Polyaenus of Lampsacus also spelled Polyenus, son of Athenodorus, was an ancient Greek mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

 and a friend of Epicurus

Epicurus

Epicurus was an ancient Greek philosopher and the founder of the school of philosophy called Epicureanism.Only a few fragments and letters remain of Epicurus's 300 written works...

. His friendship with Epicurus started after the latter's escape from Mytilene

Mytilene

Mytilene is a town and a former municipality on the island of Lesbos, North Aegean, Greece. Since the 2011 local government reform it is part of the municipality Lesbos, of which it is a municipal unit. It is the capital of the island of Lesbos. Mytilene, whose name is pre-Greek, is built on the...

 in 307 or 306 BC when he opened a philosophical school at Lampsacus

Lampsacus

Lampsacus was an ancient Greek city strategically located on the eastern side of the Hellespont in the northern Troad. An inhabitant of Lampsacus was called a Lampsacene. The name has been transmitted in the nearby modern town of Lapseki.-Ancient history:...

 associating himself with other citizens of the town, like Pythocles, Colotes

Colotes

Colotes of Lampsacus was a pupil of Epicurus, and one of the most famous of his disciples. He wrote a work to prove That it is impossible even to live according to the doctrines of the other philosophers . It was dedicated to king Ptolemy Philopator...

, and Idomeneus

Idomeneus of Lampsacus

Idomeneus of Lampsacus was a friend and disciple of Epicurus. We have no details of his life, except that he married Batis of Lampsacus, the sister of Metrodorus, and he was a court dignitary at Lampsacus around 306-301 BC...

. With the other fellow citizens previously cited he moved to Athens

Athens

Athens , is the capital and largest city of Greece. Athens dominates the Attica region and is one of the world's oldest cities, as its recorded history spans around 3,400 years. Classical Athens was a powerful city-state...

, where they founded a school of philosophy with Epicurus as head, or hegemon, while Polyaenus, Hermarchus

Hermarchus

Hermarchus or Hermarch , sometimes incorrectly written Hermachus , was an Epicurean philosopher. He was the disciple and successor of Epicurus as head of the school. None of his writings survive. He wrote works directed against Plato, Aristotle, and Empedocles. A fragment from his Against...

 and Metrodorus were kathegemones.

A man of mild and friendly manners, as Philodemus

Philodemus

Philodemus of Gadara was an Epicurean philosopher and poet. He studied under Zeno of Sidon in Athens, before moving to Rome, and then to Herculaneum. He was once known chiefly for his poetry preserved in the Greek anthology, but since the 18th century, many writings of his have been discovered...

 refers, he adopted fully the philosophical system of his friend, and, although he had previously acquired great reputation as a mathematician, he now maintained with Epicurus the worthlessness of geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

. But the statement may be at least doubted, since it is certain Polyaenus wrote a mathematical work called Puzzles in which the validity of geometry is maintained. It was against this treatise that another Epicurean, Demetrius Lacon

Demetrius Lacon

Demetrius Lacon or Demetrius of Laconia was an Epicurean philosopher of the late 2nd century BC, and a disciple of Protarchus. He was an older contemporary of Zeno of Sidon and a teacher of Philodemus...

, wrote Unsolved questions of Polyaenus in the 2nd century BCE. Like Epicurus, a considerable number of spurious works seem to have been assigned to him; one of these was Against the Orators, whose authenticity was attacked both by Zeno of Sidon

Zeno of Sidon

Zeno of Sidon was an Epicurean philosopher from the Phoenician city of Sidon. His writings do not survive, but there are some epitomes of his lectures preserved among the writings of his pupil Philodemus.-Life:...

 and his pupil Philodemus.

The works attributed to Polyaenus include:

• On Definitions
• On Philosophy
• Against Aristo
• Puzzles (Aporiai)
• On the Moon
• Against the Orators
• and his collected Letters.