Branches of Mathematics

Pure mathematics

• Algebra
• Calculus
• Geometry
• Topology
• Trignometry
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• Logic
• Number theory

Applied mathematics

• Dynamical systems and differential equations
• Mathematical physics
• Computing
• Information theory and signal processing
• Probability and statistics
• Game theory
• Operations research

Related Topics

• Electromagnetic Spectrum
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• Computational Mathematics
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• Acceleration
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• Alexis Clairaut
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• Cornell University
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• Johannes Kepler
• Jordanus de Nemore
• Kepler's laws
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• Lagrangian mechanics
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• Leibniz
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• Quantum field theory
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• Second
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• Tycho Brahe
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• Vector (geometric)
• Vector analysis
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• Virtual work
• Wave interference
• Waves
• Wiktionary Composite
• Work (physics)
• Work-energy theorem
• 
  

• 
  Cornell University
  Cornell University ( /kɔrˈnɛl/ kor-NEL) is a private Ivy League research university located in Ithaca, New York, United States. It is a private land-grant university, receiving annual funding from the State of New York for certain educational missions. Founded in 1865 by Ezra Cornell and Andrew Dickson White, the university was intended to teach and make contributions in all fields of knowledge—from the classics to the sciences, and from the theoretical to the applied. These ideals, unconventional for the time, are captured in Cornell's motto, a popular 1865 Ezra Cornell quotation: "I would found an institution where any person can find instruction in any study."
  The university is broadly organized into seven undergraduate colleges and seven graduate divisions at its main Ithaca campus, with each college and division defining its own admission standards and academic programs in near autonomy. The university also administers two satellite medical campuses, one in New York City and one in Education City, Qatar. Cornell is one of two private land grant universities, and its seven undergraduate colleges include three private, state-supported statutory or contract colleges. As a land grant college, it also operates a cooperative extension outreach program in every county of New York.
  
  wn.com/Cornell_University

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  Alexis Clairaut
  Alexis Claude de Clairaut (or Clairault) (3 May 1713 – 17 May 1765) was a prominent French mathematician, astronomer, geophysicist, and intellectual.
  Clairaut was born in Paris, France, where his father taught mathematics. He was a prodigy — at the age of twelve he wrote a memoir on four geometrical curves and under his father's tutelage he made such rapid progress in the subject that in his thirteenth year he read before the Académie française an account of the properties of four curves which he had discovered. When only sixteen he finished a treatise on tortuous curves, Recherches sur les courbes a double courbure, which, on its publication in 1731, procured his admission into the French Academy of Sciences, although he was below the legal age as he was only eighteen.
  In 1736, together with Pierre Louis Maupertuis, he took part in the expedition to Lapland, which was undertaken for the purpose of estimating a degree of the meridian arc. After his return he published his treatise Théorie de la figure de la terre (1743). In this work he promulgated the theorem, known as Clairaut's theorem, which connects the gravity at points on the surface of a rotating ellipsoid with the compression and the centrifugal force at the equator. This hydrostatic model of the shape of the Earth was founded on a paper by Colin Maclaurin, which had shown that a mass of homogeneous fluid set in rotation about a line through its centre of mass would, under the mutual attraction of its particles, take the form of an ellipsoid. Under the assumption that the Earth was composed of concentric ellipsoidal shells of uniform density, Clairaut's theorem could be applied to it, and allowed the ellipticity of the Earth to be calculated from surface measurements of gravity. In 1849 Stokes showed that Clairaut's result was true whatever the interior constitution or density of the Earth, provided the surface was a spheroid of equilibrium of small ellipticity.
  
