What's up in

set theory

Measuring tapes
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.

Image of spiral staircase.
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.