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Can the Most Abstract Math Make the World a Better Place?
Columnist Natalie Wolchover explores whether applied category theory can be “green” math. “I’ve spent a long time exploring the crystalline beauty of traditional mathematics, but now I’m feeling an urge...
The Man Who Stole Infinity
Long-Lost Letters Reveal the Lies That Gave Rise To Modern Math In an 1874 paper, Georg Cantor proved that there are different sizes of infinity and changed math forever. A...
The Evolving Foundations of Math
An exploration of how mathematicians are still renovating and rebuilding the core pillars of their field today....
Long-Sought Proof Tames Some of Math’s Unruliest Equations
...held for this kind of PDE. Unfortunately, “the real world is nonuniformly elliptic,” said Giuseppe Mingione, a mathematician at the University of Parma in Italy. That meant mathematicians were stuck....
The Year in Mathematics
Explore a shape that can’t pass through itself, a teenage prodigy, and two new kinds of infinity. At 17, Hannah Cairo Solved a Major Math Mystery Mathematics is, at its...
String Theory Inspires a Brilliant, Baffling New Math Proof
...solutions have a richer, more complicated structure. The second category is where the mathematical juice is: It’s where mathematicians want to focus their attention to make major advances. But after...
What Are Lie Groups?
By combining the language of groups with that of geometry and linear algebra, Marius Sophus Lie created one of math’s most powerful tools. In mathematics, ubiquitous objects called groups display...
A New Bridge Links the Strange Math of Infinity to Computer Science
Descriptive set theorists study the niche mathematics of infinity. Now, they’ve shown that their problems can be rewritten in the concrete language of algorithms. All of modern mathematics is built...
New Proofs Probe Soap-Film Singularities
Mathematicians have broken through a long-standing barrier in the study of “minimizing surfaces,” which play an important role in both math and physics. In the mid-19th century, the Belgian physicist...