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Number theorist Peter Scholze, who became Germany’s youngest ever full professor at the age of 24, and geometrician Caucher Birkar — a Kurdish refugee — are among the winners of this year’s Fields Medals, the most coveted awards in mathematics. The medals, which are given out every four years, were also awarded on 1 August to Alessio Figalli, a network-analysis researcher and Akshay Venkatesh, who also works on number theory. Their names were announced in Rio de Janeiro, Brazil, at the opening of the International Congress of Mathematicians.