  wn.com/Alexis_Clairaut
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  Aristotle
  Aristotle (Ancient Greek: Ἀριστοτέλης, Aristotélēs) (384 BC – 322 BC) was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology. Together with Plato and Socrates (Plato's teacher), Aristotle is one of the most important founding figures in Western philosophy. Aristotle's writings were the first to create a comprehensive system of Western philosophy, encompassing morality, aesthetics, logic, science, politics, and metaphysics.
  Aristotle's views on the physical sciences profoundly shaped medieval scholarship, and their influence extended well into the Renaissance, although they were ultimately replaced by Newtonian physics. In the zoological sciences, some of his observations were confirmed to be accurate only in the 19th century. His works contain the earliest known formal study of logic, which was incorporated in the late 19th century into modern formal logic. In metaphysics, Aristotelianism had a profound influence on philosophical and theological thinking in the Islamic and Jewish traditions in the Middle Ages, and it continues to influence Christian theology, especially the scholastic tradition of the Catholic Church. His ethics, though always influential, gained renewed interest with the modern advent of virtue ethics. All aspects of Aristotle's philosophy continue to be the object of active academic study today. Though Aristotle wrote many elegant treatises and dialogues (Cicero described his literary style as "a river of gold"), it is thought that the majority of his writings are now lost and only about one-third of the original works have survived.
  
  wn.com/Aristotle
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  Christiaan Huygens
  Christiaan Huygens, FRS (/ˈhaɪɡənz/; [ˈɦœyɣə(n)s] ( listen); 14 April 1629 – 8 July 1695) was a prominent Dutch mathematician, astronomer, physicist and horologist. His work included early telescopic studies elucidating the nature of the rings of Saturn and the discovery of its moon Titan, the invention of the pendulum clock and other investigations in timekeeping, and studies of both optics and the centrifugal force.
  Huygens achieved note for his argument that light consists of waves, now known as the Huygens–Fresnel principle, which two centuries later became instrumental in the understanding of wave-particle duality. He generally receives credit for his discovery of the centrifugal force, the laws for collision of bodies, for his role in the development of modern calculus and his original observations on sound perception (see repetition pitch).
  Christiaan Huygens was born in April 1629 at The Hague, the second son of Constantijn Huygens, (1596–1687), a friend of mathematician, philosopher and minor physicistRené Descartes, and of Suzanna van Baerle (deceased 1637), whom Constantijn had married on 6 April 1627. Christiaan studied law and mathematics at the University of Leiden and the College of Orange in Breda. After a stint as a diplomat, Huygens turned to science.
  
  wn.com/Christiaan_Huygens
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  Clinton Davisson
  Clinton Joseph Davisson (October 22, 1881 – February 1, 1958), was an American physicist who won the 1937 Nobel Prize in Physics for his discovery of electron diffraction. Davisson shared the Nobel Prize with George Paget Thomson, who independently discovered electron diffraction at about the same time as Davisson.
  Davisson was born in Bloomington, Illinois. He graduated from Bloomington High School in 1902, and entered the University of Chicago on scholarship. Upon the recommendation of Robert A. Millikan, in 1905 Davisson was hired by Princeton University as Instructor of Physics. He completed the requirements for his B.S. degree from Chicago in 1908, mainly by working in the summers. While teaching at Princeton, he did doctoral thesis research with Owen Richardson. He received his Ph.D. in physics from Princeton in 1911; in the same year he married Richardson's sister, Charlotte.
  Davisson was then appointed as an assistant professor at the Carnegie Institute of Technology. In 1917 he took a leave from the Carnegie Institute to do war-related research with the Engineering Department of the Western Electric Company (later Bell Telephone Laboratories). At the end of the war, Davisson accepted a permanent position at Western Electric after receiving assurances of his freedom there to do basic research. He had found that his teaching responsibilities at the Carnegie Institute largely precluded him from doing research. Davisson remained at Western Electric (and Bell Telephone) until his formal retirement in 1946. He then accepted a research professor appointment at the University of Virginia that continued until his second retirement in 1954.
  
