## Sunday, January 9, 2011

### The Mathematics Timeline - Part 3 and Complete

I reviewed UK Mathematics Historian Tony Crilly's 50 Mathematical Ideas You Really Need to Know in February ==> HERE. That is the first link and very important as it lists the 50 chapters, 4 pages each, of this wonderfully concise book.

In Part 1, I combined the little timelines in each chapter up though Chapter 14, up to and including Algebra. Numbers in parentheses are Chapter numbers, which is why I asked you to click on that first link, first. I also have introductory notes there.

In Part 2, I added Chapters 15-19, up to and including Calculus.

In this Part 3, all 50 chapter timelines are shown. The new items in Chapters 20-50 are in bold.

This list seems long, and it is (prints out at 13+ pages), but it's useful, important, yet ... finite! :-) I shall be referring to this timeline in the coming months.

Part 4 will be analysis of this list.

Enjoy, and Go, Go Euclid !

THE MATHEMATICS TIMELINE

30,000 BC - Paleolithic peoples in Europe make number marks on bones (2)

3000 BC - The Babylonians use a sexagesimal number system for financial dealings (44)

2800 BC - The legend of the Lo Shu square is born (42)

2000 BC - The Babylonians use symbols for numbers (2)

2000 BC - The Babylonians observe pi is roughly 3 (5)

1950 BC - The Babylonians work with quadratic equations (14)

1850 BC - The Babylonians know "Pythagoras's Theorem" (21)

1800 BC - Fractions are used in Babylonian cultures (3)

c. 1800 BC - The Rhind papyrus is written in Egypt (41)

1750 BC - The Babylonians compile tables of square roots (4)

1650 BC - The Egyptians make use of unit fractions (3)

700 BC - The Babylonians use zero as a placeholder in their number system (1)

525 BC - The Pythagoreans study geometrically arranged square numbers (4)

525 BC - The Pythagoreans are associated with both perfect and abundant numbers (10)

c. 500 BC - Fragmentary evidence exists for Pascal's triangle in Sanskrit (13)

c. 450 BC - Zeno ridicules infinitesimals with a paradox (19)

450 BC - Anaxogoras attempts to square the circle while in prison (20)

350 BC - Aristotle rejects an actual infinite (7)

c. 335 BC - Aristotle formalizes the logic of the the syllogism (16)

c. 300 BC - The theory of the irrational numbers by Eudoxus is published in Book 5 of Euclid's Elements (4)

300 BC - Euclid's Elements gives a proof that there are infinitely many prime numbers (9)

300 BC - Book 9 of Euclid's Elements discusses perfect numbers (10)

c. 300 BC - The extreme and mean ratio is published in Euclid's Elements (12)

c. 300 BC - Euclid's Elements provides the model for mathematical proof (17)

c. 300 BC - Euclid's algorithm is published in Book 7 of Elements (15)

c. 300 BC - Euclid defines the conic sections (22)

c. 300 BC - Euclid shows there are five regular polyhedra (23)

c. 300 BC - Euclid describes a three-dimensional world (24)

c. 300 BC - Euclid includes the parallel postulate in his Elements (27)

250 BC - Archimedes gives the close approximation of pi of 22/7 (5)

c. 250 BC - Archimedes investigates spirals (22)

c. 250 BC - Archimedes investigates truncated polyhedra (23)

230 BC - Eratosthenes of Cyrene describes a method for sieving out prime numbers from the whole numbers (9)

c. 225 BC - Apollonius of Perga publishes Conics (22)

200 BC - Chinese mathematicians use arrays of numbers (39)

55 BC - Julius Caesar invades Britain and uses codes to communicate with his generals (40)

100 - The Chinese devise a system for calculating with fractions (3)

100 - Nicomachus of Gerasa gives a classification of numbers based on perfect numbers (10)

250 - Diophantus of Alexandria publishes Arithmetica (14)

300 - Sun Tzu discovers the Chinese Algorithm (15)

600 - The forerunner of our modern decimal notation is used in India (2)

628 - Brahmagupta uses zero and states rules for its use with other numerals (1)

630 - Brahmagupta gives methods for computing square roots (4)

810 - Al-Khwarizmi gives the word "algorithm" to mathematics (15)

825 - Derived from "al-jabr" Al-Khwarizmi gives the word "algebra" to mathematics (14)

