I was following some lectures by Edward Frenkel about Langlands correspondence. He was describing some analogies between number theory and theoretical physics (Mirror symmetry). At some point ( my lack of knowledge) I had the impression that the relation between number theory and "real" physics is a speculation, probably I am wrong. I wanted to ask if there is more basic examples to explain such interaction between number theory and physics. Examples are welcome.

Edit November 25: Thank you for your answers, my question was vague, sure. I have noticed that all mathematical talks related to some "unrealistic" physics start with a claim saying "the motivation comes from physics". I find this way to motivate some wonderful mathematics (Langlands program,...) not really helpful, and in some sense not honest. I don't claim that there is no relation. I would like to see a clear example in the particular case of number theory and physics with an explanation, references are welcome but a personal explanation will be better. I'm sure I'm not the only one curious about these questions...