The Ionians, Greeks, and Hellenics had some of the most progressive mathematicians of their time—a list that includes such mathematicians as Heron of Alexandria, Zeno of Elea, Eudoxus of Cnidus, Hippocrates of Chios, and Pappus. The following are only a few of the more influential mathematicians.

Ptolemy (center), depicted in this 1632 engraving discussing ideas with Aristotle (left) and Copernicus (right), discovered valuable concepts concerning cartography, geometry, and astronomy.

• Thales of Miletus (c. 625-c. 550 B.C.E., Ionian), besides being purportedly the founder of a philosophy school and the first recorded Western philosopher known, Thales made great contributions to Greek mathematics, especially by presenting Babylonian mathematics to the Greek culture. His travels as a merchant undoubtedly exposed him to the geometry involved in measurement. Such concepts eventually helped him to introduce geometry to Greece, solving such problems as the height of the pyramids (using shadows), the distance of ships from a shoreline, and reportedly predicting a solar eclipse.
• Hipparchus of Rhodes (c. 170-c. 125 B.C.E., Greek; also seen as Hipparchus of Nicaea) was an astronomer and mathematician who is credited with creating some of the basics of trigonometry. This helped immensely in his astronomical studies, including the determination of the Moon’s distance from Earth.
• Geminus (c. 1st century B.C.E., Greek) was an astronomer and mathematician; his astronomy text, the Introduction to the Phenomena, still survives today, and was an introductory astronomy book for students. His mathematical texts did not survive as well, and most of his extensive mathematical writings survive in the writings of his contemporaries and beyond.
• Claudius Ptolemaeus (or Ptolemy; c. 100-c. 170 C.E., Hellenic) was one of the most influential Greeks, not only in the field of astronomy, but also in geometry and cartography. Basing his works on Hipparchus, Ptolemy developed the idea of epicycles, in which each planet revolves in circular orbits, and each around an Earth-centered universe. The Ptolomaic way of explaining the solar system—which we now know is incorrect—dominated astronomy for more than a thousand years.
• Diophantus (c. 210-c. 290 C.E.) was considered by some scholars to be the “father of algebra.” In his treatise Arithmetica, he solved equations in several variables for integral solutions, or what we called diophantine equations today. (For more about these equations, see “Algebra.”) He also calculated negative numbers as solutions to some equations, but he considered such answers absurd.