A mathematician describes using an AI model to write and verify proofs in real time using Lean, literate programming, and LaTeX.
Adapted from @nasqretI tested GPT-Astra on mathematics. It's a quantum leap. You can talk with the model and prove the statements live in Lean. The feeling is absolutely stunning. You can verify your ideas, compile truth. For a mathematician it feels like finally we arrived in the era where we can focus entirely on the ideation and exploration. Each lemma flows once the logic is set. Before the verification was lagging behind but Astra is very fast and for many tasks the formalization happens as you write your argument in Codex. If you tell the model to use literate programming + LaTeX you end up with your proof combined with the Lean code, everything explained as you wrote, mixed with small chunks of Lean which are digestible. I don't want to go back to the era where the only confirmation of the proof was "aha". Now the "aha" is followed by a green tick that indeed tells you that you have captured the essence. Imagine how cool it will be to have all the lemmas of the world combined in one giant database, pointing to people and models who found them. You compose and mix your ideas and build on the shoulders of the giants. But you see much further now and build much faster. And we are just at the beginning of those changes. So much work to do, so much fun!
