Mathematics in the Age of AI

Tao's Rule of Thumb (which applies very well to software):

> My own suggested rule of thumb: if the authors cannot convincingly demonstrate that they are able to give a clear, expert-level talk on their results, one that is correct and properly attributed, then the result should not be published. A proof that no human can properly explain should be viewed as incomplete, even if it has been formally verified.

Terence argues that explanation of results ("understanding") will be the new bottleneck in math research but I am not sure this is the real bottleneck for progress.

Understanding was critical for the field to progress when only humans were involved but if humans are not needed to make progress, I wonder if we split into two worlds: an AI math-world where amazing new results continue at a rapid pace bottlenecked only by compute/cost and a human math-world where we understand a subset of the AI math-world as a hobby (similar to Stockfish vs human chess).

Terence Tao's quote about AI's math proofs is relatable outside of pure math: "the writing very often dwells at length on trivialities while passing briefly through — or even actively obscuring — the most interesting and novel portions of the argument."

If the title have said in the age of "LLMs", I might have given it a try.

Anyone else print their white papers before reading? (At least the short ones)

Maybe the Hitchhikers Guide to the Galaxy series was predictive in pointing out the problems of ill defined questions (The Answer to the Ultimate Question of Life, the Universe, and Everything).

Not using AI puts one at a huge disadvantage in a career setting. Ai can find deep references better than humans now, let alone actually doing the math. The challenge is knowing which problems to tackle given the cost limitations. If you have $10k to spend on tokens, you have to choose problems that can conceivably be solved within this budget.

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