La Habra High School
Math History Timeline

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Age of Revolutions
1789-1848 A.D.

1794	Legendre publishes Eléments de géométrie, an account of geometry which would be a leading text for 100 years. It will replace Euclid's Elements as a textbook in most of Europe and, in succeeding translations, in the United States. It becomes the prototype of later geometry texts.
1796	Laplace presents his famous nebular hypothesis in Exposition du systeme du monde which views the solar system as originating from the contracting and cooling of a large, flattened, and slowly rotating cloud of incandescent gas.
1797	Lagrange publishes Théorie des fonctions analytiques (Theory of Analytical Functions). It is the first treatise on the theory of functions of a real variable. It uses modern notation like dy/dx for derivatives.
1797	Lazare Carnot publishes Réflexions sur la métaphysique du calcul infinitésimal in which he treats zero and infinity as limits. He also considers that infinitely small quantities are real objects, being representable as differences between limits.
1797	Wessel presents a paper on the vector representation of complex numbers which is published in Danish in 1799. The idea first appears in a report he wrote in 1787.
1799	Gauss proves the fundamental theorem of algebra and notes that earlier proofs, such as by d'Alembert in 1746, could easily be corrected.
1799	Monge publishes Géométrie descriptive which describes orthographic projection, the graphical method used in modern mechanical drawing.
1799	Ruffini publishes the first proof that algebraic equations of degree greater than four cannot be solved by radicals. It was largely ignored as were the further proofs he would publish in 1803, 1808 and 1813.
1801	Gauss proves Fermat's conjecture that every number can be written as the sum of three triangular numbers.
1801	Gauss publishes Disquisitiones Arithmeticae (Discourses on Arithmetic). It contains seven sections, the first six of which are devoted to number theory and the last to the construction of a regular 17-gon by ruler and compasses.
1806	Argand introduces the Argand diagram as a way of representing a complex number geometrically in the plane.
1806	Legendre develops the method of least squares to find best approximations to a set of observed data.
1807	Fourier discovers his method of representing continuous functions by the sum of a series of trigonometric functions and uses the method in his paper On the Propagation of Heat in Solid Bodies which he submits to the Paris Academy.
1809	Gauss describes the least-squares method which he uses to find orbits of celestial bodies in Theoria motus corporum coelestium in sectionibus conicis Solem ambientium (Theory of the Movement of Heavenly Bodies).
1811	Poisson publishes Traité de mécanique (Treatise on Mechanics). It includes Poisson's work on the applications of mathematics to topics such as electricity, magnetism and mechanics.
1812	Laplace publishes the two volumes of Théorie Analytique des probabilités (Analytical Theory of Probabilities). The first book studies generating functions and also approximations to various expressions occurring in probability theory. The second book contains Laplace's definition of probability, Bayes's rule, and mathematical expectation.
1815	Peter Roget (the author of Roget's Thesaurus) invents the "log-log" slide rule.
1817	Bessel discovers a class of integral functions, now called "Bessel functions", in his study of a problem of Kepler to determine the motion of three bodies moving under mutual gravitation.
1817	Bolzano publishes Rein analytischer Beweis (Pure Analytical Proof) which contain an attempt to free calculus from the concept of the infinitesimal. He defines continuous functions without the use of infinitesimals. The work contains the Bolzano-Weierstrass theorem.
1821	Cauchy publishes Cours d'analyse (A Course in Analysis), which sets mathematical analysis on a formal footing for the first time. Designed for students at the Ecole Polytechnique it was concerned with developing the basic theorems of the calculus as rigorously as possible.
1821	Navier gives the well known "Navier-Stokes equations" for an incompressible fluid.
1823	Babbage begins construction of a large "difference engine" which is able to calculate logarithms and trigonometric functions. He was using the experience gained from his small "difference engine" which he constructed between 1819 and 1822.
