Lecture: How to Write a 21st Century Proof
Mathematicians have made a lot of progress in the last 350 years, but not in writing proofs. The proofs they write today are just like the ones written by Newton. This makes it all too easy to prove things that aren't true. I'll describe a better way that I've been using for more than 25 years.
(Please note the lecture contains an error. The correction can be found on this web page: https://lamport.azurewebsites.net/tla/proof-statistics.html)