Math
149 articles-
Alan Turing and the Power of Negative Thinking
Mathematical proofs based on a technique called diagonalization can be relentlessly contrarian, but they help reveal the limits of algorithms.
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Risky Giant Steps Can Solve Optimization Problems Faster
New results break with decades of conventional wisdom for the gradient descent algorithm.
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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.
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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?
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The Unbelievable Untangling Worms
Solving nature’s greatest Gordian knot.
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Are All Brains Good at Math?
Math provokes dread in so many people—yet we are all born with a sense for numbers.
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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.
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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.
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Imaginary Numbers Are Reality
How the modern world arose from imaginary numbers.
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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.
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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.
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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.
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Computer Scientists Discover Limits of Major Research Algorithm
The most widely used technique for finding the largest or smallest values of a math function turns out to be a fundamentally difficult computational problem.
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Why You May Have More Friends Than Your Friends Do
There’s a rude charm to the title, “Why Your Friends Have More Friends Than You.” It’s catchy, like the title of an antagonistic explainer: Here are the causes of your lackluster social life. It sounds more like a New York Times op-ed than an academic paper. But in fact, “Why Your Friends Have More Friends […]
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Pandemic Puts Mathematical Modeling Through Its Paces
Mathematical tools that proved essential during the pandemic were in many cases invented by mathematicians who had no particular goal in mind.
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Mathematicians Answer Old Question About Odd Graphs
A pair of mathematicians solved a legendary question about the proportion of vertices in a graph with an odd number of connections.
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How Mathematicians Use Homology to Make Sense of Topology
Originally devised as a rigorous means of counting holes, homology provides a scaffolding for mathematical ideas, allowing for a new way to analyze the shapes within data.
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New Quantum Algorithms Finally Crack Nonlinear Equations
Two teams found different ways for quantum computers to process nonlinear systems by first disguising them as linear ones.
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How the Slowest Computer Programs Illuminate Math’s Fundamental Limits
The goal of the “busy beaver” game is to find the longest-running computer program. Its pursuit has surprising connections to some of the most profound questions and concepts in mathematics.
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Undergraduate Math Student Pushes Frontier of Graph Theory
At 21, Ashwin Sah has produced a body of work that senior mathematicians say is nearly unprecedented for a college student.
