Where is Mathematics Going?

Over the last 2,500 years, the way we do mathematics has changed surprisingly little. In Euclid’s Elements, we see lemmas, theorems and proofs, with material building on earlier work and presented in essentially the same style as a modern mathematics textbook. As a consequence of this inertia, humanity now possesses an extraordinary body of mathematical knowledge. This knowledge is mostly correct, sometimes poorly presented and poorly referenced, is sometimes only “known to the experts,” contains plenty of errors (some serious), and gives rise to farcical situations such as the ABC conjecture, an important conjecture with a published proof in a reputable journal that many do not believe is correct.

Is there a better way to do this? In this Presidential Lecture, Kevin Buzzard will discuss the future of mathematics and the role computers can play in proof development through tools such as Lean.