Regarding your remark on finding low-dimensional representations, I have added a section on physical intuitions for the challenge. Here I explain how the prime recognition problem corresponds to reliably finding a low-dimensional representation of high-dimensional data.
The best physicists on Earth, including Edward Witten and Alain Connes, believe that the distribution of primes and Arithmetic Geometry encode mathematical secrets that are of fundamental importance to mathematical physics. This is why the Langlands program and the Riemann Hypothesis are of great interest to mathematical physicists.
If number theory, besides being of fundamental importance to modern cryptography, allows us to develop a deep understanding of the source code of the Universe then I believe that such advances are a critical part of human intelligence, and would be highly unlikely if the human brain had a different architecture.
1Thank you for bringing up these points:
- Riemann's analysis back then was far from trivial and there were important gaps in his derivation of the explicit formulas for Prime Counting. What appears obvious now was far from obvious then.
- I just appended a summary of Yang-Hui He's experiments on the Prime Recognition problem.
Either way, I believe that additional experiments may be enlightening as the applied mathematics that mathematicians do is only true to the extent that it has verifiable consequences.
I agree. I don't think he had to attempt to address this problem, if it may be addressed at all.
He has since taken into account the work of experimentalists doing related work, that validates his thesis of Quantum Theory essentially predicting what an observer will see next:
Thank you for sharing this. 👌