How is music like math? In two ways:

1) The mechanism of music and sound is a physical process, and the phenomena of physics are elaborated upon with numerical and mathematical language. For instance, consider the note a tuning fork produces, an A. This note sounds at 440Hz, or consists of pressure waves that hit the ear drum at a rate of 440 times a second, because they are produced by a tuning fork that vibrates in the medium of air 440 times a second.

2) Music theory is concerned with dividing up music into elements, naming those elements, analyzing relationships between those elements, naming those relationships, making analyses of the relationship between those relationships, etc. This is a mathematical process.

For example, let's look at a C9 chord. The notes in this chord are C, E, G, B-flat and D. This chord is used as the dominant for the key of F-major, because c is the fifth note in the scale of F, and the fifth is considered the dominant note of any root (in this case, C is the dominant of F). We use the notes C, E, G, B-flat and D because we use every-other-note in our system of tertiary harmony, or harmony that moves in thirds -- from C to E is a third (a major third), from E to G is a third (a minor third), from G to B-flat is a third (a minor third), etc. It's called a C9 chord because a note a third away from the seventh (B-flat) is a D in the next octave up. If you extend the numbering system past 8, that D is referred to as a 9th as opposed to a 2nd of the next scale, since our context is the original scale.

This is a network of strict and complex algorithms -- practically the definition of mathematics.

Furthermore, it is possible to derive relationships from simpler relationships in an axiomatic way. For instance, from pitch we derive the extant notes in the Western musical lexicon. From the extant notes and tertiary harmonic principles we derive chord theory. From chord theory, we can derive, identify and name complex, altered, and polyphonous chords. The progressive nature of music theoretical concepts (one relies on the one before it and so on) is analogous to axiomatic deduction in mathematics.

See? Inherently mathematical.