Robert Langlands (born in 1936) is a Canadian mathematician who is now professor emeritus at Princeton University. Langlands is best known for the “Langlands program,” which is a profound and far-reaching set of conjectures forging connections between many areas of mathematics. Using the language of physics, the Langlands program is sometimes called the grand unified field theory of mathematics.
In March 2018, the Norwegian Academy of Science and Letters awarded its highly prestigious Abel prize to Langlands. One of the past winners is Andrew Wiles, who proved Fermat’s last theorem in the 1990’s. There is no Nobel prize in Mathematics, and the Fields medals only go to those under forty. The Abel prize, therefore, may be considered as a kind of lifetime achievement award given to the greatest mathematicians.
The Langlands Program
The Langlands program can be described accurately in highly technical language, or imprecisely in language that is more accessible. I’m no expert in the mathematics around the program, and I don’t think referencing “automorphic L-functions” or “admissible irreducible representations of a reductive group” here will be that illuminating for most readers.
At its core, the Langlands program relates algebra (representation theory, group theory, Galois theory) to number theory and analysis (automorphic forms, reciprocity theorems) and geometry (curves, motives, and bundles). The connections it provides and conjectures it poses are deep and give insights into unexpectedly connected parts of mathematics.
Here is a short video by the Toronto Star to explain the Langland’s program to the layperson.
Mathematician Edward Frenkel lectures on the Langlands program, in a video accessible to a mathematics graduate student or advanced mathematics undergraduate. Be warned: there are four hours of lectures over four parts!
Finally, for even more background, Robert Langlands, James Arthur, and Edward Frenkel gave Abel Lectures at the University of Oslo this May 23.
Langland’s second win
As if winning the Abel prize was not enough, Robert Langlands did something truly extraordinary and donated the associated cash prize (which equals about $700,000 US dollars) to various institutions for the teaching of mathematics and to the benefit of Canadian indigenous peoples.
That is wonderfully generous, and Langlands should be celebrated as much for winning the Abel prize but also for his act of selflessness. I’ve said before that students would benefit significantly from enrichment in mathematical education, and supporting such a cause will improve numeracy and lift up a generation of budding mathematicians. Financial support is also critical for underrepresented groups who have been traditionally discouraged from education in higher mathematics.
Congratulations to Langlands! His program will keep mathematicians active for the foreseeable future, and his act of selfless charity won’t soon be forgotten.