From Cicero's De Divinatione I.1:
Itaque ut alia nos melius multa quam Graeci, sic huic praestantissimae rei nomen nostri a divis, Graeci, ut Plato interpretatur, a furore duxerunt.
(My trans.)
And just as we have done many things better than the Greeks, thus we derived our name for this most excellent matter [divination] from "the Gods" [divi], while as Plato explains, the Greeks derived theirs [manteía] from "frenzy" [manía].
This is an interesting etymology, though I'm hesitant to trust Cicero's derivations. But what's more interesting is that he attributes it to Plato.
Does Plato, or any other Greek writer, draw an etymological connection between μαντεία and μανία? And do modern linguists agree with this assessment?