Three is the second prime and the first odd prime, and the triangle it makes is the only polygon that is rigid: fix the three side lengths and the shape cannot deform, whereas a quadrilateral with fixed sides can be pushed flat. That rigidity is why surveying works by triangulation and why bridges and roof trusses are built from triangles, and it is a genuine mathematical reason for associating three with stability, an association that esoteric writing usually justifies on far vaguer grounds.
Three points also fix a circle, and three is the number of dimensions of ordinary space. The first three counting numbers are the only run for which the sum and the product agree: 1 plus 2 plus 3 and 1 times 2 times 3 both give 6, which is itself the first perfect number.
In modern numerology three is the number of expression, creativity and communication. That reading is not ancient. The digit-reduction system in which every name and date collapses to a single figure was assembled in the United States in the first decade of the twentieth century, principally by L. Dow Balliett, whose The Philosophy of Numbers appeared in 1908, and it was systematised by Juno Jordan and others across the following decades. The letter-to-number chart it depends on assigns A to 1 and runs to I at 9 before repeating. It fits the Latin alphabet and works in no other, which means the numbers it produces for a name are properties of modern spelling.
The system is habitually described as Pythagorean. Almost nothing survives from Pythagoras himself, and nothing resembling this procedure is attributed to him by any ancient source. The label is a borrowing of authority, not a lineage, and the distinction matters: the arithmetic of three is genuinely old, and the character assigned to three by numerology is about a hundred and twenty years old.