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foundations of mathematics
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.
geometry
A Fight to Fix Geometry’s Foundations
When two mathematicians raised pointed questions about a classic proof that no one really understood, they ignited a years-long debate about how much could be trusted in a new kind of geometry.
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.
algorithms
In Computers We Trust?
As the role of computers in pure mathematics grows, researchers debate their reliability.