During the Classical era prior to the conquests of Alexander the Great the universe was believed to be dominated rigidly mathematically and Earth was the center of the universe. Science and philosophy were intertwined and scientists were mainly concerned with the search for the first principle or what the universe was foremost composed of. This changed in the Hellenistic era. However in the Hellenistic era as in the Classical era there was a lack of incentives for innovations in science, and the concerns were for military, decorative prestige for high courts of rulers and for cities. Innovation entirely occured in the elite as the vast bulk of the populations were enslaved.

Theophrastus was the succesor to Aristotle and was the first scientist of the Hellenistic era. He had abandoned the idea of a first principle and moved away from the orthodox cosmological view. He had also distinguished plants from animals and wrote a taxonomy of plants entitle The History of Plants. Strato was the next principle scientist, who began experimentation and observation in his research and wrote a book on acceleration to expand on Aristotle's ideas, On Motion. Aristarchos was another scientist who first proclaimed the heliocentric theory, which stated that Earth revolved around the sun. He was attacked for going against the status quo by philosophers such as Cleanthes the Stoic, and contemporary astronomers.

Erastosthenes was a librarian and writer for the library at Alexandria. He made many accomplishments. His best known accomplishment was his measurement of the circumference of the Earth, which led to standard means for geometric measurements.

Medicine had been administered by feeble methods and the state of health and disease was connected to magic. However Herophilus broke with the superstition of his time and studied the cardiovascular system and dissected cadavers. Erasistratus was the succesor to Herophilus and he wrote on the digestive system. He stressed hygiene and spoke of the pneuma, or life force, that was contained the in the veins.

Accomplishments in mathematics also occurred with Euclid principally. Euclid wrote on plane and solid geometry, whole numbers, proportions and magnitudes. Archimedes had also made accomplishments in geometry and in his famous Archmides' principle to determine volumes of objects. He had written many works including On the Sphere and the Cylinder, On the Measurement of a Circle, On Conoids and Spheroids, On Floating Bodies, On the Quadrature of the Parabola, On the Method, The Sandreckoner, On Spirals, and On the Equilibrium of Planes. Archimedes had made inventions including an Archimedes' Claw to uplift ships, which was used to stop the Roman invasion of Syracuse, and a computer.

The paper also notes that Egyptians made accomplishments in math, yet Egyptians were more concerned with practical. Greek mathemenatics was concerned with the theoretical.