Researchers Discover a Pattern to the Seemingly Random Distribution of Prime Numbers

The pattern has a surprising similarity to the one seen in atom distribution in crystals. Often known as “the building blocks of mathematics,” prime numbers have fascinated mathematicians for centuries due to their highly unpredictable and seemingly random nature. However, a team of researchers at Princeton University have recently discovered a strange pattern in the […]

A Classical Math Problem Gets Pulled into the Modern World

A century ago, the great mathematician David Hilbert posed a probing question in pure mathematics. A recent advance in optimization theory is bringing Hilbert’s work into a world of self-driving cars. A collision-free path can be guaranteed by a sum-of-squares algorithm. Long before robots could run or cars could drive themselves, mathematicians contemplated a simple […]

How a Kalman filter works, in pictures

Surprisingly few software engineers and scientists seem to know about it, and that makes me sad because it is such a general and powerful tool for combining information in the presence of uncertainty. At times its ability to extract accurate information seems almost magical— and if it sounds like I’m talking this up too much, […]

An Interesting New Pattern in the Prime Numbers: Parallax Compression

Shaun explained that he had developed a new algorithm (he calls it “Parallax Compression”) for wrapping the primes on a plane, and visualizing their distribution, inspired by the Ulam Spiral. Shaun’s algorithm revealed an interesting non-random, fractal-like pattern in the distribution of primes, that to our knowledge, had not been found before.It made it possible […]

Mathematicians Disprove Conjecture Made to Save Black Holes

Nearly 40 years after it was proposed, mathematicians have settled one of the most profound questions in the study of general relativity. In a paper posted online last fall, mathematicians Mihalis Dafermos and Jonathan Luk have proven that the strong cosmic censorship conjecture, which concerns the strange inner workings of black holes, is false. The […]

A Chemist Shines Light on a Surprising Prime Number Pattern

About a year ago, the theoretical chemist Salvatore Torquato met with the number theorist Matthew de Courcy-Ireland to explain that he had done something highly unorthodox with prime numbers, those positive integers that are divisible only by 1 and themselves. Torquato told de Courcy-Ireland, a final-year graduate student at Princeton who had been recommended by […]

The best representations of mathematics may not exist yet

Humility. It’s all I can feel after watching 3Blue1Brown’s latest maths video, in which Grant Sanderson and his team provide the most novel of approaches to solving 2D equations, using colour. It is the second time 3Blue1Brown has blown my mind to pieces in just a few weeks, following their earlier video that solved the […]

The path that the decimal number system took from India to medieval Europe

The history of the early development of the place value decimal number system is long, complicated and full of holes and I shan’t be dealing with it here. It also throws up some important and unanswered questions. The Babylonians developed a place value number system as early as the beginning of the second millennium BCE […]

We Need Bug Bounties for Bad Algorithms

Algorithmic auditors are a growing discipline of researchers specializing in computer science and human-computer interaction. They employ a variety of methods to tinker with and uncover how algorithms work, and their research has already sparked public discussions and regulatory investigations into the most dominant and powerful algorithms of the Information Age. From Uber and […]

The Gambler Who Cracked the Horse-Racing Code

On the evening of Nov. 6, 2001, all of Hong Kong was talking about the biggest jackpot the city had ever seen: at least HK$100 million (then about $13 million) for the winner of a single bet called the Triple Trio. The wager is a little like a trifecta of trifectas; it requires players to […]