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Equations, like numbers, cannot always be split into simpler elements.

Alexander Smith’s work on the Goldfeld conjecture reveals fundamental characteristics of elliptic curves.

A new statistical model appears to undermine long-held assumptions in number theory. How much should it be trusted when all that really matters is proof?

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.

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

When a crystallographer treated prime numbers as a system of particles, the resulting diffraction pattern created a new view of existing conjectures in number theory.

Generations of researchers have pursued his “Langlands program,” which seeks to create a grand unified theory of mathematics.

A famously difficult mathematical problem resisted solution for over 40 years. Mathematicians have finally resolved it by following an intuition that links number theory to physics.

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