81. HISTORY OF MATHEMATICS HISTORY OF MATHEMATICS including Nature's abacus, Babylon and Egypt, Pythagoras, Euclid and Archimedes, Circumference of the earth, Algebra http://www.historyworld.net/wrldhis/PlainTextHistories.asp?historyid=aa50

82. Levi Summary Biographical article with links and bibliography, from the MacTutor History of Mathematics. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Levi.html

Levi ben Gerson Levi ben Gerson was a French scholar who wrote on trigonometry as well as astronomy and philosophy. Full MacTutor biography [Version for printing] List of References (60 books/articles) A Quotation Mathematicians born in the same country Show birthplace location Honours awarded to Levi ben Gerson (Click below for those honoured in this way) Lunar features Crater Rabbi Levi Previous (Chronologically) Next Main Index Previous (Alphabetically) Next Biographies index JOC/EFR © July 2009 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Levi.html

83. Hippias Summary Concise scholarly biography of this discoverer of the quadratrix, from the MacTutor History of Mathematics. http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Hippias.html

Hippias of Elis about 460 BC - about 400 BC Hippias was a contemporary of Socrates whose only contribution to mathematics seems to be the quadratrix - a curve he may have used for squaring the circle and trisecting angles. Full MacTutor biography [Version for printing] List of References (4 books/articles) Mathematicians born in the same country Show birthplace location Other Web sites Encyclopaedia Britannica Internet Encyclopedia of Philosophy Previous (Chronologically) Next Main Index Previous (Alphabetically) Next Biographies index JOC/EFR © January 1999 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Hippias.html

84. Hamilton Summary Biographical article, with bibliography and links, from the MacTutor History of Mathematics. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Hamilton.html

Sir William Rowan Hamilton Click the picture above to see five larger pictures In 1843 Hamilton discovered the quaternions, the first noncommutative algebra to be studied. He felt this would revolutionise mathematical physics and he spent the rest of his life working on quaternions. Full MacTutor biography [Version for printing] List of References (31 books/articles) Some Quotations Mathematicians born in the same country Show birthplace location Additional Material in MacTutor J L Synge and Hamilton W R Hamilton's Elements of Quaternions Honours awarded to William Rowan Hamilton (Click below for those honoured in this way) Royal Society Royal Medal Fellow of the Royal Society of Edinburgh Lunar features Crater Hamilton Popular biographies list Number 92 Other Web sites Encyclopaedia Britannica NNDB Hamilton 2005 pages David R Wilkins ... Maynooth University Ireland (The Hamilton walk) European Mathematical Society (Hamilton's papers) Mathematical Genealogy Project Previous (Chronologically) Next Main Index Previous (Alphabetically) Next Biographies index JOC/EFR © June 1998 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Hamilton.html

85. Reichenbach Summary Biography, bibliography, quotations and links. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Reichenbach.html

Hans Reichenbach Click the picture above to see a larger version Full MacTutor biography [Version for printing] List of References (7 books/articles) Some Quotations Mathematicians born in the same country Show birthplace location Other Web sites Encyclopaedia Britannica Internet Encyclopedia of Philosophy University of California Mathematical Genealogy Project ... Previous (Chronologically) Next Main Index Previous (Alphabetically) Next Biographies index JOC/EFR © November 2006 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Reichenbach.html

86. Ramus Summary Biography and bibliography, with links to related topics. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Ramus.html

Peter Ramus Click the picture above to see two larger pictures Peter Ramus was a French mathematician who wrote a whole series of textbooks on logic and rhetoric, grammar, mathematics, astronomy, and optics. Full MacTutor biography [Version for printing] List of References (7 books/articles) Mathematicians born in the same country Show birthplace location Other Web sites The Catholic Encyclopedia The Galileo Project Chris Dawson Mathematical Genealogy Project ... Previous (Chronologically) Next Main Index Previous (Alphabetically) Next Biographies index JOC/EFR © May 2000 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Ramus.html

87. Boyle Summary Biography from the MacTutor History of Mathematics Archive. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Boyle.html

88. Porphyry Summary A concise biography with references, and links to related thinkers. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Porphyry.html

Porphyry Malchus Click the picture above to see a larger version Porphyry Malchus wrote a commentary on Euclid's Elements and a Life of Pythagoras Full MacTutor biography [Version for printing] List of References (9 books/articles) Mathematicians born in the same country Other Web sites Encyclopaedia Britannica Previous (Chronologically) Next Main Index Previous (Alphabetically) Next Biographies index JOC/EFR © April 1999 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Porphyry.html

89. Pascal Summary An overview and selection of links. http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Pascal.html

90. Xenocrates Summary Biography, bibliography and list of related topics. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Xenocrates.html

