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A graduate student has helped illuminate a long-suspected connection between addition and multiplication.

Digital security depends on the difficulty of factoring large numbers. A new proof shows why one method for breaking digital encryption won’t work.

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.