  wn.com/Clinton_Davisson
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  Galileo Galilei
  Galileo Galilei (Italian pronunciation: [ɡaliˈlɛːo ɡaliˈlɛi]; 15 February 1564 – 8 January 1642), was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations and support for Copernicanism. Galileo has been called the "father of modern observational astronomy", the "father of modern physics", the "father of science", and "the Father of Modern Science".
  His contributions to observational astronomy include the telescopic confirmation of the phases of Venus, the discovery of the four largest satellites of Jupiter (named the Galilean moons in his honour), and the observation and analysis of sunspots. Galileo also worked in applied science and technology, inventing an improved military compass and other instruments.
  Galileo's championing of heliocentrism was controversial within his lifetime, when most subscribed to either geocentrism or the Tychonic system. He met with opposition from astronomers, who doubted heliocentrism due to the absence of an observed stellar parallax. The matter was investigated by the Roman Inquisition in 1615, and they concluded that it could only be supported as a possibility, not as an established fact. Galileo later defended his views in Dialogue Concerning the Two Chief World Systems, which appeared to attack Pope Urban VIII and thus alienated him and the Jesuits, who had both supported Galileo up until this point. He was tried by the Inquisition, found "vehemently suspect of heresy", forced to recant, and spent the rest of his life under house arrest. It was while Galileo was under house arrest that he wrote one of his finest works, Two New Sciences. Here he summarized the work he had done some forty years earlier, on the two sciences now called kinematics and strength of materials.
  
  wn.com/Galileo_Galilei
• Herbert Goldstein
  Herbert Goldstein (June 26, 1922 – January 12, 2005) was an American physicist and the author of the standard graduate textbook Classical Mechanics.
  He received a B.S. from City College of New York in 1940 and a Ph.D. from Massachusetts Institute of Technology in 1943.
  From 1942 to 1946, Goldstein was a staff member of the wartime Radiation Laboratory at M.I.T., where he engaged in research on the theory of waveguides and magnetrons and on the characteristics of radar echoes. He was an instructor in the Physics Department at Harvard University from 1946 to 1949. In 1949–50 he was an AEC postdoctoral Fellow at M.I.T., and served as a Visiting Associate Professor of Physics at Brandeis University, 1952–53. From 1950, Goldstein was a Senior Physicist at Nuclear Development Corporation of America, where he directed theoretical research on the shielding of nuclear reactors and on neutron cross sections of interest for reactor design.
  He was a founding member and served as president of the Association of Orthodox Jewish Scientists. When he died he was a Professor Emeritus of nuclear science and engineering at Columbia University.
  
  wn.com/Herbert_Goldstein
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  Isaac Newton
  Sir Isaac Newton PRS MP (25 December 1642 – 20 March 1727 [NS: 4 January 1643 – 31 March 1727]) was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived." His monograph Philosophiæ Naturalis Principia Mathematica, published in 1687, lays the foundations for most of classical mechanics. In this work, Newton described universal gravitation and the three laws of motion, which dominated the scientific view of the physical universe for the next three centuries. Newton showed that the motions of objects on Earth and of celestial bodies are governed by the same set of natural laws, by demonstrating the consistency between Kepler's laws of planetary motion and his theory of gravitation, thus removing the last doubts about heliocentrism and advancing the Scientific Revolution.
  
  wn.com/Isaac_Newton
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  Jeremiah Horrocks
  Jeremiah Horrocks (1618 – 3 January 1641), sometimes given as Jeremiah Horrox (the Latinised version that he used on the Emmanuel College register and in his Latin manuscripts), was an English astronomer who was the only person to predict the transit of Venus of 1639, an event which he and his friend William Crabtree were the only two people to observe and record.
  Jeremiah Horrocks was born at Lower Lodge farm, in Toxteth Park, a former royal deer park, near Liverpool. His father, James, was a watchmaker who had moved to Toxteth Park to be apprenticed to Thomas Aspinwall and subsequently married his master's daughter, Mary. Both families were well educated Puritans; the Horrocks' sent their younger sons to the University of Cambridge and the Aspinwalls favoured Oxford. The unorthodox beliefs of the Puritans excluded them from public office and pushed them towards trade and industry and thus, by 1600 the Aspinwalls had become a successful family of watchmakers. As a boy, Jeremiah had an early introduction to astronomy as one of his chores was to measure the local noon in order to set the watches accurately, and his Puritan upbringing gave him an inbuilt suspicion of witchcraft, magic and astrology.
  
