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I know it's incredibly presumptuous for me, a nobody, to say this to 25 Fields Medalists, but: Perhaps you are misaligned. Who decided the goal of math must b
by brap 21d ago
I know it's incredibly presumptuous for me, a nobody, to say this to 25 Fields Medalists, but:
Perhaps you are misaligned.
Who decided the goal of math must be human insight?
First off, some mathematical truths might simply be far beyond our biological comprehension.
Second, for us non-mathematicians, the value of math isn't in understanding exactly why a result is true, it’s in how those results can be applied to actually improve our lives.
Isn't this why we have math in the first place? To solve our real problems? Over time it morphed into this pursuit of pure theoretical insight, probably out of necessity at the time, but is it still necessary?
- kaffekaka 21d ago> Second, for us non-mathematicians, the value of math isn't in understanding exactly why a result is true, it’s in how those results can be applied to actually improve our lives. This is just the problem with the Navier-Stokes solution. We now (supposedly) know the truthiness of the statement, but we have no more understanding of why or how it applies to our quality of life. This is exactly the issue Tao is pointing at.
- brap 21d agoRight, but this leads to my main question: is this still necessary? By analogy with code, do we still need code to be maintainable/readable if machines write it all? (Obviously for now the answer is yes, but I’m not sure this will be the case in 5-10 years)
- timmg 21d agoWhat I don’t get: this letter seems to argue that if a human had solved this problem then that wouldn’t be the case (?)