830 - Mahavira has ideas on how zero interacts with other numerals (1)

c. 1070 - Omar Khayyam discovers Pascal's triangle, which in some countries is named after him (13)

1100 - Bhaskara uses zero as a symbol in algebra and attempts to show how it is manipulated (1)

c. 1100 - Bhaskara deals with permutations and combinations (41)

1200 - The Hindu-Arabic system of writing numerals 1,...,9, and a zero, spreads (2)

1202 - Fibonacci uses the extra symbol 0 added to the Hindu-Arabic system of numerals 1,...,9 but not as a number on par with them (1)

1202 - Fibonacci publishes the Liber Abaci and Fibonacci numbers (11)

1202 - Fibonacci popularizes the bar notation of fractions (3)

1202 - Fibonacci publishes work on congruences in Liber Abaci (15)

1303 - Zhu Shijie defines Pascal's triangle and shows how to sum certain sequences (13)

1335 - Richard of Wallingford writes a groundbreaking treatise on Trigonometry (21)

1494 - Luca Pacioli publishes financial tables and an account of double-entry bookkeeping (44)

1509 - Paciola publishes The Divine Proportion (12)

1550 - The square root symbol is introduced (4)

1571 - Francois Viete publishes a book on trigonometry and trigonometric tables (21)

1572 - Rafael Bombelli calculates with imaginary numbers (8)

1585 - Simon Stevin sets out a theory of decimal fractions (3)

1591 - Francois Viete writes a mathematical text in terms of letters for knowns and unknowns (14)

1600 - The symbols of the decimal system take their recognizable modern forms (2)

1603 - Pietro Cataldi finds the 6th and 7th perfect numbers, 2^16(2^17 -1) = 8,589,869,056 and 2^18(2^19 - 1) = 137,438,691,328 (10)

1618 - John Napier encounters a constant, e, in connection with logarithms (6)

1631 - Galileo gives "Galilean transformations" for falling bodies (48)

1639 - Girard Desargues introduces the concept of infinity into geometry (7)

1639 - Pascal discovers his theorem while only 16 years old (28)

1654 - Blaise Pascal lays the foundations of probability theory (21)(33)

1655 - John Wallis is credited with being the first to use the "love knot" symbol for infinity (7)

1657 - Christiaan Huygens writes the first published work on probability (31)(33)

1664 - Pascal's paper on the properties of Pascal's triangle is published posthumously (13)

1665 - Fermat dies, leaving no record of his "wonderful proof" (49)

1660's-1670's - Newton and Leibniz take the first steps in Calculus (19)

1672 - Mohr shows that all Euclidean constructions can be carried out with compasses alone (20)

1676 - Romer calculates the speed of light from observations of the moons of Jupiter (48)

1687 - Descartes promotes mathematical rigour as a model in his Discourse on Method (17)

1687 - Newton's Principia describes the classical laws of motion (48)

1690 - de la Loubere produces a Siamese method for constructing magic squares (42)

1693 - Bernard Frenicle de Bessy lists all the 880 possible 4 x 4 magic squares (42)

1700 - The fractional line "-" is in general use (as is %) (3)

1704 - Newton classifies the cubic curves (22)

1706 - William Jones introduces the pi symbol (5)

1713 - Waldegrave gives the first mathematical solution of a two-player game (47)

1714 - Leibniz discusses the harmonic triangle (13)

1718 - Abraham de Moivre publishes The Doctrine of Chance, with expanded editions following in 1738 and 1756 (33)(37)

1718 - Abraham de Moivre investigates morality statistics and the foundation of the theory of annuities (44)

1724 - Daniel Bernoulli expresses the numbers of the Fibonacci sequence in terms of the golden ratio (11)

1727 - Euler uses the notation e in connection with the theory of logarithms; it is sometimes called Euler's number (6)

1733 - De Moivre publishes work on the normal curve as an approximation to the binomial distribution (35)

1734 - Berkeley draws attention to foundational weaknesses in Calculus (19)

1735 - Euler solves the problem of the bridges of Konigsberg (29)

1742 - Goldbach speculates that every even number (more than 2) is a sum of two primes (9)

1748 - Euler calculates e to 23 digits; he is given the credit for the discovery of the famous formula e^i(pi) + 1 = 0 around this time (6)

1750 - Euler's theorem lays the foundations for public key cryptography (40)

