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The most popular blog posts about math & algorithms on Hacker News. 2,391 posts.
Yesterday several people asked my opinion of a preprint claiming to solve the Graph Isomorphism problem in deterministic polynomial time. I responded: If I read all such papers, then I wouldn’t hav…
An interactive, illustrated timeline of historic moments in humankind's quest for information. With annotations by Jeremy Norman.
In this tutorial, we will learn about solving Differential Equations with Julia. Differential Equations are everywhere in Science and Engineering problems. And, being able to solve Differential Equations using computers is very convenient. We will use the DifferentialEquations.jl package for solving Differential…
Today I’m releasing Let’s Play: Ancient Greek Geometry . It’s a Compass and Straightedge tool/puzzle game written in JavaScript. I’ve always thought Geometric Construction felt like a puzzle, so to me this pairing was quite natural. Compass and Straight edge is a technique for constructing shapes out of circles…
I have been seeing this paper by cryptographer Peter Schnorr making the rounds: “Fast Factoring Integers by SVP Algorithms.” It describes a new factoring method, and its abstract ends with the provocative sentence: “This destroys the RSA cryptosystem.” It does not. At best, it’s an improvement in factoring—and I’m not…
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Almost exactly a year ago, Google made one of the most remarkable press releases in the Web 2.0 era. Of course, by "press release", I actually mean keynote at their own conference, and by "remarkable" I mean potentially-transformative and groundbreaking. I am referring of course to the announcement of Google Wave , a…
It is known that mathematics is heavily reliant on set theory, but no one can agree on what set theory is. Many people today understand that we have a choice between set theory and type theory , but they don’t know what type theory is either. Many think that type theory refers to some sort of dependent type theory, as…
Tutorials and articles of Inigo Quilez on computer graphics, fractals, math, art, demoscene, shaders and more.
Do adventure games have dead ends? The author of The Teeny Tiny Mansion proves the absence of dead ends in that game via formal verification (in particular, with the help of the cbmc model-checking program ). Here I’ll demonstrate how to prove the same thing via Markov theory. The Markov approach requires more…
I remember thinking at school when will I ever in my “real life” use maths. Well much to my utter surprise I’ve come to the stark realisation that there is a link between mathematics and crochet. …
· Read in · 1499 words · All posts in series · [dropcap]This[/dropcap] trick is unlike the others we’ve conjured. It will not reveal a clever manipulation of a probability or an integral or a…
In this post I describe the Asynchronous Computability Theorem, which uses tools from Algebraic Topology to show whether a task is solvable…
📍 This article has moved. Read the current version at This is the third part in a short series of blog posts about quantum Monte Carlo (QMC). The series is derived from an introductory lecture I ga…
A guide for getting started with Bayesian Statistics! Start your way with Bayes' Theorem and end up building your own Bayesian Hypothesis test!
tl;dr. In 2024, pre-election polls were off by about 2 percentage points. Election forecasters were aware of this and incorporated this into their uncertainties. But if you were not following the forecasts carefully, you might’ve not realized this. You might have mistakenly thought that, when predictions happened to…
A wintertime climate change solution
WARNING: the following contains a whole lot of pedantry about proving theorems at a level of detail such that you could likely convince a co...
Hamilton’s quaternion number system $latex {\mathbb{H}}&fg=000000$ is a non-commutative extension of the complex numbers, consisting of numbers of the form $latex {t + xi + yj + zk}&f…
A good colleague of mine, Rich Geldreich put up a interesting article talking about his viewpoints in future directions in lossless…
What are Gray codes, and why are they so useful?
I found the creator of Rainbow Table's paper, aimed at cryptanalysts, was pretty inaccessible considering the simplicity and elegance of Rainbow Tables, so this is an overview of it for a layman.
You are sitting in a rowing boat in the middle of a circular lake. How do you escape from a smart monster on the shore who can run four times faster than you can row?
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...
Printer Friendly: The whole text in one file , all 164,000 words, convenient for printing. (The printed length will vary, depending to your browser settings. For me it’s 401 pages.)
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.
