History of Mathematics

Mathematics is the science of numbers and there are several different branches of mathematical science including algebra, geometry, and calculus. The Merriam-Webster dictionary defines mathematics as the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations.

Mathematics is not an invention. Discoveries and laws of science are not considered inventions. Inventions are material things and processes. However, there is a history of mathematics, a relationship between mathematics and inventions, and mathematical instruments are considered inventions.

According to Mathematical Thought from Ancient to Modern Times, mathematics as an organized science did not exist before the classical Greeks of the period from 600 to 300 BC entered upon the scene. There were, however, prior civilizations in which the beginnings or rudiments of mathematics were created.

When civilization began to trade, a need to count was created. When humans traded goods, they needed a way to count the goods and to calculate the cost of those goods. The very first device for counting numbers was the human hand, counting on fingers. To count beyond ten fingers, mankind used natural markers, rocks or shells. From that point, counting boards and the abacuswere invented.

Abacus

One of the first tools for counting invented, the abacus was invented around 1200 A.D. in China.

Accounting

The innovative Italians of the Renaissance (fourteenth through sixteenth century) are widely acknowledged to be the fathers of modern accounting .

Algebra

The first treatise on algebra was written by Diophantus of Alexandria in the 3rd century AD. Algebra comes from the Arabic word al-jabr an ancient medical term meaning "the reunion of broken parts.''

Archimedes

Archimedes was a mathematician and inventor from ancient Greece, best known for his discovery of the relation between the surface and volume of a sphere and its circumscribing cyclinder, for his formulation of a hydrostatic principle (Archimedes' principle) and for inventing the Archimedes screw (a device for raising water).

Differential

Gottfried Wilhelm Leibniz (b. 1646, d. 1716) was a German philosopher, mathematician, and logician who is probably most well known for having invented the differential and integral calculus (independently of Sir Isaac Newton).

Graph

A graph is a pictorial representation of statistical data or of a functional relationship between variables. William Playfair (1759-1823) is generally viewed as the inventor of most of graphical forms used to display data, including: line plots, bar chart, and pie chart.

Logarithms and the Decimal Point

John Napier was the Scottish mathematician who invented logarithms and the decimal point.

Pythagoreanism

Pythagoreanism is a school of philosophy school and a religious brotherhood, believed to have been founded by Pythagoras of Samos, who settled in Croton in southern Italy about 525 BC. The group had a profound effect on the development of mathematics.

Protractor

An instrument used to construct and measure plane angles. The simple protractor looks like a semicircular disk marked with degrees, from 0º to180º. The simple protractor is an ancient device. The first complex protractor was created for plotting the position of a boat on navigational charts. Called a three-arm protractor or station pointer, it was invented in 1801, by Joseph Huddart, a U.S. naval captain. The centre arm is fixed, while the outer two are rotatable, capable of being set at any angle relative to the centre one.

Slide Rulers

Circular and rectangular slide rules, an instrument used for mathematical calculations were both invented by mathematician William Oughtred .

Zero

Zero was invented by the Hindu mathematicians Aryabhata and Varamihara in India around or shortly after the year 520 A.D.

Math Symbol

In 1557, the = sign first used by Robert Record. In 1631, >,

It should be noted that the brief descriptions given are just that "brief." Their purpose is to hopefully instill a little curiosity and encourage the reader to seek out further knowledge on these people and topics.

