过去三十年相关领域的数学家一致期望Langlands Program中的一个基本引理会被证明的确是精确的。
Ngo Bao Chau一位在法国Université Paris-Sud 和普林斯顿Institute for Advanced Study (IAS) 工作的越南数学家（1972年生于越南河内），证明了这一引理，2009年相关领域的数学家验证了他的证明。这一结果被《时代》杂志列为2009年度十大科学发现的第七项。

The Fundamental Lemma, Solved

In 1979 the Canadian-American mathematician  Robert Langlands developed an ambitious and revolutionary theory that  connected two branches of mathematics called number theory and group theory. In a dazzling set of conjectures and insights, the theory captured deep symmetries  associated with equations that involve whole numbers, laying out what is now known as the  Langlands program. Langlands knew that the task of proving the assumptions that underlie his theory would be the work of generations. But he was convinced that one  stepping stone that needed confirmation — dubbed the  "fundamental lemma" — would be reasonably straightforward. He, his —  collaborators and his students were able to prove special cases of this fundamental theorem. But  proving the general case proved more difficult than Langlands anticipated — so difficult, in fact, that it took 30  years to  finally achieve. Over the past few years, Ngo Bao Chau, a Vietnamese  mathematician working at Université Paris-Sud and the Institute for Advanced  Study (IAS) in Princeton, formulated an ingenious proof of the fundamental lemma. When it was checked this year and confirmed to be  correct, mathematicians around the globe breathed a sigh of relief. Mathematicians'  work in this area in the last three decades was predicated on the principle that the  fundamental lemma was indeed accurate and would one day be proved. "It's as if  people were working on the far side of the river waiting for someone to throw this bridge  across," says Peter Sarnak, a number theorist at IAS. "And now all of sudden everyone's work on the other side of the river has been proven."

《时代》杂志列为2009年度十大科学发现

1.         Our Oldest Ancestor, "Ardi"
2.         The Human Epigenome, Decoded
3.         Gene Therapy Cures Color Blindness
4.         A Robot Performs Science
5.         Breeding Tuna on Land
6.         Water on the Moon
7.         The Fundamental Lemma, Solved
8.         Teleportation!
9.         The Large Hadron Collider, Revived
10.        A New Planet (or Brown Dwarf ) Discovered