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foundations of mathematics

<p>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.</p>
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.

<p>A surprising new proof is helping to connect the mathematics of infinity to the physical world.</p>
foundations of mathematics

Mathematicians Bridge Finite-Infinite Divide

A surprising new proof is helping to connect the mathematics of infinity to the physical world.

<p>When a legendary mathematician found a mistake in his own work, he embarked on a computer-aided quest to eliminate human error. To succeed, he has to rewrite the century-old rules underlying all of mathematics.</p>
Mathematics

Will Computers Redefine the Roots of Math?

When a legendary mathematician found a mistake in his own work, he embarked on a computer-aided quest to eliminate human error. To succeed, he has to rewrite the century-old rules underlying all of mathematics.

<p>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.</p>
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.

<p>As the role of computers in pure mathematics grows, researchers debate their reliability.</p>
algorithm

In Computers We Trust?

As the role of computers in pure mathematics grows, researchers debate their reliability.