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## Mathematics and Physics timeline

May 17, 2022   Compiled on May 17, 2022 at 1:30am  [public]

### 2 Detailed timeline

 1501-1576 Gerolamo Cardano. Born 24 September 1501 Pavia, Died 21 September 1576 (aged 74) Italy. “Algebra. ﬁrst systematic use of negative numbers. published with attribution the solutions of other mathematicians for the cubic and quartic equations, and acknowledged the existence of imaginary numbers.” 1550-1617 John Napier. discovered logarithms. Use of decimal point. 1564-1642 Galileo Galilei. Born 15 February 1564, Pisa, Duchy of Florence. Died 8 January 1642 (aged 77) Arcetri. Pendulum, Gravity, astronomy. 1584-1667 Gregory St. Vincent. Born: March 22, 1584, Bruges, Belgium, June 5, 1667, Ghent, Belgium. Publishes in 1647 Opus geometricum quadrature ciculi et sectionum coni. First use of method of exhaustion in geometry. First use of method of chords to transform one conic to another. First use of geometric series. First to settle Zeno’s Achilles paradox. 1596-1650 René Descartes. Born: March 31, 1596, France, Died: Feb. 11, 1650, Stockholm, Sweden. Wrote Descartes Meditations on First Philosophy (1641). 1607-1665 Pierre de Fermat. Born: 1607, Beaumont-de-Lomagne, France, Died: Jan. 12, 1665, Castres, France. Important contributions to analytical geometry, probability, number theory and calculus. 1616-1703 John Wallis. Publishes Arithmetica inﬁnitorum in 1655. Created the arithmetical concept of limit. First to use the symbol $$\infty$$. First to use the term hyper-geometric series in his 1655 book Arithmetica Inﬁnitorum. 1623-1662 Blaise Pascal. Born: June 19, 1623, Clermont-Ferrand, France. Died: August 19, 1662, Paris, France. projective geometry. Corresponded with Pierre de Fermat on probability theory. 1625-1686 Pietro Mengoli. Alternative proof that harmonic series diverges. posed the famous Basel problem, Solved by Euler in 1735. In 1650 proved that the sum of the alternating harmonic series is equal to the natural logarithm of 2. 1629-1695 Christiaan Huygens. One of his famous works is De horologio oscillatorio published in Paris in 1673. Invented pendulum clock. Wrote the ﬁrst formal book on probability. Proposed the wave theory of light. Publication of his Opuscula posthuma in 1703 after his death. 1630-1677 Isaac Barrow. Professor of Mathematics in London and Cambridge. Famous for method of tangents. Publishes Lectiones geometrica (1670) and Lectiones mathematica (1683). 1638-1675 James Gregory. Born in Drumoak, United Kingdom. Scottish mathematician. Taylor series. Died in Edinburgh, United Kingdom. 1643-1727 Isaac Newton. Born in Woolsthorpe, Lincolnshire, England. 1646-1716 Gottfried Wilhelm Leibniz. Born in Leipzig, Germany. 1646-1716 Michel Rolle. Born 21 April 1652, Died 8 November 1719 (aged 67) Paris, Kingdom of France French mathematician. Rolle’s theorem (1691). Apparently he also knew about Gaussian elimination. 1655-1705 Jacob Bernoulli. Born in Basel, Switzerland. 1667-1754 Abraham de Moivre. French mathematician known for de Moivre’s formula. worked on the normal distribution and probability theory. Was Friend of Newton. 1667-1748 Johann Bernoulli. Born in Basel, Switzerland. 1676-1754 Jacopo Francesco Riccati. Born 28 May 1676 Venice, Italy, Died 15 April 1754 Italy(aged 77). Named for the Riccati ODE 1669 Isaac Newton becomes Chair of Mathematics in Cambridge when Isaac Barrow vacates this position for Newton. 