Numerical Mysticism

I didn't get very much out of Nicomachus, but I do want to point out the very strong feelings he and the other Neo-Pythagoreans had about the importance of numbers.  They had an almost mystical relationship to them.  They weren't just useful tools, they were the key to understanding all of the universe. 
From Chapter VI:

All that has by nature with systematic method been arranged in the universe seems both in part and as a whole to have been determined and ordered in accordance with number, by the forethought and the mind of him that created all things; for the pattern was fixed, like a preliminary sketch, by the domination of number preexistent in the mind of the world-creating God, number conceptual only and immaterial in every way, but at the same time the true and eternal essence, so that with reference to it, as to an artistic plan, should be created all these things, time, motion, the heavens, the stars, all sorts of revolutions.

I don't know that you'd get this fervent praise of pure numbers from any mathematician of today.