The Hellenistic period's contribution to science and mathematics deserves more emphasis than it typically gets. The standard narrative skips from classical Athens to the Renaissance, leaving out several centuries of remarkable scientific work carried out in Alexandria, Pergamon, and other centers of Hellenistic learning.

Euclid's Elements (c. 300 BC) is the most successful textbook in the history of mathematics. Its axiomatic-deductive method — start from definitions and postulates, derive everything else through logical proof — is the foundation of mathematical reasoning as we still practice it. Euclid was working in Alexandria, under Ptolemaic patronage, drawing on a mathematical tradition that stretched back to Babylon and Egypt while creating something genuinely new.

Archimedes of Syracuse is arguably the greatest mathematician of antiquity. His work on the calculation of pi, on the area of curves and volumes of solids, on hydrostatics, and on mechanical advantage anticipates calculus and Newtonian mechanics by nearly two thousand years. The Archimedes Palimpsest, discovered in a Constantinople monastery in 1906 and finally fully read in the 2000s using multispectral imaging, contains previously unknown works.

Aristarchus proposed a heliocentric model of the solar system in the 3rd century BC. It was rejected — Hipparchus, the greatest observational astronomer of antiquity, preferred the geocentric model on observational grounds that weren't actually wrong given the data available. The heliocentric model that eventually displaced Ptolemy was not Aristarchus revived but a new construction by Copernicus drawing on different evidence.