Ngô Bảo Châu proves in 2008 the so-called "Fundamental Lemma", a central technical conjecture of the Langlands program originally formulated in the 1980s by Robert Langlands and Diana Shelstad, whose resolution had remained pending for more than two decades and was blocking progress on much of the broader program. Ngô employs algebraic-geometry techniques for the proof — in particular Hitchin fibrations — in an approach that novelly combines geometric methods with a problem of essentially arithmetic nature. The result was included by Time magazine among the top ten scientific discoveries of 2009. Ngô received the Fields Medal in 2010.