I have been reading a book about math "the science of patterns". And that is what mathematicians acknowledge that math is. The science of patterns.
Thus my assertion is correct: comparing and matching patterns is a more basic concept than math.
Further, music notation is not music. Nor is math notation math. (Luis made this point too).
What we call 'math' is a pattern of patterns that MATCH certain patterns we observe in nature. But 'pattern matching' itself, like the legendary 'i' (sq. rt of -1) is 'at right angles' to math!
"Number" is an AGREEMENT. "Agreement" (transactions, deals, see John Cramer's interpretation of quantum mechanics in "Schrodinger's Kittens" by John Gribben) is complementary to math.
Chess pieces and Chess boards and Chess rules do not cause Chess games! The players cause the moves in the game; they create individual games!
Math may describe the pieces, board, rules of the Universe; but what does it tell you about the players of a particular game?
Physicists are bogged down with describing the game; such that it might not occur to them that there is this whole business of PLAYING the game to be considered! They might not 'see the wood for the trees'; so involved in the wonders of the structure of the gamne as to forget that the game can be played. And math does not do that.
Behind the 'math', the 'numbers', is agreement, contract.
Alex notes the complementary inter-related logic of math and observed phenomena; but while the ground of those patterns is the law of non-contradiction; the framing of those patterns involves freedom, contracts, deals, agreements.
Until the world's top physicists are 'in on the deal'; they will not be able to teleport and will have to resort to second-guessing reality with probability methods! More fun to play directly with photons etc. instead of being stuck trying to figure out how the game 'reality' is played!
(I'm being a bit speculative I know).