The Babylonian sexagesimal number system is used to record and predict the positions of the Sun, Moon and planets. (See this History Topic.)

Panini's work on Sanskrit grammar is the forerunner of the modern formal language theory.

Hippasus writes of a "sphere of 12 pentagons", which must refer to a dodecahedron.

Greeks begin to use written numerals. (See this History Topic.)

Zeno of Elea presents his paradoxes.

Hippocrates of Chios writes the Elements which is the first compilation of the elements of geometry.

Hippias of Elis invents the quadratrix which may have been used by him for trisecting an angle and squaring the circle.

Theodorus of Cyrene shows that certain square roots are irrational. This had been shown earlier but it is not known by whom.

Babylonians use a symbol to indicate an empty place in their numbers recorded in cuneiform writing. There is no indication that this was in any way thought of as a number. (See this History Topic.)

387BC
Plato founds his Academy in Athens

Archytas of Tarentum develops mechanics. He studies the "classical problem" of doubling the cube and applies mathematical theory to music. He also constructs the first automaton.

Eudoxus of Cnidus develops the theory of proportion, and the method of exhaustion.

Aristaeus writes Five Books concerning Conic Sections.

Autolycus of Pitane writes On the Moving Sphere which studies the geometry of the sphere. It is written as an astronomy text.

Eudemus of Rhodes writes the History of Geometry.

Euclid gives a systematic development of geometry in his Stoicheion (The Elements). He also gives the laws of reflection in Catoptrics.

Aristarchus of Samos uses a geometric method to calculate the distance of the Sun and the Moon from Earth. He also proposes that the Earth orbits the Sun.

In On the Sphere and the Cylinder, Archimedes gives the formulae for calculating the volume of a sphere and a cylinder. In Measurement of the Circle he gives an approximation of the value of π with a method which will allow improved approximations. In Floating Bodies he presents what is now called "Archimedes' principle" and begins the study of hydrostatics. He writes works on two- and three-dimensional geometry, studying circles, spheres and spirals. His ideas are far ahead of his contemporaries and include applications of an early form of integration.

Eratosthenes of Cyrene estimates the Earth's circumference with remarkable accuracy finding a value which is about 15% too big.

Nicomedes writes his treatise On conchoid lines which contain his discovery of the curve known as the "Conchoid of Nicomedes".

Eratosthenes of Cyrene develops his sieve method for finding all prime numbers. (See this History Topic.)

Apollonius of Perga writes Conics in which he introduces the terms "parabola", "ellipse" and "hyperbola".

Diocles writes On burning mirrors, a collection of sixteen propositions in geometry mostly proving results on conics.

Possible earliest date for the classic Chinese work Jiuzhang suanshu or Nine Chapters on the Mathematical Art. (See this History Topic.)

Date of earliest Chinese document Suanshu shu (A Book on Arithmetic). (See this History Topic.)

Hypsicles writes On the Ascension of Stars. In this work he is the first to divide the Zodiac into 360 degrees.

127BC
Hipparchus discovers the precession of the equinoxes and calculates the length of the year to within 6.5 minutes of the correct value. His astronomical work uses an early form of trigonometry.

Chinese mathematician Liu Hsin uses decimal fractions.

List of mathematicians alive in 500BC.

List of mathematicians alive in 1AD.

 JOC/EFR May 2015 The URL of this page is: School of  Mathematics and Statistics University of  St Andrews, Scotland https://www-history.mcs.st-andrews.ac.uk/history/Chronology/500BC_1AD.html