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▲ remus 13 hours ago

These things definitely were considered valuable contributions pre-AI, but were perhaps second fiddle to proving theorems. For example, part of the reason Erdős is so acclaimed is that he posed many interesting open questions which have kept mathematicians busy for many years.

I think Tao's point is that there's a necessary rebalancing and more weight should now be given to the non-proof stuff.

▲joe_the_user 4 hours ago | parent [-]

I should say, Erdős was acclaimed but actually far from universally popular within mathematics. I had a professor who advised me to stay away from another professor because the other professor was a follower of Erdős.

Pre-AI, I think it's correct to say that math exposition was given short shrift (but to be fair, at least in the US, math education fell under the umbrella of education schools and teacher training rather than university math departments and so professors of mathematics often could do little to change the sorry state of math education even if they wanted to).

But, on the other hand, the construction of grand structures, frameworks unifying various math fields, was already a competitor of the problem-solving paradigm (and Erdős' approach was actually an extreme wing of the problem-solving wing and his activity shouldn't be considered an example of what even a significant minority of math professors did).

See "The Erdős Paradox"

https://arxiv.org/html/1812.11935v1