Disquisitiones Arithmeticae

Carl Friedrich Gauss · 1801

The founding work of modular arithmetic, the mathematics that formalizes the 'digit reduction' numerology uses intuitively.

Gauss formalized the 'remainder modulo N'. Since every number is congruent to the sum of its digits (mod 9), the Pythagorean reduction to a single digit matches exactly the remainder modulo 9.

The most important thing real mathematics brings to numerology: congruence modulo 9 explains rigorously why adding digits captures something of a number's structure. It doesn't validate the esoteric meaning, but it does validate the reduction mechanism.