After Plato's death, c. 348 BC, Speusippus inherited the Academy, near age 60, and remained its head for the next eight years.

The standard edition of the surviving fragments and testimonies is Leonardo Tarán's Speusippus of Athens: A Critical Study with a Collection of the Related Texts and Commentary (1982).

Speusippus was a native of Athens, and the son of Eurymedon and Potone, a sister of Plato,[3] he belonged to the deme of Myrrhinus.

[5] We hear nothing of his life until the time when he accompanied his uncle Plato on his third journey to Syracuse (Italy), where he displayed considerable ability and prudence, especially in his amicable relations with Dion.

[7] The report about his sudden fits of anger, his greed, and his debauchery, are probably derived from a very impure source: Athenaeus[8] and Diogenes Laërtius[9] can adduce as authority for them scarcely anything more than the abuse in some spurious[10] letters of Dionysius the Younger, who was banished by Dion, with the cooperation of Speusippus.

Speusippus maintained that no one could arrive at a complete definition who did not know all the differences by which a thing which was to be defined was separated from the rest.

By this he seems to have understood an immediate (in the first instance aesthetic) mode of conception; since he appealed, in support of this view, to the consideration that artistic skill has its foundation, not in sensuous activity, but in an unerring power of distinguishing between its objects, that is, in a rational perception of them.

The criticism of Aristotle, directed apparently against Speusippus, shows how little satisfied he was with the modification of the original Platonist doctrine.

[24] Nevertheless, Speusippus seems to have attributed vital activity to the primordial Unity, as inseparably belonging to it,[25] probably in order to explain how it could grow, by a process of self-development, into the good, spirit, etc.

Diogenes Laertius' list of Speusippus' works includes titles on justice, friendship, pleasure, and wealth.