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.

Turing's contributions during World War II, particularly in breaking the German Enigma code, were pivotal in turning the tide of the war, showcasing his genius and ingenuity.

In mathematics, there are many obstructions to solving problems, and computer scientists have been effective in ruling out certain approaches through no-go theorems, indicating that some problems may be undecidable.

The theories that explain the universe often involve the same mathematical objects that solve mathematical problems, indicating a deep connection between the two fields.

I'm often referred to as the Mozart of math, having won the Fields Medal and the Breakthrough Prize in mathematics, and contributed groundbreaking work across a wide range of fields in mathematics and physics.

Mathematics is about finding connections between different fields, and this process has been ongoing throughout history, such as the unification of geometry and number theory.

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

AI could assist in generating conjectures by identifying connections between seemingly unrelated mathematical concepts, which is a significant aspect of mathematical discovery.