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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 complete classification could lead to a wealth of new materials and technologies. But some exotic phases continue to resist understanding.
Voevodsky’s friends remember him as constitutionally unable to compromise on the truth — a quality that led him to produce some of the most important mathematics of the 20th century.
After her untimely death, Maryam Mirzakhani’s life is best remembered through her work.