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Sep 18, 2021, 3:20:30 PM9/18/21

to Algorithmic Information Theory

Dear AIT mailing list,

As some of you may know, yesterday was Riemann's birthday. His ground-breaking publication, On the number of primes less than a given magnitude(1859), is what we now know as the Riemann Hypothesis. Less than 50 years later, Jacques Hadamard and de la Vallée Poussin used Riemann's insight to prove the Prime Number Theorem using methods from complex analysis. Many considered this to be more or less the final word on the Prime Number Theorem, and nobody imagined that methods from information theory might reveal something profound about the distribution of primes.

Why should information theorists care about the distribution of primes? Perhaps I can

answer this with another question. Why should computational neuroscientists care about the distribution of primes? Based on an information-theoretic derivation of the Prime Number Theorem that occurred to me earlier this year: https://mathoverflow.net/q/384109/56328 I thought I'd share a position paper based on an idea that recently occurred to

me.

The position paper is very brief but it outlines the main idea that the mysterious

attraction that generations of number theorists have found irresistible has an

information-theoretic explanation. I suspect that this particular challenge may

serve as a very useful research direction for the Free Energy Principle.

I hope this inspires other information-theorists to explore a problem that would

otherwise be a missed opportunity.

Sincerely,

Aidan Rocke

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