Terry Tao Became an Evangelist for AI in Math

Posted by Tomte 1 day ago

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Comments

Comment by norir 1 day ago

Terry Tao is a next level vibe coder: he inspires people to do his vibe coding for him. As someone with a background in advanced math, though never even close to Tao's level, I find myself skeptical about this type of mathematics. I don't personally find it beautiful and it feels like the line between the profound and the trivial (as in of minimal importance not difficulty) is blurry. One could argue for pure mathematics that is of no practical utility but is aesthetically beautiful, but I struggle to see the beauty in a gargantuan lean proof constructed by 100 different people. Perhaps this work will lead to deeper insight about the universe and the human condition, but I catch a whiff of problem solving for the sake of problem solving untethered from a deeper sense of purpose and meaning.

Comment by throwaway67678 1 day ago

Arguments about beauty don't lead anywhere constructive because they are too observer- and context-dependent. Poincaré himself was decrying continuous non-differentiable functions as abominations. The monster group is, well, just like that. What feels intellectually ugly for one generation is natural for the next, and the field moves on

Comment by potbelly83 1 day ago

That's not what op is arguing. To use your example, coming up with singular examples of continuous non-differentiable functions is an example of "ugly" mathematics, whereas putting them into a nice framework where they can be analyzed as a whole (i.e. functional analysis, density of such functions, etc...) is an example "elegant and insightful" mathematics. The same with the monster group, on its own maybe nothing special, but then you have the connections with other branches of math. Tao seems so focused on the individual problems and not their connections/generalizations.

Comment by throwaway67678 1 day ago

Well one does have to come up with continuous non-differentiable functions to begin with, right? Weierstrass had to shock the community with his weird series that's almost everywhere nondifferentiable before people could conceive of a nice framework that includes them. People do not invent whole encompassing abstractions out of nowhere

Comment by potbelly83 1 day ago

Great point, I think the argument you could make about Tao (fairly or unfairly) is he never tries to build that framework.

Comment by Ygg2 1 day ago

According to legends Pythagoreans tried to surpress existence of irrational numbers because they couldn't be expressed as ratio of natural numbers

Supposedly even drowned their member that divulged their existence.

Comment by zem 1 day ago

the analogy with experimental physics is a good one - being sure something is true is a good first step to developing an elegant proof of its truth.

Comment by nylonstrung 1 day ago

More accurate title would be "Terry Tao Became an Evangelist for Lean"