Xenocrates of Chalcedon 396 BC - 314 BC Xenocrates was a student of Plato who went on to become head of the Academy. He was an early believer in the atomic theory and originated the classical distinction between mind, body and soul. Full MacTutor biography [Version for printing] List of References (5 books/articles) Mathematicians born in the same country Show birthplace location Other Web sites Encyclopaedia Britannica Stanford Encyclopedia of Philosophy Previous (Chronologically) Next Main Index Previous (Alphabetically) Next Biographies index JOC/EFR © April 1999 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Xenocrates.html

91. Larry Tesler S Bare Bones Page Content on Computing History, Computing Interests, Work History, Mathematics, Genealogy, Wildlife Protection. http://www.nomodes.com/

92. Isaac Newton (1642 - 1727) Detailed biography reproduced from a 1908 history of mathematics. http://www.maths.tcd.ie/pub/HistMath/People/Newton/RouseBall/RB_Newton.html

Sir Isaac Newton (1642 - 1727) From `A Short Account of the History of Mathematics' (4th edition, 1908) by W. W. Rouse Ball. The mathematicians considered in the last chapter commenced the creation of those processes which distinguish modern mathematics. The extraordinary abilities of Newton enabled him within a few years to perfect the more elementary of those processes, and to distinctly advance every branch of mathematical science then studied, as well as to create some new subjects. Newton was the contemporary and friend of Wallis, Huygens, and others of those mentioned in the last chapter, but though most of his mathematical work was done between the years 1665 and 1686, the bulk of it was not printed - at any rate in book-form - till some years later. I propose to discuss the works of Newton more fully than those of other mathematicians, partly because of the intrinsic importance of his discoveries, and partly because this book is mainly intended for English readers, and the development of mathematics in Great Britain was for a century entirely in the hands of the Newtonian school. Isaac Newton was born in Lincolnshire, near Grantham, on December 25, 1642, and died at Kensington, London, on March 20, 1727. He was educated at Trinity College, Cambridge, and lived there from 1661 till 1696, during which time he produced the bulk of his work in mathematics; in 1696 he was appointed to a valuable Government office, and moved to London, where he resided till his death.

93. Blaise Pascal (1623 - 1662) Detailed biography reproduced from a 1908 history of mathematics. http://www.maths.tcd.ie/pub/HistMath/People/Pascal/RouseBall/RB_Pascal.html

Blaise Pascal (1623 - 1662) From `A Short Account of the History of Mathematics' (4th edition, 1908) by W. W. Rouse Ball. Among the contemporaries of Descartes none displayed greater natural genius than Pascal, but his mathematical reputation rests more on what he might have done than on what he actually effected, as during a considerable part of his life he deemed it his duty to devote his whole time to religious exercises. Blaise Pascal Elements , a book which Pascal read with avidity and soon mastered. In 1650, when in the midst of these researches, Pascal suddenly abandoned his favourite pursuits to study religion, or, as he says in his , ``contemplate the greatness and the misery of man''; and about the same time he persuaded the younger of his two sisters to enter the Port Royal society. His famous Provincial Letters directed against the Jesuits, and his , were written towards the close of his life, and are the first example of that finished form which is characteristic of the best French literature. The only mathematical work that he produced after retiring to Port Royal was the essay on the cycloid in 1658. He was suffering from sleeplessness and toothache when the idea occurred to him, and to his surprise his teeth immediately ceased to ache. Regarding this as a divine intimation to proceed with the problem, he worked incessantly for eight days at it, and completed a tolerably full account of the geometry of the cycloid. I now proceed to consider his mathematical works in rather greater detail.

94. MacTutor History Of Mathematics An extensive and searchable archive covering famous people and concepts, as well as describing the development of mathematics in various cultures. http://www-groups.dcs.st-and.ac.uk/~history/

95. History Student-written history of mathematics includes short biographies of individuals responsible for a few of the most significant discoveries. http://library.thinkquest.org/4116/History/history.htm

Number problems like the Pythagorean triples (discovered by Pythagoras and the Pythagoreans, his students) were studied from 1700 BC. Linear equations were studied to solve problems, as well as quadratic equations. These led to a kind of numerical algebra. The Greeks studied similar figures, volume and area (geometry problems). Values were also determined for p The ancient Greeks discovered conic sections (circular shapes formed when cutting a cone at different angles). They also made many discoveries in astronomy and trigonometry. Major work in mathematics in Europe began in about the sixteenth century, with the mathematician Girolamo Cardan and some others, such as Tartaglia, Ferrari, and Pacioli. They reformed what people thought the universe and mathematics were like. During the seventeenth century, mathematicians made more and more progress towards calculus and added some algebraic methods to geometry. The development toward calculus continued with the great mathematicians Pierre de Fermat. Together, with Blaise Pascal, they began the mathematical theory of probability. However, calculus evolved in the seventeenth century. Newton, Sir Isaac, discovered the branch of mathematics called calculus. He called it fluxions, which meant changing. His new discoveries contained an interaction between physics, astronomy, and mathematics. His theories on light and gravitation took us to the eighteenth century.