50,000 B.C.E.		Evidence of counting	50,000 B.C.E.		Neanderthal man
25,000 B.C.E.		Primitive geometrical designs	25,000 B.C.E.		Paleolithic art: Cro-Magnon man
			4000 B.C.E.		Use of metals
			3500 B.C.E.		Writing
3000 B.C.E.		Hieroglyphic numerals in Egypt	3000 B.C.E.		Use of wheeled vehicles
2773 B.C.E.		Likely introduction of the Egyptian calendar (Some hypothesize 4241 B.C.E. as the origin.)
			2500 B.C.E.		Great Pyramid
2400 B.C.E.		Positional notation for numbers in Mesopotamia	2400 B.C.E.		Sumerian-Akkadian Empire
1850 B.C.E.		Moscow Papyrus: arithmetic
			1800 B.C.E.		Code of Hammurabi
			1700 B.C.E.		Stonehenge in England
1650 B.C.E.		Rhind Papyrus
			1400 B.C.E.		Catastrophe in Crete-fall of the Minoan Civilization
			1350 B.C.E.		Use of iron: sundials: water clocks
			1200 B.C.E.		Trojan war
			776 B.C.E.		First Olympiad
			753 B.C.E.		Founding of Rome
			740 B.C.E.		Works of Homer and Hesoid
			586 B.C.E.		Babylonia captivity
585 B.C.E.		Thales of Miletus – deductive geometry
518 B.C.E.		Pythagorean arithmetic and geometry
			538 B.C.E.		Persians took Babylon
			480 B.C.E.		Battle of Thermopylae
			461 B.C.E.		Beginning of the Age of Pericles
450 B.C.E.		Parmenides' spherical earth
430 B.C.E.		Death of Zeno: Elements of Hippocrates of Chios	430 B.C.E.		Hippocrates of Cos (the Physician)
			429 B.C.E.		Death of Pericles: The plague at Athens
427 B.C.E.		Birth of Plato
420 B.C.E.		Quadratrix (Trisectrix) of Hippias
			404 B.C.E.		End of Peloponnesian War
			399 B.C.E.		Death of Socrates
360 B.C.E.		Eudoxus' method of exhaustion
350 B.C.E.		Birth of Eudemus
332 B.C.E.		Alexandria founded
			323 B.C.E.		Death of Alexander
			322 B.C.E.		Death of Aristotle
			305 B.C.E.		Ptolemy I (Soter) of Egypt
300 B.C.E.		Euclid's Elements
			280 B.C.E.		Pharos, Lighthouse of Alexandria
			264 B.C.E.		First Punic War
260 B.C.E.		Aristarchus' heliocentric astronomy
230 B.C.E.		Sieve of Eratosthenes
225 B.C.E.		Conics of Apollonius
212 B.C.E.		Death of Archimedes
			210 B.C.E.		Great Wall of China begun
150 B.C.E.		360 degree circle
			146 B.C.E.		Destruction of Carthage
140 B.C.E.		Trigonometry of Hipparchus
75 B.C.E.		Cicero restored tomb of Archimedes	.
			44 B.C.E.		Death of Julius Caesar
60 C.E.		Geminus on the parallel postulate
75 C.E.		Works of Heron of Alexandria
100 C.E.		Menelaus' Spherica
			122 C.E.		Hadrian's Wall in Britain begun
150 C.E.		Ptolemy's Almagest
			180 C.E.		Death of Marcus Aurelius
250 C.E.		Diophantus' Arithmetica
320 C.E.		Pappus' Mathematical Collections
			324 C.E.		Founding of Constantinople
405 C.E.		Death of Theon of Alexandria
415 C.E.		Death of Hypatia
			455 C.E.		Vandals sack Rome
			476 C.E.		Traditional “fall” of Rome
524 C.E.		Death of Boethius
529 C.E.		Closing of the schools at Athens
530 C.E.		Eutocius' commentaries on Archimedes
641 C.E.		Library at Alexandria burned
			732 C.E.		Battle of Tours
775 C.E.		Hindu works translated into Arabic
			814 C.E.		Death of Charlemagne
830 C.E.		Al-Khowarizmi's  Algebra
			999 C.E.		Gebert becomes Pope Sylvester II
			1066 C.E.		Battle of Hastings
			1096 C.E.		First Crusade
1114 C.E.		Birth of Bhaskara
1142 C.E.		Adelard of Bath translated Euclid
			1170 C.E.		Murder of Thomas à Becket
1202 C.E.		Fibonacci's Liber abaci
			1204 C.E.		Crusaders sack Constantinople
			1215 C.E.		Magna Carta
1270 C.E.		William of Moerbeke translated Archimedes
			1271 C.E.		Travels of Marco Polo: mechanical clocks (approx.)
			1286 C.E.		Invention of eyeglasses (approx.)
1303 C.E.		Chu Shih-Chieh and the Pascal triangle (long before Pascal)
			1348 C.E.		The Black Death
			1364 C.E.		Death of Petrarch
			1431 C.E.		Joan of Arc burned
			1440 C.E.		Invention of the printing press
			1453 C.E.		Fall of Constantinople
