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The most popular blog posts about math & algorithms on Hacker News. 2,851 posts.
My new office space suffers from a shortage of photons, so I’ve been wiring up light fixtures. As I was snaking 14-gauge cable through the ceiling cavity, I began to wonder: Why is it called 14-gauge? I know that the gauge specifies the size of the copper conductors, but how exactly? The number can’t be a simple…
tl;dr: A team from Columbia University led by Ken Shepard and Rafa Yuste claims to beat the 100 year old Sampling Theorem [1,2]. Apparently anti-aliasing filters are superfluous now because one can…
From gene regulatory networks to artificial neural networks
I didn’t invent categories to study functors; I invented them to study natural transformations. — Saunders Mac Lane
Analysis of the classic "dropping two eggs from a building" interview question
Exploring a peculiar bit-twiddling hack at the intersection of 1980s geek sensibilities.
Materials for book: “Markov Chains for programmers”
Eller's algorithm creates 'perfect' mazes, having only a single path between any two cells, one row at a time. The algorithm itself is incredibly fast, and far more memory efficient than other popular algorithms (such as Prim's and Kruskal's) requiring storage proportional to only a single row. This makes it possible…
This idea is particularly sticky because it was more or less true 50 years ago, and it's a passable mental model to use when learning sql. But it's an inadequate mental model for building new sql frontends, designing new query languages, or writing tools likes ORMs that abstract over sql.
An explorable blog post about entropy, with sheep.
In this article, I hope to convince you that the quintic equation is unsolvable, in the sense that I can’t write down the solution to the equation \[ ax^5 + bx^4 + cx^3 + dx^2 + ex + f = 0 \] using only addition, subtraction, multiplication, division, raising to an integer power, and taking an integer root. In fact, I…
On building Mr. Baby Paint, a radically simple co-op drawing app for toddlers & accidentally discovering a flood-fill cellular automata, plus developing pixel-fattening algorithms for bitmap fonts.
What the research is: The Ribbon filter is a new data structure that is more space-efficient than the popular Bloom filters that are widely used for optimizing data retrieval. One of the ways that …
This is a followup to my previous post on the stack monoid, but is intended to be self-contained.
The Ivory Tower is a blog about software engineering and development philosophy by Anders Sundman.
There is a well-known puzzle based on the premise of an �infinite� grid of resistors connecting adjacent nodes of a square lattice. A small portion of such a grid is illustrated below.
The integral of sec(x) is well known to any beginners calculus student. Yet this integral was once a major outstanding maths problem. It was first introduced...
Learn about public engagement activities from the American Physical Society
I recently crossed 500 days of practicing math daily with Math Academy. I wrote about my experience after 100 days here. TL;DR: I am still very impressed by the Math Academy system and highly…
Fizz Buzz is a counting game that has become oddly popular in the world of computer programming as a simple test of basic programming skills. The rules of the game are straightforward. Players say the numbers aloud in order beginning with one. Whenever a number is divisible by 3, they say 'Fizz' instead. If it is…
A while ago I decided to figure out how to prove one of Ramanujan’s formulas. I feel this is the sort of thing every mathematician should try at least once. I picked the easiest one I could f…
Learn the optimal strategy for playing Hangman.
A paper on Kalman filtering and functional folds that I alluded to previously has been split into several papers and posted online.
NB: The title of this post is an intentional clickbait. Even though I do stand for its statement, a more honest one would be something like: It's NOT OK to compare floating-points using epsilons.
In this article I’m trying to explain the difference/similarities between dynamic programing and divide and conquer approaches based on two examples - binary search and minimum edit distance (Levenshtein distance)
I have been steeping myself in probabilistic exercises recently, because it’s an area where I feel like I could benefit from building better intuition. I have found a recurring key to solving many of them: conditioning on an intermediary state, and then computing the value of that intermediary state separately. This…