96. Pythagoras Summary Detailed biography, including pictures, from the MacTutor History of Mathematics archive. http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Pythagoras.html

Pythagoras of Samos about 569 BC - about 475 BC Click the picture above to see eleven larger pictures Pythagoras was a Greek philosopher who made important developments in mathematics, astronomy, and the theory of music. The theorem now known as Pythagoras's theorem was known to the Babylonians 1000 years earlier but he may have been the first to prove it. Full MacTutor biography [Version for printing] List of References (27 books/articles) Some Quotations Mathematicians born in the same country Show birthplace location Honours awarded to Pythagoras (Click below for those honoured in this way) Lunar features Crater Pythagoras Popular biographies list Number 1 Other Web sites Encyclopaedia Britannica Astroseti (A Spanish translation of this biography) The Complete Pythagoras (Web edition Guthrie's book) NNDB Theosophy Online (Pythagoras and his School) G Don Allen Internet Encyclopedia of Philosophy Mathgym Australia Simon Fraser University ... Previous (Chronologically) Next Main Index Previous (Alphabetically) Next Biographies index JOC/EFR © January 1999 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Pythagoras.html

97. Descartes Summary Biography from the MacTutor History of Mathematics archive. http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Descartes.html

98. Rene Descartes (1596 - 1650) Excerpt from A Short Account of the History of Mathematics by W. W. Rouse Ball. http://www.maths.tcd.ie/pub/HistMath/People/Descartes/RouseBall/RB_Descartes.htm

From `A Short Account of the History of Mathematics' (4th edition, 1908) by W. W. Rouse Ball. We may consider Descartes as the first of the modern school of mathematics. was born near Tours on March 31, 1596, and died at Stockholm on February 11, 1650; thus he was a contemporary of Galileo and Desargues. His father, who, as the name implies, was of good family, was accustomed to spend half the year at Rennes when the local parliament, in which he held a commission as councillor, was in session, and the rest of the time on his family estate of Les Cartes He resigned his commission in the spring of 1621, and spent the next five years in travel, during most of which time he continued to study pure mathematics. In 1626 we find him settled at Paris, ``a little well-built figure, modestly clad in green taffety, and only wearing sword and feather in token of his quality as a gentleman.'' During the first two years there he interested himself in general society, and spent his leisure in the construction of optical instruments; but these pursuits were merely the relaxations of one who failed to find in philosophy that theory of the universe which he was convinced finally awaited him. In 1628 Cardinal de Berulle, the founder of the Oratorians, met Descartes, and was so much impressed by his conversation that he urged on him the duty of devoting his life to the examination of truth. Descartes agreed, and the better to secure himself from interruption moved to Holland, then at the height of his power. There for twenty years he lived, giving up all his time to philosophy and mathematics. Science, he says, may be compared to a tree; metaphysics is the root, physics is the trunk, and the three chief branches are mechanics, medicine, and morals, these forming the three applications of our knowledge, namely, to the external world, to the human body, and to the conduct of life.

99. Durer Summary Features a biography of the artist (1471-1528). http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Durer.html

Click the picture above to see seven larger pictures Full MacTutor biography [Version for printing] List of References (23 books/articles) Some Quotations Mathematicians born in the same country Show birthplace location (Click below for those honoured in this way) Planetary features on Mercury Popular biographies list Number 33 Other Web sites Encyclopaedia Britannica Astroseti (A Spanish translation of this biography) The Galileo Project The Catholic Encyclopedia Mark Harden's Artchive (More self portraits and other works) George W Hart Previous (Chronologically) Next Main Index Previous (Alphabetically) Next Biographies index JOC/EFR © December 1996 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Durer.html

100. Alberti Summary Portrait and brief biography from MacTutor History of Mathematics archive at the University of St Andrews, concentrating on his contribution to mathematics. http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Alberti.html

Leone Battista Alberti Click the picture above to see three larger pictures Leone Alberti was an Italian mathematician who wrote the first general treatise on the laws of perspective and also wrote a book on cryptography containing the first example of a frequency table. Full MacTutor biography [Version for printing] List of References (13 books/articles) A Quotation Mathematicians born in the same country Show birthplace location Other Web sites Encyclopaedia Britannica The Catholic Encyclopedia Previous (Chronologically) Next Main Index Previous (Alphabetically) Next Biographies index JOC/EFR © August 2006 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Alberti.html

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