Math
Risky Giant Steps Can Solve Optimization Problems Faster
New results break with decades of conventional wisdom for the gradient descent algorithm.
Math Proof Draws New Boundaries Around Black Hole Formation
For a half century, mathematicians have tried to define the exact circumstances under which a black hole is destined to exist.
The Lawlessness of Large Numbers
Mathematicians can often figure out what happens as quantities grow infinitely large. What about when they are just a little big?
Are All Brains Good at Math?
Math provokes dread in so many people—yet we are all born with a sense for numbers.
A Numerical Mystery From the 19th Century Finally Gets Solved
Two mathematicians have proven Patterson’s conjecture, which was designed to explain a strange pattern in sums involving prime numbers.
Math’s “Oldest Problem Ever” Gets a New Answer
A new proof significantly strengthens a decades-old result about the ubiquity of ways to represent whole numbers as sums of fractions.
An Ancient Geometry Problem Falls to New Mathematical Techniques
Three mathematicians show, for the first time, how to form a square with the same area as a circle by cutting them into interchangeable pieces that can be visualized.
Mathematicians Find Structure in Biased Polynomials
New work establishes a tighter connection between the rank of a polynomial and the extent to which it favors particular outputs.
In Topology, When Are Two Shapes the Same?
As topologists seek to classify shapes, the effort hinges on how to define a manifold and what it means for two of them to be equivalent.