  wn.com/Jeremiah_Horrocks
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  Johannes Kepler
  Johannes Kepler (German pronunciation: [ˈkʰɛplɐ]; December 27, 1571 – November 15, 1630) was a German mathematician, astronomer and astrologer. A key figure in the 17th century scientific revolution, he is best known for his eponymous laws of planetary motion, codified by later astronomers, based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican Astronomy. These works also provided one of the foundations for Isaac Newton's theory of universal gravitation.
  During his career, Kepler was a mathematics teacher at a seminary school in Graz, Austria, where he became an associate of Prince Hans Ulrich von Eggenberg. Later he became an assistant to astronomer Tycho Brahe, and eventually the imperial mathematician to Emperor Rudolf II and his two successors Matthias and Ferdinand II. He was also a mathematics teacher in Linz, Austria, and an adviser to General Wallenstein. Additionally, he did fundamental work in the field of optics, invented an improved version of the refracting telescope (the Keplerian Telescope), and mentioned the telescopic discoveries of his contemporary Galileo Galilei.
  
  wn.com/Johannes_Kepler
• Jordanus de Nemore
  Jordanus de Nemore was a thirteenth-century European mathematician who wrote treatises on at least 6 different important mathematical subjects: the science of weights; “algorismi” treatises on practical arithmetic; pure arithmetic; algebra; geometry; and stereographic projection. Most of these treatises exist in several versions or reworkings from the Middle Ages. We know nothing about him personally, other than the approximate date of his work.
  No biographical details are known about Jordanus de Nemore. Cited in the early manuscripts simply as “Jordanus”, he was later given the sobriquet of “de Nemore” (“of the Forest,” “Forester”) which does not add any firm biographical information. In the Renaissance his name was often given as "Jordanus Nemorarius", an improper form. We know nothing of his nationality.
  An entry in the nineteenth-century manuscript catalogue for the Sächsische Landesbibliothek in Dresden suggested that Jordanus taught at the University of Toulouse, but the text in question was not written by Jordanus and this possible association is without foundation. A fourteenth-century chronicle of the Order of Preachers by the Englishman Nicholas Trivet (or Triveth, 1258–1328) suggested that the second master-general of the Dominican Order, Jordanus of Saxony (d. 1237) wrote two mathematical texts with titles similar to two by Jordanus de Nemore, but this late suggestion is more likely a confusion on the part of Trivet, rather than any proof of identity. Jordanus of Saxony never uses the name “de Nemore” and is nowhere else credited with mathematical writings – in fact he had lectured in theology at the University of Paris. Likewise the name of Jordanus of Saxony is never found with a mathematical text. This identity, popular among some in the nineteenth and twentieth centuries, has been for the most part abandoned.
  
  wn.com/Jordanus_de_Nemore
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  Leonhard Euler
  Leonhard Euler (German pronunciation: [ˈɔʏlɐ], ( Swiss German pronunciation (help·info)) ( Standard German pronunciation (help·info)) English approximation, "Oiler"; 15 April 1707 – 18 September 1783) was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function. He is also renowned for his work in mechanics, fluid dynamics, optics, and astronomy.
  Euler spent most of his adult life in St. Petersburg, Russia, and in Berlin, Prussia. He is considered to be the preeminent mathematician of the 18th century, and one of the greatest of all time. He is also one of the most prolific mathematicians ever; his collected works fill 60–80 quarto volumes. A statement attributed to Pierre-Simon Laplace expresses Euler's influence on mathematics: "Read Euler, read Euler, he is the master of us all."
  
