It is mathematical folklore that one should attempt to prove a conjecture by day, disprove it by night. Jordan Ellenberg recently popularized this in his 2014 book. He and I both heard this from Barry Mazur, but it dates at least to Bing, if not antiquity.

What is the purpose of mathematics? To be the architect of new conventions by seeing clearly past the old? If so, believing that the entire point is proving statements is a poor start. Bill Thurston was a visionary who happened to prove a great deal of what he saw, but his influence was his vision.

For those of us who like to understand every line of code we generate, and have labored for years to learn how to make best use of AI, a factor of two is a reasonable estimate for our productivity gain.

For those of us who believe mathematics is about achieving human understanding, having machines decide what's true and what isn't makes a night and day difference. Again, about a factor of two.