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 mean (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!

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