The recent announcement by OpenAI of a solution to the Clay Navier-Stokes Millennium Problem exhibits a fundamental difference between analytical mathematics based on symbols/signa and numerical mathematics based on numbers.
OpenAI thus has produced a 167 page "proof" consisting of words/signs/symbols describing a "construction" of a "solution" as a function solving Navier-Stokes equations showing development in finite time of a singularity ending existence. The "construction" consists of a 167 page string of words/signs/symbols describing the principles involved but not the numerical values of the "solution".
The "proof" is supplemented by a formal verification of steps of the "construction" based on logic and theorems expressed in words. Full verification is impossible since the words/symbols involved are not defined in finite terms.
No attempt is made to compute numerically the values of the solution to concretely inspect the development of the singularity. Such a thing would resort to numerical mathematics or number-crunching. This is most remarkable and signifies a deep rift between analytical mathematics based on words/symbols and numerical mathematics base on numbers.
A fundamental difference is that for numerical mathematics verification of correctness is possible by reducing the numerics to finite digital representation. It is thus possible to compute a numerical solution to Navier-Stokes equations and give a numerical quality measure of the constructed solution.
AI is a form of numerical mathematics and so when AI now is brought in to help mathematicians perform analytical mathematics, as in the present case with the goal of winning a prize, the whole thing appears to collapse to numerics.
We are thus back to Pythagoras and the basic difference appears to be finite vs non-finite. Formal verification is possible with finite but not with non-finite.
What does this mean for mathematics and mathematics education? To start over with what?
If we want we can compare with the difference between capital (words) and labour (numbers), with now labour coming out to control capital in a revolution. Ok?
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