Aristippus the Younger

Aristippus the Younger (/ˌærəˈstɪpəs/; Greek: Ἀρίστιππος), of Cyrene, was the grandson of Aristippus of Cyrene, and is widely believed to have formalized the principles of Cyrenaic philosophy.
He lived in the second half of the 4th century BC. His mother was Arete, daughter of the elder Aristippus, and it was she who imparted her father's philosophy to her son, hence he received the nickname "Mother-taught" (metrodidaktos). Among his pupils was Theodorus the Atheist. Not much else is known about Aristippus the Younger. The idea that he systemised his grandfather's philosophy is based on the authority of Aristocles (as quoted by Eusebius):

Among [Aristippus'] other hearers was his own daughter Arete, who having borne a son named him Aristippus, and he from having been introduced by her to philosophical studies was called his mother's pupil (μητροδίδακτος). He quite plainly defined the end to be the life of pleasure, ranking as pleasure that which lies in motion. For he said that there are three states affecting our temperament: one, in which we feel pain, like a storm at sea; another, in which we feel pleasure, that may be likened to a gentle undulation, for pleasure is a gentle movement, comparable to a favourable breeze; and the third is an intermediate state, in which we feel neither pain nor pleasure, which is similar to a calm. So of these feelings only, he said, we have the sensation.

There are indications that he was conflated with his grandfather.