[ExI] Three things that an AI taught us yesterday

[John Clark]

*The rate of AI improvement is astounding! Less than 3 years ago I was
complaining that AIs couldn't perform arithmetic as well as a two dollar
calculator and couldn't figure out how many Rs were in the word
"strawberry", but just yesterday an AI released three proofs made by one of
their AIs which, if made by a human, the first two would've won him a
fields medal, the highest honor in mathematics, and the third would've
probably won him a Nobel Prize in physics .*

*1) The **Exponential Time Hypothesis claimed that no NP Complete problem
can be solved in subexponential (2^O(n)) time, it is more general so if
it was true it would also prove that P≠NP. But yesterday an AI from OpenAI
proved that the Exponential Time Hypothesis is false by finding an
algorithm that can beat it. And Lean certified that the proof is valid.
Nearly every mathematician believed that the Exponential Time Hypothesis
was true so there are hundreds of mathematical papers out there that start
with the assumption that it is true, but it is not true, so there are
hundreds of mathematical problems that we thought had been proved but
overnight we learned that they are open problems again. *

*2) Last year a human mathematician proved that the Kakeya conjecture
<https://www.quantamagazine.org/once-in-a-century-proof-settles-maths-kakeya-conjecture-20250314/>
was true in 3 dimensions, that discovery had been called by other
mathematicians as "the proof of the century". Yesterday AI made by OpenAI
proved it is true in EVERY dimension, not just 3. And a Lean program
verified that the proof is correct. *

*3) And yesterday in physics the same AI proved that quantum chromodynamics
is logically self consistent, although there is not yet a Lien
certification. *


* OpenAI Just Made a Discovery Nobody Thought Was Possible
<https://www.youtube.com/watch?v=3uoStyWxO5M>*

*  John K Clark*
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