The system the Institute standardised is almost always sold as the Pythagorean method, and the label is worth examining because it is doing a lot of work. The Pythagoreans held numerical doctrines and the ancient world did practise isopsephy in Greek and gematria in Hebrew, in which the letters of an alphabet already carried numeral values as part of the writing system itself. That is a genuine tradition with a real history.
What the Institute standardised is different in kind. It assigns one to nine to the twenty-six letters of the modern Latin alphabet in sequence, and applies that to names spelled in modern English orthography. Neither the alphabet, nor the orthography, nor the sequence has any connection to Pythagoras, and a name transliterated differently produces a different reading. The label attaches an ancient pedigree to an arrangement fixed in California in the twentieth century.
The Institute was a private teaching and publishing body. It set examinations for its own certificates, published its own textbooks, and had no external membership requirement, peer review or independent testing of any kind, and no controlled study of its claims was ever undertaken by anyone outside it. Underwood Dudley's survey of numerological systems examines the arithmetic and the claims made for it directly. What survives today is not the Institute but its table, which is now the default in the popular literature.