On 12/9/2025 4:49 AM, John Clark wrote:
On Tue, Dec 9, 2025 at 6:40 AM 'Tomasz Rola' via Everything List
<[email protected]> wrote:
/> while my performance was not stellar, would I say thatgetting
score required any kind of superhuman abilities? Nope./
*I would say that getting a score of118 on the Putnamis _FAR_ beyond
the abilities of 99.99+% of the humans on this planet; so "superhuman"
would not be a completely inaccurate word to describe such an ability. *
*>> *Grigori Perelman got a gold medal at the International
Mathematical
>> Olympiad in 1982, but he had his 16th birthday only a few
days before so he
>> was not yet a good enough mathematician to make a
significant contribution
>> to mathematics, however he kept getting better and a few
years later he
>> proved one of the Millenium Prize Problems, the Poincare
"Conjecture", so
>> now it is no longer a conjecture, it is a fact. I think AIs
will follow a
>> similar, but steeper, trajectory. *
/>The problem is not about trajectory of some automaton going
viaexisting road (built by humans, mind you) - this is merely
solving atask of optimisation, so it does not boom into trees.The
problem isabout automaton choosing to build a wholly new road./
*So would it be correct to say thatGrigori Perelman, who happens to be
a human being, did not build a wholly new road into the mathematical
frontier, all he did was locate the end of a road that was built by
others? *
/>This is what Iexpect from a mathematician./
*There were hints of calculus before Newton or Leibniz, and before
Cantor Jain mathematicians in ancient India had a similar idea about
multiple infinite sizes. Can you name any humanmathematician who
discovered an entirely new field of mathematics completely on his own
with no previous mathematician even coming close? I can't. *
*
*
Having /"hints"/ of a new mathematical field doesn't preclude
discovering the whole new field. Aristotle's finding areas by limits
didn't include the idea of derivatives and anti-derivatives; much less
differential equations. I doubt Cantor ever heard of Jain musings about
infinities. Newton, Leibniz, and Cantor did build wholly new roads into
the mathematical frontier; even if there was a /hint/ of the possibility
beforehand. I will be interesting to see whether AI's will become
innovative in mathematics and if we can understand them when they do.
Brent
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