1669 Isaac Newton. Writes major Work on Calculus. "De analysi" or "On Analysis by Equations with an inﬁnite number of terms". First time the series for $$\sin (x)$$ and $$\cos (x)$$ derived. Also gives Quadrature rules for ﬁrst time. This work was actually published in 1711. 1671 James Gregory. Finds power series for $$\arctan (x)$$ June 13, 1676 Newton sends famous letter to H. Oldenburg, containing ﬁrst announcement of binomial theorem using negative and fractional exponents. 1676 Isaac Newton. epistola prio letter Newton sends to Leibniz giving for ﬁrst time account of the Binomial series expansion 1682-1716 Roger Cotes. Born: July 10, 1682, Burbage, United Kingdom, Died: June 5, 1716, Cambridge, United Kingdom. Apparently Cotes knew of $$e^{i \pi }=-1$$ before Euler. 1684 Gottfried Wilhelm Leibniz. Publish ﬁrst paper on diﬀerential calculus. "A new method for maxima and minima, and also tangents, which is impeded neither by fractional nor by irrational quantities, and a remarkable type of calculus for this". 1685-1731 Brook Taylor. Born 18 August 1685, Edmonton, England. Died 29 December 1731 (aged 46) London, England. Taylor’s theorem, Taylor series. 1687 Isaac Newton. First edition of Principia Mathematica published. 1689 Jacob Bernoulli. Publication of "Treatise on inﬁnite series and their ﬁnite sums". 1698-1746 Colin Maclaurin. Born February 1698 , Scotland. Died 14 June 1746 (aged 48) Edinburgh, Scotland. Euler–Maclaurin formula, Maclaurin series. Integral test for convergence. In 1742, he published a major work consisting of two volumes comprising 763 pages, A Treatise of Fluxions. 1690-1764 Christian Goldbach. Born March 18, 1690 Prussia, Died November 20, 1764 (aged 74) Moscow, Russian Empire. Goldbach’s conjecture: Every even integer greater than 2 can be expressed as the sum of two primes. 1692-1770 James Stirling. Born May 1692, Scotland. Died 5 December 1770 (Aged 78) Edinburgh, Scotland Stirling numbers, Stirling permutations, Stirling’s approximation. 1700-1782 Daniel Bernoulli. Born: Feb. 8, 1700, Groningen, Netherlands Died: March 17, 1782, Basel, Switzerland. Applications of mathematics to mechanics, ﬂuid mechanics, and work in probability and statistics. 1701-1761 Thomas Bayes. Born 1701 London, England. Died 7 April 1761 (aged 59), Kent, England. statistician. Bayes’ theorem. 1704-1752 Gabriel Cramer. Born 31 July 1704 Geneva. Died 4 January 1752 (age 47), France Cramer rule. (1750). Solution to the St. Petersburg Paradox . Treatise on algebraic curves (1750). 1705 Jacob (James) Bernoulli. Died in Basel, Switzerland 1707-1783 Leonhard Euler. Born April 15, 1707 in Basel, Switzerland. Many contributions. Graph theory, number theory, series expansion, integration, analysis, complex numbers. Hypergeometric series. 1713-1765 Alexis Clairaut. Born 13 May 1713[1] Paris. Died 17 May 1765 (aged 52) Paris Clairaut’s theorem. gravitational three-body problem 1713 Isaac Newton. Second edition of Principia Mathematica published. Nov. 14, 1716 Gottfried Wilhelm Leibniz. Died. Hannover, Germany 1717-1783 Jean le Rond d’Alembert. Born. Nov. 16, 171 Paris, France. First to propose that calculus be based on concept of limit. Analytical Solution to wave equation. 