Every four years, at an international gathering of mathematicians, the subject's youngest and brightest are honored with the Fields Medal, often described as the Nobel Prize of mathematics. The New York Times: This year's recipients, announced on Wednesday at the International Congress of Mathematicians in Rio de Janeiro, include one of the youngest ever: Peter Scholze, a professor of mathematics at the University of Bonn who is 30 years old. Two weeks ago, Peter Woit, a professor at Columbia University who blogs about mathematics and physics, was among those who anticipated that Dr. Scholze would receive the medal. Dr. Woit said Dr. Scholze was "by far the most talented arithmetic geometer of his generation." By custom, Fields medals are bestowed to mathematicians 40 years old or younger. That means Dr. Scholze would have still been eligible for another two rounds of medals. The medal, first awarded in 1936, was conceived by John Charles Fields, a Canadian mathematician. The youngest winner, Jean-Pierre Serre in 1954, was 27. The other Fields medalists this year are Caucher Birkar, 40, of the University of Cambridge in England; Alessio Figalli, 34, of the Swiss Federal Institute of Technology in Zurich; and Akshay Venkatesh, 36, of the Institute for Advanced Study in Princeton and Stanford University in California. Peter Scholze's award cites "the revolution that he launched in arithmetic geometry," the study of shapes that arise from the rational-number solutions to polynomial equations (like xy3 + x2 = 1 or x2 â" y3z = 3). More about him here. As a mathematician, Caucher Birkar has helped bring order to the infinite variety of polynomial equations -- those equations that consist of different variables raised to various powers. No two equations are exactly alike, but Birkar has helped reveal that many can be neatly categorized into a small number of families. [As a reader pointed out, Birkar's award was stolen within minutes of him receiving it.] UPDATE (8/4/18): Organizers have announced they'll provide an identical replacement medal.

Once a classics student with no particular affinity for mathematics, Alessio Figalli has gone on to shake the venerable mathematical discipline of analysis, which concerns the properties of certain types of equations. Figalli's results have provided a refined mathematical understanding of everything from the shape of crystals to weather patterns, to the way ice melts in water. Akshay Venkatesh, a former prodigy who struggled with the genius stereotype, has won a Fields Medal for his "profound contributions to an exceptionally broad range of subjects in mathematics."