The latest blog posts to take off on Hacker News. 171 posts.
Our office chair, the air we breathe, the stars in the night sky: they are all made of atoms, which in turn are composed of electrons, protons and neutrons. Electrons are negatively charged; according to current knowledge, they have no expansion, but are point-like. The positively charged protons are different …
18 x 93 is… hey, look over there!
The replication crisis is a major problem in medicine and social science; we know that a huge fraction of the published literature is outright wrong. But in math we don't seem to have a similar crisis, despite reasonably frequent minor errors in published papers. Why not, and what can this tell us about the fields…
We built a neural theorem prover for Lean that learned to solve a variety of challenging high-school olympiad problems, including problems from the AMC12 and AIME competitions, as well as two problems adapted from the IMO.
In his book Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, G. H. Hardy tells this famous story: He could remember the idiosyncracies of numbers in an almost uncanny way. It …
In this post we’ll try to make sense of what we’re seeing, and try to understand what it means to invert a circle!
About a year ago, I was contacted by Masterclass (a subscription-based online education company) on the possibility of producing a series of classes with the premise of explaining mathematical ways…
In the past few months, I’ve twice injured the same ankle while playing with my kids. This, perhaps combined with covid, led me to several indisputable realizations: I am mortal.Despite my se…
Almost all mathematical questions one could have about Wordle are settled by now. I summarize here what is known so far.
Hey all, I’ve been enjoying wordle, the puzzle game recently but also wondered how a program might do at it.
I. Allan Crossman calls parapsychology the control group for science. That is, in let’s say a drug testing experiment, you give some people the drug and they recover. That doesn’t tell …
Some friends of mine play the board game Settlers Of Catan . In this game, each player rolls two ordinary dice on their turn, and the number which comes up determines what resources people get for the turn. When a seven is rolled, something special happens: no resources are generated, and instead a robber moves on the…
You start on an enclosed lawn, surrounded by four walls with a doorway in one of them. If you go in and explore, you might begin to feel trapped. You'll find you can visit five different rooms in the house, or go back outside to the lawn, but there's no way to go anywhere else. It's not because there are walls…
Make a square, split each side into two halves, producing four cells. Put a circle into each cell such that it fills it completely. There is a small gap right in the middle of the square. Put a circle there again such that it touches the other four circles. The central circle is obviously inside the square, right?…
This is the color of something infinitely hot. Of course you’d instantly be fried by gamma rays of arbitrarily high frequency, but this would be its spectrum in the visible range. This…
Ilkka Törmä and Ville Salo, a pair of researchers at the University of Turku in Finland, have found a finite configuration in Conway’s Game of Life such that, if it occurs within a universe a…
You have heard your grandmother tell you many times: parallel programming is hard. In 2022, does it still have to be? Back in grandma’s heyday, they knew a cool and breezy way to do paralleli…
This is going to be a somewhat experimental post. In class, I mentioned that when solving the type of homework problems encountered in a graduate real analysis course, there are really only about a…
Milton Friedman’s interest rate fallacy is one of the most mystifying and counterintuitive facts in modern finance.
I recently came up with what I think is an intuitive way to explain Bayes’ Theorem. I searched in google for a while and could not find any article that explains it in this particular way.
