Evolved Virtual Creatures by Karl Sims. A more than 30 years old project, but still very interesting. www.karlsims.com/evolved-virtual-c… www.youtube.com/watch?v=RZtZia4ZkX…

Today marks the December solstice, the shortest day in the Northern Hemisphere and the longest day in the Southern Hemisphere. At 15:03 UTC the North Pole is tilted maximally (about 23.4°) away from the Sun. janmr.com/posts/equinoxes-and-sols…

Evaluation of Powers janmr.com/posts/evaluation-of-powe…

$$\begin{aligned} x^0 &= 1 \\ x^{2k} &= (x^k)^2 \\ x^{2k+1} &= x \cdot x^{2k} \\ \end{aligned}$$

The M/o/Vfuscator compiles programs into "mov" instructions, and only "mov" instructions. Arithmetic, comparisons, jumps, function calls, and everything else a program needs are all performed through mov operations; there is no self-modifying code, no transport-triggered calculation, and no other form of non-mov cheating. 🤯 github.com/xoreaxeaxeax/movfuscato…

Prime Factors of Factorial Numbers janmr.com/posts/prime-factors-of-f…

$$d_p(n!) = \sum_{k=1}^\infty \left\lfloor \frac{n}{p^k} \right\rfloor = \sum_{k=1}^{\lfloor \log_p(n) \rfloor} \left\lfloor \frac{n}{p^k} \right\rfloor$$

Every position of Rubik's Cube can be solved in twenty moves or less www.cube20.org

Computing the Integer Binary Logarithm janmr.com/posts/computing-the-inte…

$$k = \lfloor \log_2 n \rfloor \quad \Leftrightarrow \quad 2^k \leq n < 2^{k+1}$$

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…