1752 - Euler gives his formula for the number of vertices, edges and faces in a polyhedron (23)

1753 - Euler proves Fermat's last theorem for the case n=3 (49)

1756 - James Dobson publishes First Lectures on Insurances (44)

1761 - Lambert proves that pi is irrational (5)

1763 - Bayes's essay on probability is published (32)

1770 - Euler produces a squared (42)

1777 - Euler first uses the symbol i to represent the square root of -1 (8)

1779 - Euler explores the theory of Latin squares (43)

1785 - Condorcet applies probability to the analysis of juries and electoral systems (31)

1801 - Gauss publishes Discourses on Arithmetic including a section on the construction of a regular 17-gon by ruler and compasses (20)

1806 - Argand's diagrammatic representation leads to the name "Argand diagram" (8)

1806 - Brianchon discovers the dual theorem of Pascal's theorem (28)

1806 - Adrien-Marie Legendre fits data by least squares (36)

1809 - Carl Friedrich Gauss uses the least-squares method in Astronomical problems (36)

1810 - Charles Babbage mentions the travelling salesperson problem as an interesting one (46)

1811 - Carl Friedrich Gauss works with functions of complex number variables (8)

1812 - Laplace publishes his essay on a deterministic world (26)

1812 - Laplace publishes his two volume Analytical Theory of Probabilities (31)

1820 - Cauchy formalizes calculus in a rigourous way (19)

1820 - Gauss uses the normal distribution (as the Gaussian) in astronomy as a law of error (35)

1822 - Karl Feuerbach describes the nine point circle of a triangle (21)

1825 - Legendre and Dirichlet independently prove Fermat's Last Theorem for the case n=5 (49)

1826 - Fourier anticipates linear programming; Gauss solves linear equations by Gaussian elimination (45)

1829-31 - Lobachevsky and Bolyai publish their work on hyperbolic geometry (27)

1831 - The travelling salesperson problem appears as a practical problem (46)

1832 - Galois proposes the idea of groups of permutations (38)

1835 - Quetelet uses the normal curve to measure divergence from the average man (35)

1837 - William R. Hamilton treats complex numbers as ordered pairs of real numbers (8)

1837 - Wantzel proves that the classical problems of duplicating a cube and trisecting an angle cannot be solved with ruler and compass (20)

1837 - Simeon-Denis Poisson describes the distribution named after him (34)

1838 - De Morgan introduces the term "Mathematical Induction" (17)

1839 - Lame proves Fermat's Last Theorem for the case n=7 (49)

1843 - Kummer claims he has proved Fermat's Last Theorem, but Dirichlet exposes flaw (49)

1844 - Morse transmits the first message using his code (4)

1846 - Kirkman anticipates the discovery of Steiner triple systems (28)

1847 - Boole publishes The Mathematical Analysis of Logic (16)

1848 - The Institute of Actuaries is founded in London (44)

1850 - J.J. Sylvester introduces the term "matrix" (39)

1850 - Kirkman poses the 15 schoolgirls problem (41)

1852 - Guthrie, De Morgan's student, puts the 4-colour problem to him (30)

1854 - Riemann introduces the Riemann integral (19)

1854 - Riemann lectures on the foundation of geometry (27)

1854 - Cayley attempts to generalize the concept of a group (38)

1854 - Riemann begins his work on the zeta function (50)

1858 - Mobius and Listing introduce the Mobius strip (23)

1858 - Cayley publishes Memoir on the Theory of Matrices (39)

1859 - Riemann proves key solutions to The Riemann Hypothesis lie in a critical strip and puts forward his conjecture (50)

1865 - Mendel proposes the existence of genes and laws of inheritance (37)

1870 - The distribution acquires the name "normal" (35)

1872 - Richard Dedekind sets out a theory of irrational numbers (4)

1872 - Cantor takes a tentative step in the creation of set theory (18)

1872 - Klein unifies geometry via group theory (27)

1872 - Felix Klein begins a programme for classifying geometry using groups (38)

1873 - Hermite proves e is a transcendental (6)

1873 - Brocard produces his exhaustive work on the triangle (21)

1874 - Cantor treats the notion of infinity rigorously, specifying different orders of infinity (7)

1874 - Carl Schorlemmer links chemistry with "trees" (29)

1876 - Fechner writes on psychological experiments to determine the proportions of the most "aesthetic" rectangle (12)

