Applications of advanced number theory to other areas of math

I attended a talk where a mathematician turned biologist was making the claim that genetic codes could be analyzed using p-adic numbers. Specifically he was considering explaining amino acid attraction patterns using 5-adic anaylsis. The whole thing seemed like quite a stretch though to be honest.

Möbius inversion is used to count irreducible polynomials over finite fields.

Some number theory, like the theory of elliptic curves, has been applied to cryptography. Also coding theory may be mentioned. Furthermore there are many connections between number theory and string theory. Wave phenomena in quantum mechanics and quantum chaos also applies, and graph theory, especially expander graphs (Margulis) and related spectral theory.