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In celebrating the centenary of Ramanujan's birth, Freeman Dyson presented the following career advice for talented young physicists [1]:



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> My dream is that I will live to see the day when our young physicists, struggling to bring the predictions of superstring theory into correspondence with the facts of nature, will be led to enlarge their analytic machinery to include not only theta-functions but mock theta-functions … But before this can happen, the purely mathematical exploration of the mock- modular forms and their mock-symmetries must be carried a great deal further. —Freeman Dyson
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Was Freeman Dyson guided by physical intuitions that could have convinced top-notch quantum field theorists of his generation, such as Richard Feynman? Though I am aware that Freeman Dyson and Richard Feynman collaborated on Feynman's approach to quantum field theory, the precursor to string theory, I doubt that Feynman would have advanced the hypothesis that Ramanujan's work had any important consequences for theoretical physics.


Complementary insights:
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In parallel, I wonder whether it may not be equally sensible to reconcile quantum theory with the facts of probabilistic number theory where probabilistic events are of a deterministic and frequentist nature. Upon closer inspection, this would be a complementary effort but I don't know of a systematic research program aimed at this particular objective although a large number of physicists appear to have a strong interest in the pair correlation conjecture which emerged from a tea-time discussion between Freeman Dyson and Hugh Montgomery.


These are related observations, which may be relevant for a couple reasons: (1) The theory of modular forms potentially enters mathematical physics via the analysis of the Pair-Correlation conjecture. (2) By John Bell's own admission, his 1964 theorem known as Bell's theorem was motivated by the super-deterministic theory proposed by De Broglie and Bohm.


Furthermore, I suspect that Erdős is often quoted saying:



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> God may not play dice with the universe, but something strange is
> going on with the prime numbers.
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because all mathematical systems may be constructed from Peano Arithmetic, and the prime numbers are the atomic units of the integers, so the distribution of the prime numbers may be viewed as fundamental scientific data. Based on a recent discussion with Max Tegmark [7], who believes that a physicist can only understand the mathematical relations between things, this perspective is worth consideration if we assume that the mathematical structure of the Universe emerged from an information-theoretic singularity(i.e. Big Bang Cosmology).


**Note:** Contrary to those who are voting to close this question, I believe that if there are fundamental physical insights which motivated Freeman Dyson's hypothesis then this question is of interest to the MathOverflow community.


References:
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1. Jeffrey A. Harvey. Ramanujan’s influence on string theory, black holes and moonshine. 2019.
2. Hardy, G. H.; Ramanujan, S. “The normal number of prime factors of a number n”, Quarterly Journal of Mathematics. 1917.
3. Erdős, Paul; Kac, Mark. “The Gaussian law of errors in the theory of additive number theoretic functions”. American Journal of Mathematics. 1940.
4. Montgomery, Hugh L. "The pair correlation of zeros of the zeta function", Analytic number theory, Proc. Sympos. Pure Math. 1973.
5. Bell, J.S.“On the Einstein-Podolsky-Rosen paradox,” Physics. 1964.
6. Tegmark, Max. "The Mathematical Universe". Foundations of Physics. Arxiv. 2008.
7. Email discussion with Max Tegmark on tabletop experiments for the Mathematical Universe Hypothesis via Probabilistic Number Theory. Dec 18 2021.



Freeman Dyson's approach to string theory
Dyson's [A walk through Ramanujan's garden](https://www.semanticscholar.org/paper/A-walk-through-Ramanujan%E2%80%99s-garden-Dyson/eb6d4ec50b6666a07521157c22c14c81380ce424) gives the background of this comment: He explains that the "seeds from Ramanujan's garden have been
blowing on the wind and have been sprouting all over the landscape. Some of the seeds even blew over into physics." He then writes that he received a preprint from a superstring theorist entitled *Atkin-Lehner symmetry*, in which modular forms entered physics in ways that mathematicians never dreamt of, and concludes that "Perhaps we may one day see a preprint written by a physicist with the title *Mock Atkin-Lehner Symmetry*."


Dyson also indicates in the same text that he knows little about superstring theory, so my answer to the question: *"Was Freeman Dyson guided by physical intuitions"* is: No, he was guided by his experience that fundamental math often makes it into physics in unexpected ways.


