The International Mathematical Olympiad (“IMO”) is the world’s most prestigious competition for young mathematicians, and has been held annually since 1959. Each country taking part is represented by six elite, pre-university mathematicians who compete to solve six exceptionally difficult problems in algebra…
We have solved a traveling salesman problem (TSP) to walk to 81,998 bars in South Korea. The problem was created using the Open Source Routing Machine (OSRM) to build a table of the 3,361,795,003 point-to-point travel times, one for each pair of bar locations. Our computation produced a tour together with a proof that…
This is the companion website for the paper Understanding Optimization in Deep Learning with Central Flows , published at ICLR 2025.
A reflection on cultural differences observed at the 2025 Joint Mathematics Meeting.
As programming languages researchers, we’re entitled to a certain level of mathematical rigor behind the languages we write and analyze. Programming languages have semantics , which are definitions of what statements in the language mean. We can use those semantics to do all sorts of useful things, like error…
Today we’ve released a pre-publication version of an update to our 2022 paper “Progress toward fusion energy breakeven and gain as measured against the...
It is thought that Euclid wrote Elements in about 300 BC, but Oliver Byrne turned it into one of the true gems of visualization — and made it about 100 times more readable. By seamlessly combining typeset text (Caslon, if you’re interested) with minimalist geometric drawings in primary col
A novel data structure has been invented four times now, with three different names. We think that's a good sign.
Normalizing Flows (NFs) are likelihood-based models for continuous inputs. They have demonstrated promising results on both density…
A Penn State engineering student's work on a century-old math problem that expands research in aerodynamics, unlocking new possibilities in wind turbine design, was recently published in Wind Energy Science.
Posted by Joshua Bloch, Software EngineerI remember vividly Jon Bentley's first Algorithms lecture at CMU, where he asked all of us incoming Ph.D. ...
A geometric framework for co-designing neural net optimizers with manifold constraints.
A new algebraic method for hardware-accelerated bilinear interpolation on convex quadrilaterals is presented, using the Barycentric coordinate feature of modern GPUs.
In numerous applications of machine learning, Hessians and Jacobians exhibit sparsity, a property that can be leveraged to vastly accelerate their computation. While the usage of automatic differentiation in machine learning is ubiquitous, automatic sparse differentiation (ASD) remains largely unknown. This post…
We’re excited to announce Flummoxagon, a new geometric puzzle game that might just leave you flummoxed. Imagine a mash-up of Pentominoes and Sudoku. Your goal is to fit all the pieces into the hexa…
Educators can show in secondary school maths that AI systems don’t think, making maths more interesting while teaching core concepts of AI.
Quanta Books is delighted to announce two new upcoming books by mathematician Terence Tao and theoretical physicist David Tong. Six Math Essentials will be Tao’s first math book written for a popular…
Airline pricing may seem mystifying, but behind every airfare is a complex system of fare buckets and inventory controls. Airlines don't just sell seats - they manage a dynamic inventory of fares, divided into booking classes (fare buckets) with different prices and rules. For the technically curious, understanding…
V8’s Math.random implementation now uses an algorithm called xorshift128+, improving the randomness compared to the old MWC1616 implementation.
An exploration of the mindset, methods, and motivations behind crafting tiny, expressive shaders that combine code, art, and constraint.
Basic Economy fares are ultra-restricted airline tickets that offer a lower base price in exchange for fewer benefits than standard economy class. Introduced by major U.S. carriers in the 2010s, these fares have become a widespread strategy for market segmentation - a textbook example of price discrimination in…
Transducer: Composition, Abstraction, Performance