1726 Leonhard Euler. Dissertation published (Physical dissertation on sound). March 31, 1727 Isaac Newton. Died. Kensington, London, United Kingdom 1728-1777 Johann Heinrich Lambert. Born 26 August 1728, France. Died 25 September 1777 (aged 49) Berlin, Prussia. Introduced hyperbolic functions into trigonometry. non-Euclidean space. First proof that $$\pi$$ is irrational using a generalized continued fraction for the function $$\tan x$$. Formula for the relationship between the angles and the area of hyperbolic triangles. Theory of map projections. Oct. 1729 Leonhard Euler. Letter to Christian Goldbach showing ﬁrst proposal to extend factorial to positive numbers which can be non-integer. 1736-1813 Joseph-Louis Lagrange. Born 25 January 1736, Died 10 April 1813 (aged 77) Paris, France. Lagrange equations. Succeeded Euler as director of mathematics at Prussian Academy of Sciences in Berlin. Lagrange’s treatise on analytical mechanics. Classical mechanics. Variational calculus. Number theory. 1746 d’Alembert discovers the solution to wave equation named after him. 1748 Leonhard Euler. Publishes text "Introduction to analysis of inﬁnite". Jan. 1, 1748 Johann Bernoulli. Died in Basel, Switzerland. 1749-1827 Pierre-Simon Laplace. Born: March 23, 1749, Beaumont-en-Auge, France Died: March 5, 1827, Paris, France. Laplace’s equation, and the Laplace transform. Wrote ﬁve-volume Mécanique Céleste 1752-1833 Adrien-Marie Legendre. Born Sep. 18 1752, in Paris, France. French mathematician. Legendre polynomials. Legendre transformation. 1765-1822 Paolo Ruﬃni. Born September 22, 1765 Italy, Died May 10, 1822 (aged 56) Italy. First proof (Abel–Ruﬃni theorem) that quintic (and higher-order) equations cannot be solved by radicals. Ruﬃni’s rule. group theory. probability. quadrature of the circle. 1768-1830 Joseph Fourier. Born March 21,1768 in Auxerre, France. Most famous for of Fourier series, and Harmonic analysis. Discovery of Greenhouse eﬀect. 1768-1822 Jean-Robert Argand. Born July 18, 1768 Geneva, Died August 13, 1822 (aged 54) Paris. Argand diagram in complex analysis, the ﬁrst rigorous proof of the Fundamental Theorem of Algebra. 1776-1831 Sophie Germain. Born 1 April 1776, France. Died 27 June 1831 (aged 55) Paris, France. Elasticity theory (grand prize Paris Academy of Sciences). Worked on Fermat’s Last Theorem. correspondence with Lagrange, Legendre, and Gauss 1777-1855 Carl Friedrich Gauss. Born in Brunswick, Germany. Born April 20, 1777. Many contributions to Mathematics and Prime number theory. ﬁrst satisfactory proof of the fundamental theorem of algebra. Quadratic reciprocity law. Full systematic treatment of Hypergeometric series. Hypergeometric function. 1781-1840 Siméon Denis Poisson. Born 21 June 1781, France. Died 25 April 1840 (aged 58) memoirs on the theory of electricity and magnetism. Applied mathematics. Poisson PDE named after him. Sep. 18, 1783 Leonhard Euler. Died in Saint Petersburg, Russia Oct. 29, 1783 Jean le Rond d’Alembert. Died. Paris, France 1784-1846 Friedrich Wilhelm Bessel. Born 22 July 1784 Germany. Died 17 March 1846 (aged 61) Russia. Distance from the sun to another star by the method of parallax. Bessel functions. 1785-1836 Claude-Louis Navier. Born 10 February 1785, France. Died 21 August 1836 (aged 51) Paris Known for Navier–Stokes equations. 1789-1857 Augustin-Louis Cauchy. Born August 21, 1789 Paris, France. Foundation of analysis, complex number theory. 