The Pythagoreans’ ideas were a mixture of prescience (the numerical features of musical sounds) and mysticism (3 is male, 4 is female, and 10 is the most perfect number).
Numbers were associated with names for magical purposes: the biblical “number of the beast,” 666, is probably an example of this practice.
Numerology sheds light on the innermost workings of the human mind but very little on the rest of the universe.
Mathematics, meanwhile, sheds light on much of the universe but, as yet, very little on human psychology.
The Pythagoreans invested specific numbers with mystical properties.