Different civilizations and forms of government form on the banks of big rivers in Afrika (Egypt), Asia (including Mesopotamia, India, China), later also in the Mediterranean Area (Greece, Roman Empire). Although different in regions and time of origin, all these state forms have still a lot in common: a hierarchical system of social classes, with aristocracy on the top and many specialized classes below, including priests, scribes, soldiers, craftsmen, farmers, and slaves. Most of these state forms lasted for millennia and centuries. This allowed the melting of the religion with the state forms.

The mathematics in these different state forms was developed to serve practical means, for instance, administration or collection of taxes. But over the centuries, this practical respect of mathematics became more and more independent from the practical application. Scribes and priests began to bring more abstraction into the practical calculations, to think about the concepts behind the pure practical meaning of arithmetics and geometry.

Unfortunately, the knowledge of mathematics of this time is very limited, because only a little evidence is left. It did not survive, either because the material used by scribes to write what they knew was not so resistant (e.g. bamboo, papyrus, tree bark, clay), or because of wars, fire, or intentional destruction of generations which came after.

Year | Mathematician | Achievements | Mathematics Category |
---|---|---|---|

about 2050 BC | unknown | Place-value sexagesimal system, numerical notation | Sumerian |

about 2000 BC | Megalithic Stone and Wood Settings | Western | |

ca. 1850 BC | unknown | solving linear, quadratic and some cubic equations, square roots, interpolation of logarithms, Pythagoras’ theorem; all theorems without proofs | Babylonian Mathematics |

ca. 1400 BC | unknown | Decimal numeration carved on oracle bones | Chinese |

1680 BC | Ahmes | solving simple practical problems using additive mathematics, Pythagorean theorem (without proof), volume formula for a pyramid trunk | Egyptian Mathematics |

800 BC | Baudhayana | Co-author of Sulbasutras, written for concrete religious purposes (e.g. building altars or sacrificial offerings), Pythagoras’ theorem, approximation of $\sqrt{2}$, constructing squares with sides equal to the diameter of a given circle |
Indian |

750 BC | Manava | Co-author of Sulbasutras |
Indian |

624 BC | Thales of Miletus | First Theorems in Geometry | Greek |

611 BC | Anaximander of Miletus | First idea of the Universe: Sun, Moon, and planets revolving around the Earth, construction of a sundial | Greek |

600 BC | Apastamba | Co-author of Sulbasutras |
Indian |

569 BC | Pythagoras of Samos | The Pythagoreans find interconnections between number theory, geometry, astronomy, and music. | Greek |

520 BC | Panini | Forerunner of the modern formal language theory, notation analogous to modern Backus-Naur Form used to specify the syntax of computer languages. | Indian |

499 BC | Anaxagoras of Clazomenae | Proposition that the Moon reflects light from the “red-hot stone” which was the Sun; first understanding of centrifugal force; first known trials of squaring the circle with ruler and compasses (which was proven impossible not before 1882. | Ionian |

492 BC | Empedocles of Acragas | Four element theory of the world: fire, air, water, and earth; beginnings of empiric science: experiment showing that air exists and is not just empty space by observing that water did not enter a vessel when placed under water. | Greek |

490 BC | Oenopides of Chios | First estimation of the period after which the motions of the sun and moon came to repeat themselves to 59 years. Development of a theory for the Nile floods. | Greek |

490 BC | Zeno of Elea | Book containing forty paradoxes concerning the continuum (“paradoxes of motion”), some of which had an influence on the later development of mathematics. | Greek |

480 BC | Leucippus of Miletus | Together with Democritus, joint founder of the atomic theory, i.e. the theory that matter and space are not infinitely divisible. | Greek |

480 BC | Antiphon the Sophist | First to propose a “method of exhaustion”, i.e. calculating an area by approximating it by the areas of a sequence of polygons. | Greek |

470 BC | Hippocrates of Chios | In his attempts to square the circle, Hippocrates was able to find the areas of “lunes”, i.e. crescent-shaped figures, using his theorem that the ratio of the areas of two circles is the same as the ratio of the squares of their radii. | Greek |

465 BC | Theodorus of Cyrene | Contribution to the development of irrational numbers, Theodorus proved that $\sqrt 3, \sqrt 5, \ldots, \sqrt {17}$ were not commensurable in length with the unit length. | Greek |

460 BC | Democritus of Abdera | Together with Leucippus, joint founder of the atomic theory, i.e. the theory that matter and space are not infinitely divisible. | Greek |

460 BC | Hippias of Elis | Probably, the inventor of “quadratrix” which may have been used by him for trisecting an angle and squaring the circle. | Greek |

450 BC | Bryson of Heraclea | Bryson claimed that the circle was greater than all inscribed polygons and less than all circumscribed polygons. | Greek |

428 BC | Archytas of Tarentum | Finding two mean proportionals between two line segments; a solution to the problem of duplicating the cube; proof, that there can be no number which is a geometric mean between two numbers in the ratio $\frac{n+1}n.$ | Greek |

427 BC | Plato | Main contributions are in philosophy, mathematics, and science. Plato’s name is attached to the Platonic solids representing the “elements” i.e. cube (=earth), tetrahedron (=fire), octahedron (=air), icosahedron (=water). Plato associated the dodecahedron with the whole universe. | Greek |

417 BC | Theaetetus of Athens | Greek | |

408 BC | Eudoxus of Cnidus | theory of proportion, astronomy, exhaustion method | Greek |

400 BC | Gan De | ||

400 BC | Thymaridas of Paros | Greek | |

396 BC | Xenocrates of Chalcedon | Greek | |

390 BC | Dinostratus | Greek | |

387 BC | Heraclides of Pontus | Greek | |

384 BC | Aristotle | Beginnings of Propositional Logic | Greek |

380 BC | Menaechmus | Greek | |

370 BC | Callippus of Cyzicus | Greek | |

370 BC | Aristaeus the Elder | Greek | |

360 BC | Autolycus of Pitane | ||

350 BC | Eudemus of Rhodes | ||

325 BC | Euclid of Alexandria | ||

310 BC | Aristarchus of Samos | ||

287 BC | Archimedes of Syracuse | Greek | |

280 BC | Chrysippus of Soli | Greek | |

280 BC | Conon of Samos | ||

280 BC | Nicomedes | ||

280 BC | Philon of Byzantium | ||

276 BC | Eratosthenes of Cyrene | ||

262 BC | Apollonius of Perga | ||

250 BC | Dionysodorus | ||

240 BC | Diocles of Carystus | ||

200 BC | Katyayana | ||

200 BC | Zenodorus | ||

190 BC | Hipparchus of Rhodes | ||

190 BC | Hypsicles of Alexandria | ||

160 BC | Theodosius of Bithynia | ||

150 BC | Zeno of Sidon | ||

135 BC | Posidonius of Rhodes | ||

130 BC | Luoxia Hong | ||

85 BC | Marcus Vitruvius Pollio | ||

10 BC | Geminus | ||

0 BC | Hippasus of Metapontum |

| | | | created: 2016-08-22 23:25:49 | modified: 2019-08-03 19:10:08 | by: *bookofproofs* | references: [8244]

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[8244] **Struik, D.J.**: “Abriss der Geschichte der Mathematik”, Studienbücherei, 1976