1823	János Bolyai completes preparation of a treatise on a complete system of non-Euclidean geometry. When Bolyai discovers that Gauss had anticipated much of his work, but not published anything, he delays publication.
1826	Ampère publishes Memoir on the Mathematical Theory of Electrodynamic Phenomena, Uniquely Deduced from Experience. It contains a mathematical derivation of the electrodynamic force law and describes four experiments. It lays the foundation for electromagnetic theory.
1827	Jacobi writes a letter to Legendre detailing his discoveries on elliptic functions. Abel was independently working on elliptic functions at this time.
1827	Möbius publishes Der barycentrische Calkul on analytical geometry. It becomes a classic and includes many of his results on projective and affine geometry. In it he introduces homogeneous coordinates and also discusses geometric transformations, in particular projective transformations.
1828	Gauss introduces differential geometry and publishes Disquisitiones generales circa superficies. This paper arises from his geodesic interests, but it contains such geometrical ideas as "Gaussian curvature". The paper also includes Gauss's famous theorema egregrium.
1829	Galois submits his first work on the algebraic solution of equations to the Académie des Sciences in Paris.
1829	Lobachevsky develops non-euclidean geometry, in particular hyperbolic geometry, and his first account of the subject is published in the Kazan Messenger. When it was submitted for publication in the St Petersburg Academy of Sciences Ostrogradski rejects it.
1831	Cauchy gives power series expansions of analytic functions of a complex variable.
1831	Möbius publishes Über eine besondere Art von Umkehrung der Reihen which introduces the "Möbius function" and the "Möbius inversion formula".
1832	János Bolyai's work on non-Euclidean geometry is published as an appendix to an essay by Farkas Bolyai, his father.
1833	Legendre points out the flaws in 12 "proofs" of the parallel postulate.
1836	Liouville founds a mathematics journal Journal de Mathématiques Pures et Appliquées. This journal, sometimes known as Journal de Liouville, did much to advance mathematics in France throughout the 19th century.
1836	Ostrogradski rediscovers Green's theorem.
1837	Dirichlet gives a general definition of a function.
1837	Poisson publishes Recherches sur la probabilité des jugements (Researches on the Probabilities of Opinions). In this work he establishes the rules of probability, gives "Poisson's law of large numbers" and describes the "Poisson distribution" for a discrete random variable which is a limiting case of the binomial distribution.
1838	De Morgan invents the term "mathematical induction" and makes the method precise.
1839	Lamé proves Fermat's Last Theorem for n = 7.
1840	Cauchy publishes the first volume of the four volume work Exercises d'analyse et de physique mathematique.
1841	Gauss publishes a treatise on optics in which he gives a formulae for calculating the position and size of the image formed by a lens with a given focal length.
1841	Jacobi writes a long memoir De determinantibus functionalibus devoted to the functional determinant now called the Jacobian.
1843	Cayley is the first person to investigate "geometry of n dimensions" which occurs in the title of his paper of that year. He uses determinants as the major tool.
1843	Kummer invents "ideal complex numbers" in his study of unique factorisation. This leads to the development of ring theory.
1843	Liouville announces to the Académie des Sciences in Paris that he had found deep results in Galois's unpublished work and promises to publish Galois's papers together with his own commentary.
1844	Liouville finds the first transcendental numbers - numbers that cannot be expressed as the roots of an algebraic equation with rational coefficients.
1845	While examining permutation groups Cauchy proves a fundamental theorem of group theory which became known as "Cauchy's theorem".
1846	Liouville publishes Galois' papers on the solution of algebraic equations in Liouville's Journal.
1847	Boole publishes The Mathematical Analysis of Logic, in which he shows that the rules of logic can be treated mathematically rather than metaphysically. Boole's work lays the foundation of computer logic.
1847	De Morgan proposes two laws of set theory that are now known as "de Morgan's laws".
1848	Thomson (Lord Kelvin) proposes the absolute temperature scale now named after him.

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