AI systems like AlphaProof are on the right track and will continue to improve, suggesting that the future of mathematics could be transformed by AI.

AI systems like DeepMind's AlphaProof are trained using reinforcement learning on both successful and failed formal proofs, demonstrating the potential for AI to assist in solving high-level mathematical problems.

If AI can develop a sense of viability for proof strategies, it could potentially collaborate with human mathematicians, enhancing the problem-solving process.

AI struggles with generating long-form proofs because it often produces outputs that appear correct but contain subtle errors that are difficult to detect.

AI is expected to change mathematics significantly, with projects like AlphaProof focusing on proving conjectures and potentially leading to new interesting conjectures in the future.

The bottleneck for AI development may shift from generating solutions to verifying their accuracy and reliability.

While AI is currently proving mathematical concepts, the future challenge is whether AI can propose interesting new hypotheses, which remains uncertain.

Turing's work on uncomputable numbers and Gödel's incompleteness theorems reveal that not all mathematical truths can be proven, challenging the belief that every mathematical problem is solvable.

Humans possess a 'mathematical smell' that helps them identify flawed proofs, a quality that AI has yet to replicate effectively.