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set theory
Abstractions blog
How Gödel’s Proof Works
His incompleteness theorems destroyed the search for a mathematical theory of everything. Nearly a century later, we’re still coming to grips with the consequences.
Multimedia
The Map of Mathematics
Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.
foundations of mathematics
With Category Theory, Mathematics Escapes From Equality
Two monumental works have led many mathematicians to avoid the equal sign. The process has not always gone smoothly.
infinity
Mathematicians Measure Infinities and Find They’re Equal
Two mathematicians have proved that two different infinities are equal in size, settling a long-standing question. Their proof rests on a surprising link between the sizes of infinities and the complexity of mathematical theories.
foundations of mathematics
Mathematicians Bridge Finite-Infinite Divide
A surprising new proof is helping to connect the mathematics of infinity to the physical world.
foundations of mathematics
Will Computers Redefine the Roots of Math?
The Fields medalist Vladimir Voevodsky has died at 51. This 2015 article describes his computer-aided quest to eliminate human error and rewrite the century-old rules underlying all of mathematics.
Mathematics
To Settle Infinity Dispute, a New Law of Logic
To determine the nature of infinity, mathematicians face a choice between two new logical axioms. What they decide could help shape the future of mathematical truth.