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Two mathematicians have found what they say is a hole at the heart of a proof that has convulsed the mathematics community for nearly six years.

In math, sometimes the most common things are the hardest to find.

The 19th-century discovery of numbers called “quaternions” gave mathematicians a way to describe rotations in space, forever changing physics and math.

An upstart field that simplifies complex shapes is letting mathematicians understand how those shapes depend on the space in which you visualize them.

Quanta’s In Theory video series returns with an exploration of a mysterious mathematical pattern found throughout nature.

Studying the structure of existing friendships in your community can help you forge the best connections when forming a new circle of friends.

Akshay Venkatesh, a former prodigy who struggled with the genius stereotype, has won a Fields Medal for his “profound contributions to an exceptionally broad range of subjects in mathematics.”

The theoretical computer scientist Constantinos Daskalakis has won the Rolf Nevanlinna Prize for explicating core questions in game theory and machine learning.

The 30-year-old math sensation Peter Scholze is now one of the youngest Fields medalists for “the revolution that he launched in arithmetic geometry.”