At 8:15 am CET sharp I started my first lecture for our math majors entitled "Computer assisted solutions to mathematical problems". No, I did not expect that I will have to start this lecture at such a historic moment for mathematics. So what I did? I told students a nice story about the passage from mathematical numerics, to symbolic methods, to formalization of mathematical proofs. We had many examples, like "what is square root of 2?", "is Python float actually a number?", "what it means to show equality in 1+1/(1+1/(... ) = (1+sqrt(5))/2?". I barely talked about AI because it was my story about human UNDERSTANDING. I told my students that it's particularly important now to understand that they need to work hard to stay in the loop with the reality and it's going to be fascinating to learn beautiful new concepts that will emerge soon. After 90 minutes they missed the moment where we were supposed to stop, so I had to pause abruptly. But then they stayed with many questions about simplify tactic in SymPy, about the distinction between truth and provability etc. They even developed a healthy paranoia about checking the domain of the variables they discuss. It was good time. So, yeah, bring upon this world more of these AI generated new results. We are still here and we need to train people to think. That won't change. And there is an infinite number of new directions we can develop from this point on. Brave new world!
We’re releasing a broad range of new mathematical results produced by an internal frontier model.
We’ve been consulting with the independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study, and we have drawn on their advice and public recommendations to inform how we release these results.
github.com/openai/math