For a century and a half after Marsilio Ficino translated them for Cosimo de' Medici in 1463, these treatises were read as the oldest theology in the world. Hermes Trismegistus was taken to be an Egyptian sage contemporary with Moses, or earlier, and the correspondence between his teaching and Christian doctrine was therefore evidence that the truth had been given to the gentiles as well. That was the basis on which Renaissance Europe could take pagan magic seriously: it was not innovation but recovery, and it had priority over Greek philosophy rather than descending from it.
In 1614 Isaac Casaubon ended this, in a section of a book about something else. His De rebus sacris et ecclesiasticis exercitationes, written to refute Cardinal Baronius's ecclesiastical history, took up the Hermetic texts as one item among many and demolished the dating on grounds of language.
His method is the part that matters. The Greek of the treatises is not archaic. It contains vocabulary and constructions belonging to the Hellenistic and Roman periods, not to any conceivable Egyptian antiquity in Greek translation. The texts quote Plato rather than being quoted by him, and the direction of borrowing is fixed by which passages make sense as adaptations of which. They use technical terms from Stoic and Middle Platonic philosophy that did not exist before those schools. Casaubon concluded that they were composed in the early Christian centuries by Greek-speaking writers in Egypt, which is where scholarship still places them: broadly the second and third centuries CE.
Anthony Grafton has written on what this demonstration represented, and the assessment is worth keeping. Casaubon was not applying scepticism to a subject he disliked; he was applying to a sacred text the same philological technique that humanist scholarship had been developing on classical authors for a century, and it worked. It is among the founding demonstrations that internal linguistic evidence can date a document against its own claims about itself.
Frances Yates made the consequence the hinge of her account of Renaissance magic. The redating did not disprove anything in the treatises; their philosophy is unaffected by when it was written. What it removed was the priority, and the priority was the whole argument. A text that is the wisdom of ancient Egypt and a text that is a late antique Greek religious philosophy are the same text with entirely different standing.
Some later esoteric writing has never accepted the result, and continues to present these treatises as pharaonic. Brian Copenhaver's standard edition sets out the evidence, and it has not moved in four hundred years.