The historical Pythagoras and the school that followed him did hold that number underlies the structure of reality, most famously through the tetractys, a triangular arrangement of ten points read as the source of all proportion and harmony. Ancient Pythagorean arithmology assigned symbolic qualities to numbers themselves, odd against even, the perfection of the decad, and connected number to music through ratios of string length. None of that ancient material, however, assigns numeric values to the letters of the Latin alphabet, and no source earlier than the modern period reduces a name to a single digit by the method taught today.
The alphanumeric grid now called Pythagorean numerology took shape in the late nineteenth and early twentieth centuries within Western esoteric and New Thought circles, popularized above all by the Irish palmist and numerologist known as Cheiro and, in the United States, by writers such as L. Dow Balliett, whose books on names and numbers set much of the vocabulary the practice still uses. Attaching the name of Pythagoras lent the method a classical authority his own teaching never specifically claimed for it. The honest description is therefore a system that draws its philosophical mood from real Pythagorean number mysticism while its actual mechanism, the letter grid and the digit reduction, is a modern invention with no unbroken lineage back to Samos.
Sources Numerology: Or, What Pythagoras WroughtUnderwood Dudley with Pythagoras: His Life, Teaching, and InfluenceChristoph Riedweg (trans. Steven Rendall)