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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.