  wn.com/Leonhard_Euler
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  Lester Germer
  Lester Halbert Germer (October 10, 1896 – October 3, 1971) was an American physicist. With Clinton Davisson, he proved the wave-particle duality of matter in the Davisson–Germer experiment, which was important to the development of the electron microscope. These studies supported the theoretical work of De Broglie. He also studied thermionics, erosion of metals, and contact physics. He was awarded the Elliott Cresson Medal in 1931.
  A former fighter pilot in World War I, Germer subsequently worked at Bell Labs in New Jersey.
  In 1945 (at the age of 49), Germer launched a side career as a rock climber. He climbed widely around the Northeast United States, and especially at New York's Shawangunk Ridge. Although the Appalachian Mountain Club was dominant in the area at the time, and strictly regulated rock climbing, Lester was never associated with the club, and found himself in conflict with the leading climber in the area Hans Kraus, who was head of the AMC's Safety Committee. He was once turned down for climbing certification with the comment "Likes people too much and is too enthusiastic." Lester was known for being generous and friendly. He was once called "A one man climbing school."
  
  wn.com/Lester_Germer
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  Siméon Denis Poisson
  Siméon Denis Poisson (French: [si.me.ɔ̃ də.ni pwa.sɔ̃]; 21 June 1781 – 25 April 1840), was a French mathematician, geometer, and physicist. He obtained many important results, but within the elite Académie des Sciences he also was the final leading opponent of the wave theory of light and was proven wrong on that matter by Augustin-Jean Fresnel.
  Poisson was born in Pithiviers, Loiret, the son of soldier Siméon Poisson.
  In 1798, he entered the École Polytechnique in Paris as first in his year, and immediately began to attract the notice of the professors of the school, who left him free to make his own decisions as to what he would study. In 1800, less than two years after his entry, he published two memoirs, one on Étienne Bézout's method of elimination, the other on the number of integrals of a finite difference equation. The latter was examined by Sylvestre-François Lacroix and Adrien-Marie Legendre, who recommended that it should be published in the Recueil des savants étrangers, an unprecedented honour for a youth of eighteen. This success at once procured entry for Poisson into scientific circles. Joseph Louis Lagrange, whose lectures on the theory of functions he attended at the École Polytechnique, recognized his talent early on, and became his friend (the Mathematics Genealogy Project lists Lagrange as his advisor, but this may be an approximation); while Pierre-Simon Laplace, in whose footsteps Poisson followed, regarded him almost as his son. The rest of his career, till his death in Sceaux near Paris, was nearly occupied by the composition and publication of his many works and in fulfilling the duties of the numerous educational positions to which he was successively appointed.
  
  wn.com/Siméon_Denis_Poisson
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  Tycho Brahe
  Tycho Brahe (14 December 1546 – 24 October 1601), born Tyge Ottesen Brahe, was a Danish nobleman known for his accurate and comprehensive astronomical and planetary observations. Coming from Scania, then part of Denmark, now part of modern-day Sweden, Tycho was well known in his lifetime as an astronomer and alchemist.
  In his De nova stella (On the new star) of 1573, he refuted the Aristotelian belief in an unchanging celestial realm. His precise measurements indicated that "new stars" (novae or also now known as supernovae), in particular that of 1572, lacked the parallax expected in sub-lunar phenomena, and were therefore not "atmospheric" tail-less comets as previously believed, but occurred above the atmosphere and moon. Using similar measurements he showed that comets were also not atmospheric phenomena, as previously thought, and must pass through the supposed "immutable" celestial spheres.
  Tycho Brahe was granted an estate on the island of Hven and the funding to build the Uraniborg, an early research institute, where he built large astronomical instruments and took many careful measurements, and later Stjerneborg, underground, when he discovered that his instruments in the former were not sufficiently steady. Something of an autocrat on the island he nevertheless founded manufactories such as paper-making to provide material for printing his results. After disagreements with the new Danish king in 1597, he was invited by the Bohemian king and Holy Roman emperor Rudolph II to Prague, where he became the official imperial astronomer. He built the new observatory at Benátky nad Jizerou. Here, from 1600 until his death in 1601, he was assisted by Johannes Kepler. Kepler later used Tycho's astronomical results to develop his own theories of astronomy.
  
  wn.com/Tycho_Brahe