1793-1841 George Green. Born 14 July 1793, Died 31 May 1841. England. Green function, Green’s theorem. 1802-1829 Niels Henrik Abel. Born 5 August 1802 Norway. Died 6 April 1829 (aged 26) Norway. First complete proof demonstrating the impossibility of solving the general quintic equation in radicals. Elliptic functions. Abelian functions. 1803-1855 Jacques Charles François Sturm. Born 29 September 1803 Geneva. Died 15 December 1855 (aged 52) Paris Sturm-Liouville form of ODE. 1804-1851 Carl Gustav Jacob Jacobi. Born December 10, 1804, Potsdam, Germany, Died Feb. 18, 1851, Berlin, Germany. German mathematician. Elliptic functions, dynamics, diﬀerential equations, determinants, and number theory. 1805-1859 Johann Peter Gustav Lejeune Dirichlet. Born, 13 Feb. 1805, Duren, French Empire. Analytic number theory, formulated conditions for Fourier series convergence. 1805-1865 William Rowan Hamilton. Born: August 4, 1805, Dublin, Ireland. Died Sep. 2, 1865, Dublin, Ireland. Irish mathematician. Optics, classical mechanics and algebra, Hamiltonian mechanics. Quaternions. Hamiltonian equations. 1809-1882 Joseph Liouville. Born 24 March 1809, France. Died 8 September 1882 (aged 73) Paris, France number theory, complex analysis, diﬀerential geometry and topology. Sturm-Liouville form of ODE. 1809-1877 Hermann Grassmann. Born 15 April 1809 Poland. Died 26 September 1877 (aged 68), German Empire. First known appearance of linear algebra and the notion of a vector space. First axiomatic presentation of arithmetic, use of the principle of induction. Grassmann’s color law. Exterior algebra. 1810-1893 Ernst Kummer. Born 29 January 1810 Sorau, Prussia. Died 14 May 1893 (aged 83) Berlin, Germany. Hypergeometric series, Fermat’s last theorem. Kummer extensions of ﬁelds. 1811-1832 Évariste Galois. Born: Oct. 25, 1811, Bourg-la-Reine, France Died: May 31, 1832, Paris, France. Galois theory: necessary and suﬃcient condition for a polynomial to be solvable by radicals. 1815-1897 Karl Weierstrass. Born, Oct. 31, 1815. Ennigerloh, Germany. 1821 Augustin-Louis Cauchy. the Cours d’analyse, to accompany his course in analysis at the Ecole Polytechnique 1821-1895 Arthur Cayley. Born: August 16, 1821, Richmond, United Kingdom. Died: Died: Jan. 26, 1895, Cambridge, United Kingdom. Algebra. Cayley–Hamilton theorem, Cayley’s theorem. 1822-1901 Charles Hermite. Born 24 December 1822. Died 14 January 1901 (aged 78) Paris. Famous for Hermite polynomials and Hermite interpolation, spline, quadratic forms, elliptic functions and algebra. 1822 Joseph Fourier Publishes "The analytical theory of heat". 1823 Augustin-Louis Cauchy. Published Calcul Inﬁnitésimal 1826-1866 Bernhard Riemann. Born: Sep. 17, 1826, Kingdom of Hanover. Died: July 20, 1866, Verbania, Italy. Formulation of the integral, the Riemann integral, and work on Fourier series. His famous 1859 paper on the prime-counting function. Riemann geometry. May 16, 1830 Joseph Fourier Died in Paris, France Jan. 10, 1833 Adrien-Marie Legendre. Died in Paris, France 1831-1879 James Clerk Maxwell. Born 13 June 1831 Edinburgh, Scotland. Died 5 November 1879 (aged 48) Cambridge, England. Mathematical physics. Maxwell’s equations. Published "A Dynamical Theory of the Electromagnetic Field" in 1865. 