Singular Value Decomposition (SVD) is a fundamental concept in linear algebra, and it is particularly important in the field of machine learning for tasks such as dimensionality reduction, data compression, and noise reduction.
Cistercian numerals were invented by the Cistercian order of monks in the 13th century. Giuseppe Frisella explains how the notation system works: A vertical str
This summer, 3Blue1Brown launched the third installment of the Summer of Math Exposition contest. Every year, I’ve been impressed and inspired by the quality of some of the videos in this con…
My last article had tips for for arena allocation . This next article demonstrates a technique for building bespoke hash maps that compose nicely with arena allocation. In addition, they’re fast, simple, and automatically scale to any problem that could reasonably be solved with an in-memory hash map. To avoid…
The phrase “foundations of mathematics” is bandied about frequently these days, but it’s clear that there is widespread confusion about what it means. Some say that a proof assistant must be based on a foundation of mathematics, and therefore that the foundations of mathematics refers to some sort of formal system…
When learning a new programming language, there is usually a table in the documentation that shows the various operators that can be used with numbers.
and other horrible things you do to get into stanford
Series Introduction In this series of articles I would like to share with you a set of ideas that are meant to help non-technical people build a better intuition as to what the current software and…
The eigenvectors of a circulant matrix do not depend on the matrix itself, only on the size, and the eigenvectors are columns of the FFT matrix.
Watabou’s Cave Generator is one in a series of RPG-ready map generators that Watabou has created over the years. All his work oozes style, but the cave generator was always the one I found mo…
A brief overview of the formal specification landscape
ConvNets Match Vision Transformers at Scale
Tutorials and articles of Inigo Quilez on computer graphics, fractals, math, art, demoscene, shaders and more.
Binary search is a workhorse of competitive programming. There are occasional easy problems where binary search is the solution in and of itself; more often, it’s used as a primitive building block…
Concise summary of the Hilbert transform: mathematics, effects on signals, and applications in telecommunications.
When I first learned about Fourier series and integrals, I hated it because it seemed like a collection of many ad-hoc definitions, formally related but very different.
This is a continuation of my post Dividing a square into similar rectangles, in which I discussed this puzzle: if you partition a square into n similar rectangles, what proportions can these rectan…
Chess puzzles, but you are what you eat.
When NP-hardness pops up on the internet, say because some silly blogger wants to write about video games, it’s often tempting to conclude that the problem being proved NP-hard is actually very hard! “Scientists proved Super Mario is NP-hard? I always knew there was a reason I wasn’t very good at it!” Sorry, these two…
The mathematical field of information theory attempts to mathematically describe the concept of “information”. In the first two posts, we discussed the concepts of self-information and information entropy. In this post, we step through Shannon’s Source Coding Theorem to see how the information entropy of a probability…
Use these rules to avoid boring your audience
This is a Mega-Update ®™ that focuses on features that people have been requesting for a long time. I have a ton of stuff in Miegakure that could be shared with 4D Toys but what takes development time is not the cool 4D stuff but all the UI/UX around it. First of all because there is the VR version, the mouse/keyboard…
But, I guess he did win the Nobel Prize for Physics in 2020 so I can't really brag. However, it was a great surprise when looking at two pa...
A book I was recently reading mentioned a mathematical curiosity I haven't seen before - Tupper's self-referential formula . There are some resources about it online, but this post is my attempt to explain how it works - along with an interactive implementation you can try in the browser.
The unreasonable persistence of an old standard
Minimalist 3D Tetris.
Open-source research project that explores the design space of binary search trees to implement persistent and concurrent linear list data structures.
This is a fun challenge: The NIST elliptic curves that power much of modern cryptography were generated in the late ’90s by hashing seeds provided by the NSA. How were the seeds generated? Rumor has it that they are in turn hashes of English sentences, but the person who picked them, Dr. Jerry Solinas, passed away in…
