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Logic
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How Close Are Computers to Automating Mathematical Reasoning?
AI tools are shaping next-generation theorem provers, and with them the relationship between math and machine.
Hidden Computational Power Found in the Arms of Neurons
The dendritic arms of some human neurons can perform logic operations that once seemed to require whole neural networks.
Why the Proof of Fermat’s Last Theorem Doesn’t Need to Be Enhanced
Decades after the landmark proof of Fermat’s Last Theorem, ideas abound for how to make it even more reliable. But such efforts reflect a deep misunderstanding of what makes the proof so important.
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.
Mathematicians Bridge Finite-Infinite Divide
A surprising new proof is helping to connect the mathematics of infinity to the physical world.
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.
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.
In Computers We Trust?
As the role of computers in pure mathematics grows, researchers debate their reliability.