1842-1899 Marius Sophus Lie. Born: December 17, 1842, Nordfjordeid, Norway. Died: Died: Feb. 18, 1899, Oslo, Norway. Norwegian mathematician. Theory of continuous symmetry, study of geometry and diﬀerential equations. diﬀerential topology. 1843-1921 Karl Hermann Amandus Schwarz. Born 25 January 1843 Prussia. Died 30 November 1921 (aged 78) Berlin, Germany. Cauchy–Schwarz inequality. Improved the proof of the Riemann mapping theorem. 1844 Joseph Liouville proved the existence of transcendental numbers 1845-1918 Georg Cantor. Born: March 3, 1845, Saint Petersburg, Russia Died: Jan. 6, 1918, Halle (Saale), Germany. Set theory. 1849-1917 Ferdinand Georg Frobenius. Born 26 October 1849 Berlin. Died 3 August 1917 (aged 67) Berlin. Diﬀerential equations (Frobenius series). ﬁrst full proof for the Cayley–Hamilton theorem. Frobenius–Stickelberger formulae 1849-1925 Felix Klein. Born 25 April 1849, Germany. Died 22 June 1925 (aged 76) Germany. Group theory, complex analysis, non-Euclidean geometry. Died: Jan. 6, 1918, Halle (Saale), Germany. Set theory. 1851 Joseph Liouville. Publish paper showing for ﬁrst time a transcendental number $$\sum _{k=1}^\infty \frac {1}{10^{k!}}$$ 1854-1912 Henri Poincare, Born April 29,1854. Died July 17, 1912 Feb. 23, 1855 Carl Friedrich Gauss Died in Gottingen, Germany 1856-1941 Émile Picard.Born 24 July 1856 Paris, France. Died 11 December 1941 (aged 85) Paris, France French mathematician. Picard iteration. diﬀerential equations. Picard’s little theorem. algebraic topology. 1856-1894 Thomas Joannes Stieltjes. Born 29 December 1856, Netherlands. Died 31 December 1894 (aged 38) , France. continued fractions. Riemann–Stieltjes integral. May 23, 1857 Augustin-Louis Cauchy Died. Sceaux, France May 5, 1859 Johann Peter Gustav Lejeune Dirichlet. Died (aged 54), Gottingen, Kingdom of Hanover 1857-1918 Aleksandr Mikhailovich Lyapunov. Born June 6, 1857, Russian Empire. Died November 3, 1918 (aged 61) Ukrainian People’s Republic. stability theory of a dynamical system. 1859-1929 Karl Heun. Born 3 April 1859, Germany; died 10 January 1929, Germany. Heun’s equation, Heun special function, Heun’s method. 1861-1947 Alfred North Whitehead. Born 15 February 1861, England. Died 30 December 1947 (aged 86) Cambridge, Massachusetts, US. mathematical logic. Wrote Principia Mathematica with Bertrand Russell. 1861-1935 Ivar Otto Bendixson. Born August 1, 1861, Stockholm Sweden. Died November 29, 1935 (aged 74) Stockholm Sweden. Poincaré–Bendixson theorem. “The Poincaré–Bendixson theorem, which says an integral curve which does not end in a singular point has a limit cycle, was ﬁrst proved by Henri Poincaré but a more rigorous proof with weaker hypotheses was given by Bendixson in 1901” “In 1902, he derived Bendixson’s inequality which puts bounds on the characteristic roots of matrices” 1862-1943 David Hilbert. Born: Jan. 23, 1862, Königsberg. Died: Feb. 14, 1943, Göttingen, Germany. German mathematician. Invariant theory, calculus of variations, commutative algebra, algebraic number theory, Spectral theory of operators and its application to integral equations, mathematical physics. 1864-1909 Hermann Minkowski. Born: June 22, 1864, Aleksotas, Kaunas, Lithuania. Died: Jan. 12, 1909, Göttingen, Germany. German mathematician. Geometry of numbers. Mathematical physics. Theory of relativity. 