1464 C.E.		Death of Nicolas of Cusa
1482 C.E.		First printed edition of Euclid's Elements
			1483 C.E.		Murder of the princes in the Tower
			1485 C.E.		Henry VII, the first Tutor
1489 C.E.		Use of + and – by Widmann
1492 C.E.		Use of decimal point by Pellos	1492 C.E.		Columbus discovers the Americas
			1517 C.E.		Protestant Reformation
			1520 C.E.		Field of the Cloth of Gold
1527 C.E.		Apian publishes the Pascal triangle
			1534 C.E.		Act of Supremacy
1543 C.E.		Tartaglia publishes Moerbeke's translation of Archimedes
1544 C.E.		Stifel publishes Arithmetica integra
1545 C.E.		Cardan publishes Ars magna
			1553 C.E.		Servetus burned at Geneva
			1558 C.E.		Accession of Elizabeth I in England
1564 C.E.		Birth of Galileo	1564 C.E.		Birth of Shakespeare and death of Michelangelo
1572 C.E.		Bombelli's Algebra	1572 C.E.		Saint Bartholomew's Day Massacre (French religious war)
1579 C.E.		Viète publishes Canon mathematicus
			1584 C.E.		Assassination of William of Orange
			1588 C.E.		Drake's defeat of the Spanish armada
1595 C.E.		Pitiscus publishes Trigonometria
			1598 C.E.		Edict of Nantes
			1603 C.E.		Death of Elizabeth I
1609 C.E.		Kepler's Astronomia nova : Galileo's telescope
1614 C.E.		Napier's logarithms
			1616 C.E.		Deaths of Shakespeare and Cervantes
1620 C.E.		Bürgi's logarithms	1620 C.E.		Landing of Pilgrims in America
			1626 C.E.		Death of Francis Bacon
			1628 C.E.		Harvey's De motu cordis et sanguinis
1629 C.E.		Fermat's method of maxima and minima
			1636 C.E.		Harvard College founded
1637 C.E.		Descartes' Discours de la méthode
1639 C.E.		Desargues' Brouillon project
1640 C.E.		Pascal's Essay pour les coniques
1642 C.E.		Birth of Newton: Death of Galileo
			1643 C.E.		Assassination of Louis XIV
			1644 C.E.		Torricelli's Barometer
			1649 C.E.		Charles I beheaded
1655 C.E.		Wallis publishes Arithmetica infinitorium
1658 C.E.		Huygens' cyclodial pendulum clock
			1660 C.E.		The Restoration
1662 C.E.		Royal Society founded
1666 C.E.		Académie des Sciences founded
1667 C.E.		Gregory's Geometriae pars universalis
1668 C.E.		Mercator publishes Logarithmotechnia
1670 C.E.		Barrow's Lectiones geometriae
1678 C.E.		Ceva's Theorem
			1679 C.E.		Writ of Habeas Corpus
			1683 C.E.		Siege of Vienna
1684 C.E.		Leibniz' first paper on the calculus
			1685 C.E.		Revocation of the Edict of Nantes
1687 C.E.		Newton's Principia
			1689 C.E.		The Glorious Revolution
1690 C.E.		Rolle's Trait d`algèbre
1696 C.E.		The Bernoulli's Brachistochrone and L'Hospital's Rule
			1702 C.E.		The start of Queen Anne's War
1706 C.E.		The use of the symbol π by William Jones
1715 C.E.		Taylor's Methodus incrementorium
1718 C.E.		De Moive's Doctrine of Chances	1718 C.E.		Fahrenheit's thermometer
1730 C.E.		Stirling's formula
1733 C.E.		Saccheri's attempt to vindicate Euclid
1734 C.E.		Berkeley's The Analyst
			1740 C.E.		Accession of Frederick the Great
1742 C.E.		Maclaurin's Treatise of Fluxions	1742 C.E.		Centigrade thermometer
1748 C.E.		Euler's Introductio in analysin infinitorum : Agnesi's Istituzioni Analitiche
1750 C.E.		Cramer's Rule
			1752 C.E.		Franklin's kite experiment
			1767 C.E.		Watt's improved steam engine
1770 C.E.		Hyperbolic trigonometry
			1774 C.E.		Discovery of oxygen
			1776 C.E.		American Declaration of Independence
1777 C.E.		Buffon's needle problem
1781 C.E.		Discovery of Uranus by Herschel
1788 C.E.		Lagrange's Mécanique analytique
			1789 C.E.		French Revolution
1794 C.E.		Legendre's Elements de géométrie	1794 C.E.		Lavoisier (father of modern chemistry) guillotined
			1795 C.E.		École Polytechnique and École Normale established
1796 C.E.		Laplace's Systeme du monde (nebular hypothesis )	1796 C.E.		Vaccination
