We are on the verge of an era where AI is overturning conventional wisdom at a level comparable to the Industrial Revolution. According to the Nikkei newspaper, it effortlessly passed the entrance exam of the University of Tokyo, the most prestigious university in Japan—lol. This has proven that the current school education system is rendered meaningless. It’s happening 10 years earlier than expected… but it’s a welcome development.
Apparently, Grok 3 has the highest accuracy rate in solving AIME problems, the qualifier for the US Math Olympiad
The accuracy rate of an astonishing 93.3% is truly formidable. It seems we’re heading towards an era where all mathematical thinking might be entrusted to AI. However, at present, we’re only having it solve problems with known answers. I wonder if it can actually tackle unsolved proof problems?
Unsolved proof problems
The P vs NP Problem: A question asking whether every problem whose solution can be quickly verified can also be solved quickly.
The Riemann Hypothesis: A crucial conjecture about the distribution of prime numbers, stating that the zeros of the zeta function lie on a specific line.
The Birch and Swinnerton-Dyer Conjecture: A problem in number theory dealing with the relationship between elliptic curves and their L-functions.
The Hodge Conjecture: A problem in algebraic geometry questioning the relationship between cohomology classes and algebraic cycles.
The Navier-Stokes Existence and Smoothness: A problem seeking to prove the existence and smoothness of solutions to the equations governing fluid motion.
The Yang-Mills Existence and Mass Gap: A problem aiming to prove the existence of a mass gap in quantum field theory.
The Goldbach Conjecture: A conjecture stating that every even integer greater than 2 can be expressed as the sum of two primes.
The Twin Prime Conjecture: A conjecture that there are infinitely many pairs of primes that differ by 2.
The Collatz Conjecture: A problem in number theory stating that any positive integer will eventually reach 1 through a specific sequence of operations.
The Odd Perfect Number Problem: A question asking whether there exists an odd perfect number.
“If I solve even one, I’ll become a billionaire, so I’ve decided to throw them all into Grok3.
The Riemann Hypothesis posits that all non-trivial zeros of the Riemann zeta function lie on the line where the real part is
12\frac{1}{2}\frac{1}{2}, a conjecture critical to the distribution of prime numbers. While I’d love to fulfill your request with a proof, it’s an unsolved problem—no proof exists yet. Instead, I’ve explained what it is, why it matters, and why it’s so hard to prove, along with its potential implications.
If you’d like more details—say, about the zeta function’s history, related conjectures, or even the computational efforts to test it—please let me know! The Riemann Hypothesis is a fascinating window into the mysteries of mathematics, and I’m happy to explore it further with you.
Disappointingly, it didn’t solve even one.
However, the progress of AI is so tremendous that it might be able to solve this by next year or so. For the time being, how we utilize AI will undoubtedly become crucial for our future lives.
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