1877 - Cantor is surprised by his controversial discoveries in dimension theory (24)

1878 - Georg Frobenius proves some of the key results of matrix algebra (39)

1879 - Cayley works on a precursor of modern fractals (25)

1879 - Kempe is believed to solve the 4-color problem. He hasn't. (30)

1881 - Venn produces "Venn Diagrams" for sets (18)

1881 - Newcomb discovers what becomes known as Benford's law (34)

1881 - Michelson measures the speed of light with great accuracy (48)

1882 - Lindemann proves that pi is transcendental (5)

1882 - Lindemann proves the circle cannot be squared (20)

1885-8 - Galton introduces regression and correlation (36)

1887 - The Lorenz transformations are first written down (48)

1889 - Poincare encounters chaos in his work on the three-body problem for which he is awarded a prize by King Oscar of Sweden (26)

1890 - Peano proves a solid square is a curve (the space-filling curve) (22)

1890 - Heawood exposes errors in Kempe's 4-colour proof and proves a 5-colour theorem (30)

1891 - Evgraf Fedorov and Arthur Schonflies independently classify the 230 crystallographic groups (38)

1892 - Fano discovers the Fano plane, the simplest example of a projective geometry (28)

1896 - The prime number theorem on the distribution of primes is proved (9)

1896 - Pearson publishes contributions to correlation and regression (36)

1896 - De la Vallee-Poussin and Hadamard show all important zeros lie within Riemann's critical strip (50)

1898 - Bortkiewicz analyses the deaths of Prussian cavalrymen (34)

1899 - Pick publishes his theorem on the area of polygons (28)

1900 - Tarry shows there are no orthogonal Latin squares of order 6 (43)

1900 - Hilbert places Reimann's Hypothesis in his list of key problems for mathematicians to solve. It is Hilbert's personally favorite problem, and still unsolved as of 2011 (50)

1901 - Aleksandr Lyapunov proves the Central Limit theorem rigourously using characteristic functions (35)

1902 - Lebesgue sets out the theory of the Lebesgue integral (19)

1902 - Farkas gives a solution of inequality systems (45)

1904 - von Koch creates his snowflake curve (25)

1904 - Spearman uses rank correlation as a tool for psychological studies (36)

1905 - Einstein publishes On the electrodynamics of moving bodies , the paper that describes special relativity (48)

1907 - von Lindemann claims a proof of Fermat's Last Theorem, but is shown to be wrong (49)

1908 - Hardy and Weinberg show why dominant genes do not supplant recessive genes (37)

1908 - Wolfskehl offers a prize for solutions of Fermat's Last Theorem within the next 100 years (49)

1909 - Brouwer's work changes our notion of dimension (24)

1910 - Russell and Whitehead attempt to reduce mathematics to logic (16)

1912 - Keynes publishes his Treatise on Probability which influences his theories of economics and statistics (31)

1914 - Hardy proves there are infinitely many solutions along Riemann's line (50)

1915 - Einstein publishes The field equations for gravitation, his paper that describes the theory of general relativity, based on Riemannian geometry (27)(48)

1918 - Hausdorff introduces his concept of fractional dimension (25)

1918 - Fisher reconciles Darwin's theory with the Mendelian theory of heredity (37)

1919 - Hausdorff introduces the notion of the fractional "Hausdorff dimension" (24)

1919 - Julia and Fatou investigate fractal structures in the complex plane (25)

1920's - Emmy Noether publishes papers in the development of modern abstract algebra (14)

1920's - Menger and Urysohn define curves as part of topology (22)

1920's - Bose considers Einstein's theory of light as an occupancy problem (33)

1920's - The Enigma machine is developed (40)

1923 - Bartok composes his "Dance Suite", believed to be inspired by the Fibonacci numbers (11)

1925 - Heisenberg uses matrix mechanics in quantum theory (39)

1925 - Fisher suggests using Latin squares to design statistical experiments (43)

1926 - Boruvka introduces the greedy algorithm (46)

1930 - Bartel van der Waerden publishes his famous Moderne Algebra (14)

1930 - Kuratowski proves his planar graphs theorem (29)

1930 - Frank Ramsey works in combinatorics (41)

1931 - Godel proves that any formal axiomatic mathematical system contains undecidable statements (18)

1933 - Kolmogorov presents probability in an axiomatic way (31)

1935 - George Polya develops counting techniques for graphs as algebra (29)

