These 10 unsolved problems in computer science, from P versus NP to quantum advantage, bear on cryptography, algorithm design and computing's limits — here is what each asks That distinction sounds abstract, but it decides what is feasible. A problem solvable in…
A question posed by Sir Walter Raleigh about cannonballs inadvertently led to a puzzle that mathematicians have been trying to solve for centuries By Manon Bischoff edited by Daisy Yuhas Astronomer Johannes Kepler hypothesized that this arrangement of spheres would…
OpenAI released solutions to three blockbuster math problems that have long vexed researchers yesterday. One was a surprise rejection of the Exponential Time Hypothesis (ETH), a durable assumption in computer science that plays a large role in how we understand…
So I've been familiar with the basics of polarization since forever, but I recently realized circular polarization is a mystery to me. I've heard of it in conjunction with eg satellite broadcasts, but I always thought it described aggregate behavior…
Joshua Biro reports from an online workshop he held to find out how we know if a student has really understood a piece of physics How do you know when a student has really understood a piece of physics? That…
The educator behind Super 30 is taking his teaching online, aiming to reach students who dream of cracking competitive examinations but cannot afford expensive coaching. For a student struggling with mathematics, the difference between understanding a difficult concept and giving up…
Terence Tao, who was born in Australia, demonstrated extraordinary mathematical skills from a young age. He began learning calculus at the age of 7 and became the youngest winner of the International Mathematical Olympiad at 13. After earning his Ph.D. from Princeton…
The reduced system's answers at relax / aniso1 / aniso2, for the 23 orbits of type (N4): The per-instance times, proof sizes and the SHA-256 of every certified CNF are in cube_groups/results/m98b (m98b_rows.json, m98b_grade.json). The proofs were deleted after checking; anyone can rebuild a CNF with…
For decades, a fundamental question about the difficulty of computing in high-dimensional spaces has resisted proof. New research resolves this question, removing a major theoretical obstacle to understanding the efficiency of randomized algorithms used across science and computing. The Kannan…
The activity in the room may look like learning, but how can teachers be sure? These three interconnected strategies can help. One of the biggest challenges for math teachers is consistently recognizing a student’s thought process. Research has shown that…
The branches of Geometry.
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