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!

## 1 comment:

One of the oldest known Latin Squares is the Sator Square. This Square was supposedly found amongst the ruins of Pompeii in the volcanic ashes resulting Mount Vesuvius in 79 AD, pressed in clay or carved in stone. Read more about it on my blog: http://www.glennwestmore.com.au/category/latin-squares/.

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