The historical Theano belongs to early Pythagorean legend (6th c. BCE Croton/Metapontum), but the letters and teachings transmitted under her name are pseudepigrapha. Modern scholarship dates the core didactic letters to the late Hellenistic and early Imperial periods—commonly the 1st–2nd centuries CE (Städele and related work)—not the Archaic age of the legendary namesake.
The surviving Greek addresses practical Pythagorean household ethics: how a woman should rear children, manage servants, and behave when a husband is unfaithful. Lexical features such as the developed sense of φιλοστοργία in the letter on infants are themselves a dating signal that the texts are Imperial, not sixth-century.
On Eulogikon, Theano of Croton is therefore catalogued by the date of the transmitted corpus (Roman, 1st–2nd c. CE). The legendary early Pythagorean woman remains the literary persona; the Greek we publish is later Pythagorean epistolography in her name.
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