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The most popular blog posts about math & algorithms on Hacker News. 2,851 posts.
Are the prime numbers sprinkled randomly along the number line, like windblown seeds? Of course not: Primality is not a matter of chance but a product of simple arithmetic. A number is prime if and only if no smaller positive integer other than 1 divides it evenly.
Or, “how not to GIS”.
In the Game of Life, which still lifes can be produced by crashing gliders together? We’ve known for a few years that the answer cannot be “all of them”, because in 2022 Ilkka Törmä and Ville Salo found a patch of still life that, if it exists in the universe, must have existed since the beginning of time. And so…
For today’s post, I’ve drawn material not just from one paper, but from five! The subject matter is ‘word2vec’ – the work of Mikolov et al. at Google on efficient vect…
History of mathematician Srinivasa Ramanujan’s lost notebooks and an exploration of solutions to those equations using Mathematica.
Basketball has evolved into a game of calculated decision-making. From a game of points, assists, and rebounds, it has progressed into using thousands of data points to optimize every element of the game.
The ubiquitous IEEE floating-point standard defines two numbers to represent zero, the positive and the negative zeros. You also have the positive and negative infinity. If you compute the inverse of the positive zero, you get the positive infinity. If you compute the inverse of the negative zero, you get the negative…
I’m a (50%) professor of mathematics and (50%) professor of molecular & cell biology at UC Berkeley. There have been plenty of days when I have spent the working hours with biologists and…
Roughly speaking, Gödel’s Incompleteness Theorem states that there are true mathematical statements that cannot be proven. When I was in 11-th grade, my geometry teacher Mr. Olsen, my friend …
A Japanese man came into the restaurant. I had seen him before, wandering around; he was trying to sell abacuses. He started to talk to the waiters, and challenged them: He said he could add numbers faster than any of them could do.
Most of us learn how to write technical articles by osmosis. After reading a hundred or so papers, we unconsciously pick up the common patterns of the field and begin to imitate them. This phenomenon is largely beneficial, but there are several truly odious habits that are almost universally and inadvertently adopted…
The first task of the 21st Weekly Challenge was a very old one: to find (what would eventually become known as) Euler’s number.
First of all, don’t panic. I’m going to try in this post to introduce you to quantum field theory, which is probably the deepest and most intimidating set of…
by Erin Baldinger, University of Minnesota; Shawn Broderick, Keene State College; Eileen Murray, Montclair State University; Nick Wasserman, Columbia University; and Diana White, Contributing Editor , University of Colorado Denver.
There are lots of interesting little subproblems in compilation like instruction selection, register allocation and instruction scheduling. These can be expressed in declarative interlinked way to constraint solvers.
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…
Gradient descent is a standard tool for optimizing complex functions iteratively within a computer program. Its goal is: given some arbitrary function, find a minumum. For some small subset of functions - those that are convex - there's just a single minumum which also happens to be global. For most realistic…
the forgotten data structure (not really)
The way that most physicists teach and talk about partial differential equations is horrible, and has surprisingly big costs for the typical understanding of the foundations of the field even among professionals. The chief victims are students of thermodynamics and analytical mechanics, and I've me
Authors: Yanbo Zhang, Benedikt Hartl, Hananel Hazan, Michael Levin
Proposing technology for pure mathematics: curating concepts, constructs, theorems, & literature; precise symbolic language; automated computations...
Why graphical representation and visualization are so important to...
Since I’m a good mood today—at a beautiful science camp with my kids, high in the mountains near Big Bear Lake in California—I thought I’d blog about something positive. Las…
MIT graduate students have developed a new “cutting-plane” algorithm, a general-purpose algorithm for solving optimization problems. They’ve also developed a new way to apply their algorithm to specific problems, yielding orders-of-magnitude efficiency gains.
Edit 12/19/2017: added a new subsection on analyzing Chutes & Ladders as an Absorbing Markov Chain.
Many theorems in mathematics are important enough that they have been proved repeatedly in surprisingly many different ways. Examples of this include the existence of infinitely many prime numbers , the evaluation of \(\zeta(2)\), the fundamental theorem of algebra (polynomials have roots), quadratic reciprocity (a…
