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Math Team
and other horrible things you do to get into stanford
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Introduction to P vs. NP
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…
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Unexpected link between pure mathematics and genetics
An interdisciplinary team of mathematicians, engineers, physicists, and medical scientists have uncovered an unexpected link between pure mathematics and genetics.
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Circulant Matrices, Eigenvectors, and the FFT
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.
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How does Cave/Glade Generator Work
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…
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The seven specification ur-languages
A brief overview of the formal specification landscape
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The convolution empire strikes back
ConvNets Match Vision Transformers at Scale
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Domain Repetition
Tutorials and articles of Inigo Quilez on computer graphics, fractals, math, art, demoscene, shaders and more.
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Competitive programming in Haskell: better binary search
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…
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Hilbert Transform
Concise summary of the Hilbert transform: mathematics, effects on signals, and applications in telecommunications.
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Generalizations of Fourier analysis (2021)
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.
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Dividing a Square into 7 Similar Rectangles
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…
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Echo Chess: The Quest for Solvability
Chess puzzles, but you are what you eat.
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NP-hard does not mean hard (2017)
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…
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Shannon’s Source Coding Theorem (2020)
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…
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When to Shut Up: A Visual Guide (With Included Algorithm)
Use these rules to avoid boring your audience
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4D Toys Update 8: Rotating the 3D Slice, 2D Faces Projections, Marble Scenes
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…
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My primality testing code is faster than Sir Roger Penrose's
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...
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Demystifying Tupper's Formula
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.
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A new quantum algorithm for classical mechanics with an exponential speedup
Posted by Robin Kothari and Rolando Somma, Research Scientists, Google Research, Quantum AI Team Quantum computers promise to solve some problems e...
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P < 0.05 Considered Harmful
The unreasonable persistence of an old standard
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The Tetris Effect
Minimalist 3D Tetris.
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Exploring the design space of binary search trees
Open-source research project that explores the design space of binary search trees to implement persistent and concurrent linear list data structures.
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Bounty to Recover NIST's Elliptic Curve Seeds
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…
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How Many People? Ancient Demography
Bret Devereaux (A Collection of Unmitigated Pedantry)2023121 points5 commentscited by 3History & Retro Computing details
One of the first questions anyone asks about past societies is, ‘how many people were there?’ It is one of those basic bits of information and generally speaking those of us who teach t…
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Four Kinds of Optimisation
Premature optimisation might be the root of all evil, but overdue optimisation is the root of all frustration. No matter how fast hardware becomes, we find it easy to write programs which run too slow. Often this is not immediately apparent. Users can go for years without considering a program’s performance to be an…
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Algebraic graph calculus (2021)
We describe a graph-theoretic analogue of vector calculus. The linear operators of vector calculus (gradient, divergence, laplacian) correspond to the matrices naturally associated to graphs (incidence matrix, adjacency matrix). This analogy is useful for formalizing the discretization of some problems in image and…