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elliptic curves
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New Proof Shows Infinite Curves Come in Two Types
Alexander Smith’s work on the Goldfeld conjecture reveals fundamental characteristics of elliptic curves.
Without a Proof, Mathematicians Wonder How Much Evidence Is Enough
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?
A Master of Numbers and Shapes Who Is Rewriting Arithmetic
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.”
Mathematicians Find Moonshine Link for Pariah Symmetries
A type of symmetry so unusual that it was called a “pariah” turns out to have deep connections to number theory.
The Oracle of Arithmetic
At 28, Peter Scholze is uncovering deep connections between number theory and geometry.
The Musical, Magical Number Theorist
The search for artistic truth and beauty has led Manjul Bhargava to some of the most profound recent discoveries in number theory, which have helped earn him the Fields Medal.
Mathematicians Shed Light on Elliptic Curves
Two young mathematicians are illuminating a frontier in the study of rational solutions to polynomial equations: the cubics.