1870-1951 Abraham Cohen. Born 11 Sep 1870, Died 25 Apr 1951 (aged 80) Professor of Mathematics, Johns Hopkins University. Published "AN INTRODUCTION TO THE LIE THEORY OF ONE PARAMETER GROUPS WITH APPLICATIONS TO THE SOLUTION OF DIFFERENTIAL EQUATIONS" and "The Diﬀerential Equation" book. No image found. 1875 Karl Weierstrass. Paul duBois Reymond publishes account of Karl Weierstrass pathological function which is continuous at every point but diﬀerentiable nowhere. Karl ﬁrst discovered this function in the 1860’s. If $$a\geq 3$$ is an odd integer and if $$01+\frac {3 \pi }{2}$$ then the function $$f(x)=\sum _{k=0}^{\infty } b^k \cos (\pi a^k x)$$ is such. 1877-1947 G. H. Hardy. English mathematician. Born: Feb. 7, 1877, Cranleigh, United Kingdom. Died: December 1, 1947, Cambridge, United Kingdom. Number theory and mathematical analysis 1879-1955 Albert Einstein. Born: March 14, 1879, Ulm, Germany. 1882-1935 Emmy Noether. Born: March 23, 1882, Erlangen, Germany Died: April 14, 1935, Bryn Mawr, PA. Abstract algebra and theoretical physics. 1884-1944 George David Birkhoﬀ. Born March 21, 1884, Michigan. Died November 12, 1944 (aged 60) Cambridge, Massachusetts. American mathematician best. ergodic theorem. Dynamical systems. Geometry. 1885-1955 Hermann Weyl. Born 9 November 1885, Germany. Died 8 December 1955 (aged 70) Zurich, Switzerland. Theoretical physicist. Combining general relativity with the laws of electromagnetism. 1887-1920 Srinivasa Ramanujan. Born: December 22, 1887, Erode, India Died: April 26, 1920, Kumbakonam, India. The Ramanujan prime, the Ramanujan theta function, partition formulae and mock theta function. Prime theory. 1890-1961 Erich Kamke. Born 18 August 1890, German Empire. Died 28 September 1961 (aged 71), Germany. Diﬀerential equations. 1893-1945 Stefan Banach. Born 30 March 1892 Poland, Died 31 August 1945 (aged 53), Ukraine. modern functional analysis, Linear Operators, Banach spaces. 1932 book, Theory of Linear Operations. Feb. 19, 1897 Karl Weierstrass Died, Berlin, Germany 1898-1962 Emil Artin. Born March 3, 1898 Vienna, Austria-Hungary, December 20, 1962 (aged 64) Hamburg, West Germany. From wikipedia “He is best known for his work on algebraic number theory, contributing largely to class ﬁeld theory and a new construction of L-functions. He also contributed to the pure theories of rings, groups and ﬁelds.” 1903-1957 John von Neumann. Born: December 28, 1903, Budapest, Hungary Died: Feb. 8, 1957, Bethesda, USA. physics and computer science. 1906-1978 Kurt Gödel. Born: April 28, 1906, Austria-Hungary. Died: Jan. 14, 1978, Princeton, NJ. Incompleteness theorems. 1913-1996 Paul Erdos. Hungarian mathematician. Born: March 26, 1913, Budapest, Hungary. Died: Sep. 20, 1996, Warsaw, Poland. 1917-2010 Mary L. Boas. Born March 10, 1917 Washington. Died February 17, 2010 Seattle, Washington Most known for her book Mathematical Methods in the Physical Sciences 1955 Albert Einstein. Died: April 18, 1955, Princeton Medical Center, NJ

### 3 Reference

1. https://en.wikipedia.org/wiki/Writing_of_Principia_Mathematica
2. https://blogs.uoregon.edu/scua/2019/02/04/isaac-newtons-work-on-calculus-de-analysi-1711/
3. Book: The Calculus Gallary. by William Dunham. Princeton Press 2005. https://www.britannica.com/biography/James-Gregory
4. A history of Mathematics, by Florian Cajori, 1919.
5. Images, thanks to https://en.wikipedia.org and https://archive.org and https://www.maa.org and https://cosmosmagazine.com