Teaser: Since at least Pythagoras, mathematics has shaped reasoning about the scientific basis of music. In this talk, first I will discuss selected examples of the music-math connection, focusing on theories of musical scales, consonance, and timbre. Among a review of classical examples, I will explain how recent research on music perception has demonstrated clear cultural biases, raising doubt about mathematical universals in music perception. I will thus argue that formally stated models of auditory perception, rather than mathematics itself, are critical for a better understanding of music. Secondly, I will provide illustrations from my own work on the identification of musical instruments, using mathematics-based methods of sound analysis/synthesis and auditory modeling of sound perception.