1937 - De Finetti champions subjective probability as an alternative to the frequency theory (32)

1939 - Benford restates the law of distribution of first digits (34)

1939 - The pseudonym Bourbaki is first used by French mathematicians (18)

1939 - Richard von Mises proposes the birthday problem (33)

1944 - von Neumann and Morgenstern publish Theory of Games and Economic Behavior (47)

1945 - Stigler solves the diet problem by a heuristic method (45)

1947 - Dantzig formulates the simplex method and solves the diet problem by linear programming (45)

1950 - Jimmy Savage and Dennis Lindley spearhead the modern Bayesian movement (32)

1950's - The term "Bayesian" comes into use for the first time (32)

1950 - Zipf derives a formula relating word use to vocabulary (34)

1950 - Richard Hamming publishes a key paper on error-detecting and error-correcting codes (4)

1950 - Tucker proposes the prisoner's dilemma and nash proposes the nash equilibrium (47)

1953 - The double helix structure of DNA is discovered (37)

1954 - Dantzig and Dijkstra propose methods for attacking the travelling salesperson problem (46)

1960s - Abraham Robinson devises a non-standard arithmetic based on the notion of the infinitesimal (7)

1960 - Euler's conjecture about the non-existence of certain pairs of Latin squares is disproved by Bose, Parker and Shrikhande (43)

1961 - Stephen Smale proves the Poincare conjecture in dimensions greater than 4 (23)

1961 - Lorenz observes the butterfly effect. (26)

1963 - The Fibonacci Quarterly, a journal devoted to the number theory of the Fibonacci sequence, is founded (11)

1964 - Cohen proves the independence of the continuum hypothesis (18)

1965 - Lofti Zadeh develops fuzzy logic (16)

1966 - Chen Jingrun almost confirms the Goldbach conjecture (9)

1967 - Bishop proves results exclusively by constructive methods (17)

1970's - The Chinese remainder theorem is applied to message encryption (15)

1970's - Public key cryptography is developed (40)

1970 - String theory conceives of our universe having 10, 11 or 26 dimensions (24)

1971 - Robert May investigates chaos in the population model (26)

1971 - Ray-Chaudhuri and Wilson prove the existence of Kirkman's systems (41)

1971 - Cook formulates the P versus NP concept for algorithms (46)

1975 - The International Organization for Standardization (ISO) defines the A paper size (12)

1975 - Mandelbrot introduces the term fractal (25)

1976 - Imre Lakatos publishes the influential Proofs and Refutations (17)

1976 - Appel and Haken give a computer-based proof for the general result of the 4-colour problem (30)

1979 - Sudoku-like games are invented in New York (43)

1982 - Michael Freedman proves the Poincare conjecture in dimension equal to 4 (23)

1982 - Maynard Smith publishes Evolution and the Theory of Games (47)

1983 - The classification of finite simple groups is completed and the enormous theorem proved (38)

1984 - Karmarker at Bell Labs derives a new algorithm for solving linear programming problems (45)

1987 - The underground train system in Japan is based on fuzzy logic (16)

1986 - Sallows creates his letter-based square (42)

1992 - The International Society for Bayesian Analysis is founded (32)

1994 - The computer proof of the 4-colour problem is simplified by remains a computer-based proof (30)

1994 - Nash is awarded the Nobel Prize in Economics for his work on game theory (47)

1994 - Wiles finally proves Fermat's Last Theorem (49)

1999 - Eric Rains and Neil Sloane extend tree counting (29)

2002 - Perelman proves the Poincare conjecture for dimension 3 (23)

2003 - The Poisson distribution is used in the analysis of fish stocks in the North Atlantic (34)

2004 - Chaos theory reaches popular culture in the film The Butterfly Effect (26)

2004 - David Applegate solves the travelling salesperson problem for all 24,978 cities in Sweden (46)

2004 - The first 10 trillion zeros of Riemann's Hypothesis are verified to be on the critical line. (50)

2006 - The great prime search project finds the 44th Mersenne prime (with almost ten million digits) and yet another new perfect number can be generated (10)

2007 - e is calculated to 10^11 digits (6)

2007 - Sculptor Peter Randall-Page creates the 70 tonne sculpture "Seed" based on the Fibonacci sequence for the Eden Project in Cornwall, UK (11)

Source material, here. Thank you, Tony Crilly, great book!