1797 C.E.		Lagrange's Fonctions analytique
			1799 C.E.		Metric system introduced
			1800 C.E.		Volta's battery
1801 C.E.		Gauss' Disquisitiones arthmeticae : Ceres discovered
			1803 C.E.		Dalton's atomic theory
			1804 C.E.		Napoleon crowned emperor
1810 C.E.		Gergonne started the journal Annales
			1815 C.E.		Battle of Waterloo
			1820 C.E.		Oersted discovered electromagnetism
1822 C.E.		Fourier series
1826 C.E.		Crelle's Journal founded: Principle of Duality: Elliptic functions	1826 C.E.		Ampere's work in electrodynamics
1827 C.E.		Cauchy's Calculus of Residues	1827 C.E.		Ohm's Law
1829 C.E.		Lobachevskian geometry: Death of Abel
			1831 C.E.		Faraday's electromagnetic induction
1832 C.E.		Death of Galois: Babbage's Analytical Engine
1836 C.E.		Liouville's Journal founded	1836 C.E.		Telegraph invented
1843 C.E.		Hamilton's quaternions
			1846 C.E.		Neptune discovered: Use of anesthesia
			1848 C.E.		Marx's Communist Manifesto
			1850 C.E.		Dickens' David Copperfield
1854 C.E.		Boole' Laws of Thought
			1858 C.E.		The Atlantic cable laid
			1859 C.E.		Darwin's Origin of Species
			1861 C.E.		Start of American Civil War
			1865 C.E.		Assassination of Abraham Lincoln
			1868 C.E.		Cro-Magnon caves discovered
			1869 C.E.		Suez Canal finished
1873 C.E.		Hermite proved e transcendental
1874 C.E.		Cantor's Mengenlehre
			1876 C.E.		Alexander Bell's telephone
1882 C.E.		Lindemann proved  π   transcendental
1888 C.E.		American Mathematical Society founded	1888 C.E.		Pasteur Institute founded
1889 C.E.		Peano's postulates
			1895 C.E.		Roentgen discovered X-rays
1896 C.E.		Prime Number Theorem proved	1896 C.E.		Discovery of radioactivity
			1897 C.E.		Electrons discovered
			1898 C.E.		Radium dscovered
1899 C.E.		Hilbert'sGrundlagen der Geometrie
1900 C.E.		Hilbert's Problems : Russell and Whitehead's Principia, Vol.1	1900 C.E.		Freud's Die Traumdeutung
1901 C.E.		Planck's quantum theory	1901 C.E.		First radio receiver
1903 C.E.		Lebesgue integration	1903 C.E.		First powered air flight
1905 C.E.		Einsteins's special relativity
			1906 C.E.		Kellogg invents cornflakes
			1908 C.E.		Model T Ford
			1914 C.E.		Assassination of Austrian Archduke Francis Ferdinand
			1915 C.E.		Panama Canal opened
1916 C.E.		Einstein's general theory of relativity
1917 C.E.		Hardy and Ramanujan	1917 C.E.		Russian Revolution: The Balfour Declaration
			1919 C.E.		League of Nations
			1927 C.E.		Lindberg flew the Atlantic
			1928 C.E.		Fleming discovers penicillan
1931 C.E.		Gödel's Theorem
			1932 C.E.		Atom split
			1933 C.E.		Hitler became Chancellor
1936 C.E.		Ahlfors and Douglas awarded the first Fields Medals
1939 C.E.		Volume I of Bourbaki's Eléments
			1941 C.E.		Pearl Harbor
			1945 C.E.		Bombing of Hiroshima
			1946 C.E.		First meeting of the U.N.
			1950 C.E.		Korean War began
			1957 C.E.		Sputnik I launced
			1958 C.E.		Berlin airlift
1961 C.E.		Lorenz on chaotic behavior
1963 C.E.		Paul J. Cohen on the continuum hypothesis	1963 C.E.		Assassination of President Kennedy
			1965 C.E.		Death of Sir Winston Churchill
			1967 C.E.		Summer of Love
			1969 C.E.		Man walks on the moon
1970 C.E.		Matiyasevich shows Hilbert's tenth problem is unsolvable
			1974 C.E.		President Nixon resigns
			1975 C.E.		End of Vietnam War
1976 C.E.		Four Color conjecture verified by computer
1977 C.E.		Adelman, Rivest and Shamir introduce public-key codes	1977 C.E.		First Star Wars movie released
1982 C.E.		Mandelbrot's The fractal geometry of nature
			1984 C.E.		Ethiopian famine
			1989 C.E.		Fall of Berlin Wall
			1990 C.E.		Nelson Mandela released from prison
			1991 C.E.		Soviet Union disintegrates
1994 C.E.		Wiles proves Fermat's Last Theorem
2000 C.E.		Mathematical Challenges of the 21st Century announced