Gematria is old in a way the Pythagorean and Chaldean letter systems are not. Reading numeric equivalence between Hebrew words as meaningful appears already in Hellenistic era Jewish interpretation, where a shared numeric total between two scriptural terms could be treated as evidence of a hidden connection the plain text did not state outright, a technique that runs alongside similarly aged practices in the Greek speaking world, where isopsephy performed the same operation on the Greek alphabet.
The technique found its fullest theoretical home centuries later within Kabbalah, the medieval and early modern Jewish mystical tradition, where Sefer Yetzirah, the Book of Creation, treats the Hebrew letters themselves, and by extension their numeric values, as the building blocks God used to create the world, giving gematria a cosmological rather than merely interpretive weight. Later Kabbalistic commentary elaborated the technique considerably, and it drew the attention of Christian scholars of Hebrew mysticism during the Renaissance, among them Johannes Reuchlin, whose engagement with Kabbalistic method helped carry gematria into wider European esoteric currents well outside its Jewish origin, where it continues to circulate today in a much looser and more eclectic form.
Sources Sefer Yetzirah: The Book of Creation in Theory and PracticeAryeh Kaplan with De Arte Cabalistica (On the Art of Kabbalah)Johann Reuchlin, Encyclopaedia Judaica, 2nd editionMichael Berenbaum and Fred Skolnik (eds.)