Archimedes is believed to have had a close relationship with King Hiero II of Syracuse, serving as an advisor and inventor for the king. Hiero likely supported Archimedes' scientific pursuits and commissioned him to solve practical problems. The story of the gold crown and the discovery of Archimedes' principle is often associated with Hiero's commission.

Archimedes maintained correspondence with mathematicians and scholars in Alexandria, including Eratosthenes. He shared his mathematical discoveries and sought feedback on his work. This exchange of ideas contributed to the advancement of knowledge in both Syracuse and Alexandria.

While the exact nature of their interaction is unknown, Archimedes was undoubtedly influenced by the work of Euclid, particularly his 'Elements'. Archimedes' rigorous mathematical proofs and his reliance on geometric reasoning reflect Euclid's influence.

Archimedes' father, Phidias, was an astronomer. He likely played a role in introducing Archimedes to the wonders of the cosmos and stimulating his early interest in mathematics and science.