Geometers Engineer New Tools to Wrangle Spacecraft Orbits
In October, a Falcon Heavy rocket is scheduled to launch from Cape Canaveral in Florida, carrying NASA’s Europa Clipper mission. The $5 billion mission is designed to find out if Europa, Jupiter’s...
View ArticleMathematicians Marvel at ‘Crazy’ Cuts Through Four Dimensions
The central objects of study in topology are spaces called manifolds, which look flat when you zoom in on them. The surface of a sphere, for instance, is a two-dimensional manifold. Topologists...
View ArticleTo Pack Spheres Tightly, Mathematicians Throw Them at Random
Mathematicians like to generalize concepts into higher dimensions. Sometimes this is easy. If you want to efficiently pack squares in two dimensions, you arrange them like a checkerboard. To squeeze...
View ArticleA Rosetta Stone for Mathematics
In 1940, from a jailhouse in Rouen, France, André Weil wrote one of the most consequential letters of 20th-century mathematics. He was serving time for refusing to join the French army, and he filled...
View ArticleStrangely Curved Shapes Break 50-Year-Old Geometry Conjecture
In an old Indian parable, six blind men each touch a different part of an elephant. They disagree about what the elephant must look like: Is it smooth or rough? Is it like a snake (so thinks the man...
View ArticleHow Failure Has Made Mathematics Stronger
Reading a math paper is a bit like having dinner at a nice restaurant. The entrée might taste delicious, but it doesn’t tell the full story of how it was made. Clever recipes that end up tasting funky...
View ArticleMathematicians Attempt to Glimpse Past the Big Bang
About 13.8 billion years ago, the entire cosmos consisted of a tiny, hot, dense ball of energy that suddenly exploded. That’s how everything began, according to the standard scientific story of the Big...
View ArticleIn Highly Connected Networks, There’s Always a Loop
As mathematical abstractions go, graphs are among the simplest. Scatter a bunch of points in a plane. Connect some of them with lines. That’s all a graph is. And yet they are incredibly powerful. They...
View ArticleHow Is Science Even Possible?
The universe seems like it should be unfathomably complex. How then is science able to crack fundamental questions about nature and life? Scientists and philosophers alike have often commented on the...
View ArticleHow the Square Root of 2 Became a Number
The ancient Greeks wanted to believe that the universe could be described in its entirety using only whole numbers and the ratios between them — fractions, or what we now call rational numbers. But...
View ArticleWhy Is This Shape So Terrible to Pack?
For centuries, mathematicians suspected that hexagonal tiles are the best possible way to fill space. By this they mean that if you want to subdivide a large area into tiles of equal size while...
View ArticleWhat Can Tiling Patterns Teach Us?
If you cover a surface with tiles, repetitive patterns always emerge — or do they? In this week’s episode, mathematician Natalie Priebe Frank and co-host Janna Levin discuss how recent breakthroughs in...
View ArticleHow America’s Fastest Swimmers Use Math to Win Gold
In the fall of 2014, Andrew Wilson took a front-row seat in Ken Ono’s number theory class at Emory University in Atlanta. Wilson was not only double majoring in applied math and physics, he was a...
View Article‘Sensational’ Proof Delivers New Insights Into Prime Numbers
Sometimes mathematicians try to tackle a problem head on, and sometimes they come at it sideways. That’s especially true when the mathematical stakes are high, as with the Riemann hypothesis, whose...
View ArticleWhat Are Sheaves?
In 1940, the French mathematician and artillery officer Jean Leray was taken prisoner by the Germans. He told his captors that he was a topologist, fearful that if they discovered his true area of...
View ArticleMonumental Proof Settles Geometric Langlands Conjecture
A group of nine mathematicians has proved the geometric Langlands conjecture, a key component of one of the most sweeping paradigms in modern mathematics. The proof represents the culmination of three...
View ArticleHow Does Math Keep Secrets?
Can you keep a secret? Modern techniques for maintaining the confidentiality of information are based on mathematical problems that are inherently too difficult for anyone to solve without the right...
View ArticleGrad Students Find Inevitable Patterns in Big Sets of Numbers
In late 2017, Ashwin Sah and Mehtaab Sawhney met as undergraduates at the Massachusetts Institute of Technology. Since then, the pair have written a mind-boggling 57 math proofs together, many of them...
View ArticleThe Geometric Tool That Solved Einstein’s Relativity Problem
After Albert Einstein published his special theory of relativity in 1905, he spent the next decade trying to come up with a theory of gravity. But for years, he kept running up against a problem. He...
View ArticleMathematicians Prove Hawking Wrong About the Most Extreme Black Holes
To understand the universe, scientists look to its outliers. “You always want to know about the extreme cases — the special cases that lie at the edge,” said Carsten Gundlach, a mathematical physicist...
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