Re: how long before the rest of the millennium math problems will be solved by AI?

On 02/29/2024 08:28 PM, sobriquet wrote:

Hi!
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Recently AI has bumped up its math skills and it can now compete in top
level math olympiad contests.
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https://venturebeat.com/ai/google-deepminds-ai-system-solves-geometry-problems-like-a-math-olympian/
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It seems to follow the same path as AI developments in go.
First it learned from human data and it got to top level human go
playing skills and then it learned things from scratch (without relying
on any human go knowledge/experience) and it got to skill levels way
beyond the best human go players.
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So it seems likely that AI will soon go way beyond the math skills it
has achieved so far. How long will it be before AI can solve all the 7
remaining millennium math problems?
My guess would be that it should have them solved in 10 years or less.
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https://en.wikipedia.org/wiki/Millennium_Prize_Problems

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Actually one might wonder if that first it will
"undecide" some what are "nonstandardly
undecide-able" results "standardly decided"
already, then for various "standard"
and "non-standard" results.
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Like, I wonder about the regulus and the 3-sphere.
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https://en.wikipedia.org/wiki/Smale%27s_problems
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This is that law(s) of large numbers exist,
and so lots of uniqueness results make
distinctness results, for finding these
sorts counterexamples, which "un-decide"
some of the standard things. (Which
would make them "standard" again, ....)
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Similarly the measure problem, it sort of
gets un-decided with some quite natural
results in geometry, or this "re-Vitali-ization"
bit, about quasi-invariant measure theory
and Ramsey theory, including Birkhoff.
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Sum-of-histories and sum-of-potentials and
this kind of thing, again is "continuum dynamics".
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So, just like over the past few years there have
been lots of, ..., new, results like "resonance
theory again", "wow we just rediscovered singular
integrals", "Poincare and Dirichlet at it again",
"Goldbach's Conjectures go either way", sort
of like "Independence of the Continuum Hypothesis",
"second sound", "water still fluid", "there aren't
magnetic monopoles, but there are multipole moments",
"Big Bang Theory and the Inflationary Cosmology",
it's sort of to be expected that wider, broader,
deeper analysis, is going to find counterexamples
that confound itself, given the theories it has.
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"Pseudomomentum." "Triple primes at infinity."
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It's like "hey take a look at Jordan measure or
Jordan content if you will, it's sort of like line-reals,
is that consistent and all?", and it's like, "well,
there are some unintuitive results in mathematics,
or, seemingly un-intuitive, ...."
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So, one might imagine that, given the time and
the capacity to, do mathematics, one may well
expect a proliferation of the deconstructive account,
to elements, mathematically, and in theory, then
resulting that you figure that, "it", would arrive
at a rather thorough and consistent theory.
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Thanks for reading, thanks for writing, warm regards
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