Conon settled in Alexandria and was employed as court astronomer to the Egyptian monarch Ptolemy III. None of Conon's own writings survive and what is known of his work is through secondhand references to him by other Greek mathematicians. For example, Conon's work on conics was made use of by Apollonius of Perga in his famous treatise on conics.

Among Conon's activities as an astronomer was the compilation of tables of the times of the rising and setting of the stars, known as the parapegma. He was also responsible for naming a constellation of stars. The consort of Ptolemy III, Berenice II, presented her hair as an offering at the temple of Aphrodite. This disappeared and Conon claimed that the hair now hung as a new constellation of stars, which he named Coma Berenices (‘Berenice's Hair’).

Conon was known to have been a friend of Archimedes and it is probable that the Spiral of Archimedes, a mathematical curve, was in fact Conon's discovery.