VeriBench, VerifyThisBench, VeriEquivBench, and ARIA initiatives

Every mathematician has only a few tricks (2020) (mathoverflow​.net). Explores recurring mathematical tricks: Fubini, duality, induction, probabilistic method, generating functions, and more

📚 Academic Research

DeepSeekMath-V2: Towards Self-Verifiable Mathematical Reasoning (arxiv:cs). DeepSeekMath-V2 trains language models to verify their own proofs, advancing rigorous automated theorem proving. It reaches near-human results on major math competitions with scalable verification

The Dual of Quantifier Elimination: Boolean Elimination over C and R (arxiv:math). Frank proves any Boolean combination of polynomial conditions over ℂ or ℝ can be encoded by one short quantified equation. This reshapes logical normal forms in real–complex geometry

On the $2$-torsion in class groups of number fields (arxiv:math). Bonolis sharpens upper bounds for 2-torsion in class groups using advanced analytic and ℓ-adic methods. The work refines our quantitative understanding of ideal class groups in number theory

Homomorphism Testing with Resilience to Online Manipulations (arxiv:cs). Kelman, Meir, Nayak and Raskhodnikova design optimal tests for group homomorphisms robust to adversarial query corruptions. Their framework strengthens algebraic property testing in realistic, noisy or online environments

Asymptotic yet practical optimization of quantum circuits implementing GF($2^m$) multiplication and division operations (arxiv:cs). Yosri, Gavinsky and Maslov construct asymptotically faster quantum circuits for GF(2^m) arithmetic. These improvements impact quantum algorithms for cryptography, coding theory, and algebraic computation over binary fields

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