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For decades mathematicians have searched for a specific pair of surfaces that can’t be transformed into each other in four-dimensional space. Now they’ve found them.

“Ribbon concordance” will let mathematicians compare knots by linking them across four-dimensional space.

Steven Strogatz explores the mysteries of knots with the mathematicians Colin Adams and Lisa Piccirillo.

The noted mathematician and author Steven Strogatz explains how the conversations with experts in his new *Quanta Magazine* podcast address his lifelong fascination with timeless mysteries.

Two recent collaborations between mathematicians and DeepMind demonstrate the potential of machine learning to help researchers generate new mathematical conjectures.

Even as mathematicians and computer scientists proved big results in computational complexity, number theory and geometry, computers proved themselves increasingly indispensable in mathematics.

To distinguish between fundamentally different objects, mathematicians turn to invariants that encode the objects’ essential features.

It took Lisa Piccirillo less than a week to answer a long-standing question about a strange knot discovered over half a century ago by the legendary John Conway.

The legendary mathematician, who died on April 11, was curious, colorful and one of the greatest problem-solvers of his generation.

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