Stanford Lecture: Dr. Don Knuth - Adventures with Knight's Tours (2025-12-04) www.youtube.com/watch?v=MKiRte-tnM… (playlist with many of Knuth's lectures: www.youtube.com/playlist?list=PL94…)

Bit Twiddling Hacks, a collection of fast and tested code snippets graphics.stanford.edu/~seander/bit…

Bitwise Operators and Negative Numbers janmr.com/posts/bitwise-operators-…

$$\overline{x} = -1 - x$$

Test and benchmark suite for sort implementations, github.com/Voultapher/sort-researc….

The current slice::sort_unstable implementation of the Rust standard library is based on ipnsort github.com/Voultapher/sort-researc… doc.rust-lang.org/1.92.0/std/primi…

Visualizing the Pythagorean Theorem janmr.com/posts/visualizing-the-py…

How to Draw a Straight Line (Peaucellier–Lipkin linkage) www.futilitycloset.com/2014/12/05/…

Fractions and Circles janmr.com/posts/fractions-and-circ…

Two Notes on Notation by Donald E. Knuth (Iverson's convention and Stirling numbers) arxiv.org/abs/math/9205211

$$[P] \quad \left[ { n \atop k } \right] \quad \left\{ { n \atop k } \right\}$$

The Stern-Brocot Tree of Fractions janmr.com/posts/the-stern-brocot-t…

Langford pairs: Arrange the 2n numbers {1, 1, 2, 2, ..., n, n} such that exactly k numbers occur between the two appearances of each digit k dialectrix.com/langford.html

Continued Fractions and Continuants janmr.com/posts/continued-fraction…

$$a_0 + \displaystyle\frac{1}{a_1 + \displaystyle\frac{1}{\ddots + \displaystyle\frac{1}{a_{n-1} + \displaystyle\frac{1}{a_n}}}}$$

Online book: Mining of Massive Datasets www.mmds.org

Computing the Greatest Common Divisor janmr.com/posts/computing-the-grea…

$$\text{gcd}(u,v) = \prod_{p \; \rm prime} p^{\min(u_p,v_p)}.$$

Guido on introducing the shortcut conditional expression to Python. Some usages are "intentionally ugly" and finishes by adding "It's still my language! :-)". mail.python.org/pipermail/python-d…

A if C else B

Useful Properties of the Floor and Ceil Functions janmr.com/posts/useful-properties-…

$$\begin{aligned} n=\lfloor x \rfloor \quad &\Longleftrightarrow \quad n \leq x < n+1, \\ n=\lfloor x \rfloor \quad &\Longleftrightarrow \quad x-1 < n \leq x, \\ n=\lceil x \rceil \quad &\Longleftrightarrow \quad n-1 < x \leq n, \\ n=\lceil x \rceil \quad &\Longleftrightarrow \quad x \leq n < x+1 \end{aligned}$$

Google humor: Did you mean recursion? www.google.com/search?q=recursion

Twelve Ways of Counting janmr.com/posts/twelve-ways-of-cou…

Modern Computer Arithmetic, a book about algorithms for performing arithmetic, and their implementation on modern computers maths-people.anu.edu.au/~brent/pub… members.loria.fr/PZimmermann/mca/p…

Nice Proof of a Geometric Progression Sum janmr.com/posts/nice-geometric-pro…

The first website info.cern.ch

Math.sumPrecise developer.mozilla.org/en-US/docs/W…

A leap year check in three instructions hueffner.de/falk/blog/a-leap-year-…

Full unicode emoji list unicode.org/emoji/charts/full-emoj…

An ongoing multi-author open source project to formalise a proof of Fermat's Last Theorem in the Lean theorem prover imperialcollegelondon.github.io/FL…

Fast and maintainable patterns for fetching from a database by @sophiebits.com sophiebits.com/2020/01/01/fast-mai…

Celebrate 50 years of Microsoft with the company’s original source code by Bill Gates www.gatesnotes.com/home/home-page-…

Free math texts by Jim Hefferon (Linear Algebra, Theory of Computation, Introduction to Proofs) hefferon.net

@acm.org ACM has named Andrew G. Barto and Richard S. Sutton as the recipients of the 2024 ACM A.M. Turing Award for developing the conceptual and algorithmic foundations of reinforcement learning awards.acm.org/about/2024-turing

Stanford's "The Fourier Transform and Its Applications"

Videos, problem sets & more: see.stanford.edu/course/ee261

An unexpected, and extremely inefficient, way to compute pi @3blue1brown.com www.youtube.com/watch?v=HEfHFsfGXj…

Introduction to Computer Graphics, a free, on-line textbook covering the fundamentals of computer graphics and computer graphics programming math.hws.edu/graphicsbook

Videos from Math Professor Jeffrey Chasnov. Some of the playlists are videos from his Coursera courses on Mathematics for Engineers. www.youtube.com/@Jeff-math/playlis… www.math.hkust.edu.hk/~machas/?men…

Computer Science lectures by @timroughgarden.bsky.social www.youtube.com/channel/UCcH4Ga14Y…

Online conversion from TeX/MathML to HTML/SVG (powered by MathJax) mathjax.github.io/MathJax-demos-we…

Temml is a LaTeX-to-MathML JavaScript conversion utility. Useful online converter on homepage. temml.org

KaTeX: A math typesetting library for the web katex.org

👻 Ghostty is a fast, feature-rich, and cross-platform terminal emulator that uses platform-native UI and GPU acceleration. ghostty.org

Advent of Code 2024 complete!

MarkItDown: Python tool for converting various files to Markdown. It presently supports: PDF, PowerPoint, Word, Excel, Images, Audio, HTML, csv, json, xml, etc. github.com/microsoft/markitdown

Vanilla JS vanilla-js.com

Donald Knuth's 28th annual Christmas Lecture: Strong Components and Weak Components www.youtube.com/watch?v=au26uZfuxV… (past recordings www.youtube.com/playlist?list=PLoR…)

In Python, comparisons can be chained arbitrarily, e.g., x < y <= z is equivalent to x < y and y <= z docs.python.org/3/reference/expres…

Lean: First Steps leanfirststeps.blogspot.com/p/cont…

Are all natural numbers interesting? If not, there must be a smallest uninteresting number - and that makes it interesting. 🤔 en.wikipedia.org/wiki/Interesting_…

Kaleidoscope: Implementing a Language with LLVM llvm.org/docs/tutorial

Beating OpenBLAS and MKL in FP32 Matrix Multiplication From Scratch salykova.github.io/matmul-cpu

Note that the function $s(x)=(\ln x) / x$ from the post has the following property:

$$-s(e^{-x}) = -\frac{\ln(e^{-x})}{e^{-x}} = x e^x$$

and the inverse function (branches) of $x \mapsto x e^x$ is commonly called the Lambert W function, which has undergone a lot of study.

en.wikipedia.org/wiki/Lambert_W_fu… mathworld.wolfram.com/LambertW-Fun…

Journal of Open Source Software @joss joss.theoj.org

A curated list of awesome mathematics resources github.com/rossant/awesome-math

AlphaGeometry: An Olympiad-level AI system for geometry deepmind.google/discover/blog/alph…