1081
Why are mathematicians so bad at arithmetic? (2017)
18 x 93 is… hey, look over there!
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The latest blog posts to take off on Hacker News. 2,851 posts.
1082
Why isn't there a replication crisis in math?
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…
1083
Solving some formal math olympiad problems
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.
1084
Hardy, Ramanujan and Taxi No. 1729
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 …
1085
What is the inverse of a circle?
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!
1086
Masterclass on mathematical thinking
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…
1087
Why Quantum Mechanics?
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…
1088
Wordle-solving state of the art: all optimality results so far
Almost all mathematical questions one could have about Wordle are settled by now. I summarize here what is known so far.
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Solving Wordle in 3.64 guesses on average, 99.4% of the time
Hey all, I’ve been enjoying wordle, the puzzle game recently but also wondered how a program might do at it.
1091
The control group is out of control (2014)
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 …
1092
A pair of dice which never roll 7 (2004)
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…
1093
Geometry from Another Universe
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…
1094
A high-dimensional sphere spilling out of a high-dimensional cube
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?…
1095
The Color of Infinite Temperature
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…
1096
29-year-old Conway conjecture settled
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…
1097
Provably space-efficient parallel functional programming
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…
1098
Problem solving strategies in a graduate real analysis course (2010)
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…
1099
Milton Friedman’s Interest Rate Fallacy
Milton Friedman’s interest rate fallacy is one of the most mystifying and counterintuitive facts in modern finance.
1100
Visualizing Bayes Theorem (2009)
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.
1101
Why can’t you design noise in frequency space?
The python code that goes along with this blog post can be found at To evaluate the quality of a blue noise texture, you can analyze it in frequency space by taking a discrete Fourier transform. Wh…
1102
Raytracing diamonds
This comes from a question posed to me and others in 2019 by Stefan Langerman, a computational geometer who also happens to be a diamond dealer. The classic ...
1103
Penrose: From mathematical notation to beautiful diagrams
Materials from our SIGGRAPH '20 paper.
1104
Ordering movie credits with graph theory
How Graphs & Games Untangled "The Golden Hairball": A technical deep dive from the end credits experts at Endcrawl.
1105
Kolmogorov Complicity and the Parable of Lightning (2017)
A good scientist, in other words, does not merely ignore conventional wisdom, but makes a special effort to break it. Scientists go looking for trouble. — Paul Graham, What You Can’t Sa…
1106
Quaternions
Introduction to quaternions and rotations in 3D.
1107
How a Kalman filter works, in pictures
I have to tell you about the Kalman filter, because what it does is pretty damn amazing.
1108
Learning with Not Enough Data: Semi-Supervised Learning
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1110
All Horses Are the Same Color
Problem: Show that all horses are of the same color. “Solution”: We will show, by induction, that for any set of $ n$ horses, every horse in that set has the same color. Suppose $ n=1$, this is obviously true. Now suppose for all sets of $ n$ horses, every horse in the set has the same color. Consider any set $ H$ of…