From Euclid into Chaos, Contents

• 2750 B.C., Sacred geometry
• 500 B.C., Thales, Pythagoras
• 380 B.C., Plato
• 330 B.C., Aristotle
• 280 B.C., Euclid (packaged sacred geometry in an Aristotlean form)
• 300, Byzantium
• 800, Baghdad
• 1100, Cordova
• 1200, Palermo
• 1570, Dee (first translation of Euclid into English, but also revived the Pythagorean tradition) and Viete (symbolic algebra)
• 1637, Descartes and Fermat (analytic geometry)
• 1638, Galileo (publishes Discourses on laws of motion)
• 1687, Newton (publishes the Principia, including the calculus, universal gravitation, and the equations of motion))

• 1733, Saccheri (proposes alternatives to Post. 5, only hypothetical)
• 1763, Klugel (suggests Post. 5 cannot be proved as a theorem)
• 1766, Lambert (discovers non-euclidean geometry)
• 1781, Robert Simson (publishes outstanding edition of Euclid in English)
• 1794, Gauss (develops non-euclidean geometry, tries to prove the world is Euclidean)

• 1826, Lobachevsky (develops hyperbolic geometry)
• 1827, Gauss (differential geometry, curvature)
• 1829, Lobachevsky (publishes hyperbolic geometry)
• 1831, Bolyai (publishes hyperbolic geometry)
• 1854, Riemann (lecture "On the hypotheses that lie at the foundations of geometry, manifolds, curvature)
• 1856, Weierstrass (began teaching in Berlin)
• 1860, Riemann (studied Dirichlet)
• 1868, Beltrami (proves that Post. 5 is not provable)
• 1872, Klein (Erlangen programm, works on hyperbolic geometry)
• 1873, Hilbert (studied with Weierstrass)
• 1878, Cantor (set theory, Cantor sets, fractals, continuum hypothesis)
• 1882, Poincare (works on hyperbolic geometry)
• 1884, Frege (axioms for natural numbers)
• 1885, Klein and Poincare (work on Riemann program of geometric function theory)
• 1888, Peano (axioms for vector spaces)
• 1889, Poincare (discovers chaotic dynamics)
• 1899, Hilbert (publishes Foundations of Geometry, repairs Euclid, ideas of consistency, independence, completeness)
• 1899, Poincare (reviews Hilbert's book [Reid, p. 62])

• 1900, Hilbert (23 problems)
• 1931, Husserl (student of Weierstrass, writes on the foundations of geometry)
• 1931, Godel (proves undecidability and incompleteness, refers to Liar's paradox [Wang, p. 62; Van Heijenoort, p. 89])
• 1945, von Neumann and Ulam (study chaos in 1D maps)
• 1960, Derrida (translates and comments upon Husserl)
• 1975, Mandelbrot (establishes fractal geometry)
• 1961, Ueda (discovers chaotic attractor)
• 1963, Lorenz (discovers chaotic attractor)
• 1993, Grim & Mar (establish chaotic logic, resolve Liar's paradox)