## Mathematical hunches inspire decades of research

By David Shaw, 12 April 2018

The Langlands program links geometry and number theory. *Image: ©istock.com/agsandrew*

**It’s that time of year again! The winner of the Abel prize, mathematics’ answer to the Nobel, has been announced. This year’s winner is Robert Langlands, a mathematician more famous for asking questions than answering them.**

Robert’s big contribution to maths is known as the Langlands program – a set of mathematical hunches known as conjectures. The Langlands program focuses on connecting two very different parts of mathematics. On one side is number theory, the study of whole numbers and interesting patterns like primes. On the other side is geometry, the study of shapes, curves and space.

First jotted down in a letter all the way back in 1967, Robert’s ideas have since led to a wealth of mathematical research. As one example, Andrew Wiles’ proof of Fermat’s last theorem is part of the Langlands program. This is considered one of the most important mathematical discoveries in living memory.

So far, mathematicians have proven several of these conjectures, but there’s still plenty of work to do on the Langlands program. Many mathematicians think that all of Robert’s hunches are correct, but it may take decades more to prove it, or to show where Robert’s ideas are wrong. But whether Robert is right or wrong, he’s helped mathematicians to ask and answer some really inspiring questions!

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