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In mathematics, where proofs are everything, evidence is important too. But evidence is only as good as the model, and modeling can be dangerous business. So how much evidence is enough?

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?

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.”

A type of symmetry so unusual that it was called a “pariah” turns out to have deep connections to number theory.

At 28, Peter Scholze is uncovering deep connections between number theory and geometry.

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.

Two young mathematicians are illuminating a frontier in the study of rational solutions to polynomial equations: the cubics.