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Two monumental works have led many mathematicians to avoid the equal sign. The process has not always gone smoothly.
As chemists tie the most complicated molecular knot yet, biophysicists create a “periodic table” that describes what kinds of knots are possible.
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.