What Is the Langlands Program?

By Alex Kontorovich, Member (2009–10, 2013–14, 2016) and von Neumann Fellow (2017–18) in the School of Mathematics

"Not long ago, I was asked to explain the so-called Langlands program in a single tweet. Impossible, I immediately thought. It’s one of the biggest, most sweeping projects in mathematics, capable of connecting distant realms of research and, naturally, fiendishly difficult to describe.

But then I remembered the story of a student asking the great Talmudic sage Hillel to explain the whole Bible while standing on one foot. The reply: 'Do not do to your neighbor what is hateful to you; the rest is generalization.' Of course, you can find much more wisdom in the Bible than that, and you can spend a lifetime studying said generalizations. But to Hillel, that was the kernel that started it all. Was there an analogue for Langlands? I’m no Hillel, but here is the best I can do."