Artur Avila

Avila is the new Field Medal (mathematicians’ Nobel Prize) recipient from Brazil, marking a first for his country. 

A major focus at IMPA [an institute even Brasilians themselves are surprised it exists -as most schools in the country are mired in heavy bureucracy-] is dynamical systems, the branch of mathematics that studies systems that evolve over time according to some set of rules — a collection of planets moving around a star, for example, or a billiard ball bouncing around a table, or a population of organisms that grows or declines over time [.. D]ynamical systems are everywhere in math and nature. “It’s like a glue that connects many other subjects,” Krikorian said [..]

In the decades preceding Avila’s work, mathematicians made a profound discovery: To produce complex behavior, it isn’t necessary to start with complex rules. Even simple rules when repeated again and again sometimes produce chaos: random-seeming, unpredictable behavior in which tiny changes in the starting conditions can produce dramatically different outcomes. [..]

His work “cannot be reduced to ‘one big theorem’ as Artur has so many deep results in several different topics,” said Marcelo Viana, who worked with Avila to solve a long-standing problem about the chaotic behavior of billiard balls. The two proved a formula that predicts which side of the table a ball is most likely to hit next — and which side it will likely hit after a thousand bounces, or a million, all with the same margin of error. [..]

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Losing 7:1 in a World Cup soccer game, then winning the Fields Medal? It is interesting times for Brazil.