Branches of Mathematics

Pure mathematics

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• 
  

• 
  Clark University
  Clark University is a private research university and liberal arts college in Worcester, Massachusetts. Founded in 1887, it is the oldest educational institution founded as an all-graduate university. Clark now also educates undergraduates. It is one of only three New England universities, along with Harvard and Yale, to be a founding member of the Association of American Universities, an organization of universities with the most prestigious profiles in research and graduate education. Clark withdrew its membership in 1999, citing a conflict with its mission; it is one of only four schools to do so. Clark is one of 40 schools profiled in the book Colleges That Change Lives by Loren Pope.
  Clark University was founded by American businessman Jonas Gilman Clark in 1887. He started the university with a million dollars, and later added another million dollars to the university fund because he feared the university might someday face lack of funds. The university was opened on October 2, 1889 as the first all-graduate university in the United States.
  
  wn.com/Clark_University
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  Germany
  Germany (ⁱ/ˈdʒɜrməni/), officially the Federal Republic of Germany (German: Bundesrepublik Deutschland, pronounced [ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant] ( listen)), is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km² and has a largely temperate seasonal climate. With 81.8 million inhabitants, it is the most populous member state and the largest economy in the European Union. It is one of the major political powers of the European continent and a technological leader in many fields.
  A region named Germania, inhabited by several Germanic peoples, was documented before AD 100. During the Migration Period, the Germanic tribes expanded southward, and established successor kingdoms throughout much of Europe. Beginning in the 10th century, German territories formed a central part of the Holy Roman Empire. During the 16th century, northern German regions became the centre of the Protestant Reformation while southern and western parts remained dominated by Roman Catholic denominations, with the two factions clashing in the Thirty Years' War, marking the beginning of the Catholic–Protestant divide that has characterized German society ever since. Occupied during the Napoleonic Wars, the rise of Pan-Germanism inside the German Confederation resulted in the unification of most of the German states into the German Empire in 1871 which was Prussian dominated. After the German Revolution of 1918–1919 and the subsequent military surrender in World War I, the Empire was replaced by the Weimar Republic in 1918, and partitioned in the Treaty of Versailles. Amidst the Great Depression, the Third Reich was proclaimed in 1933. The latter period was marked by Fascism and World War II. After 1945, Germany was divided by allied occupation, and evolved into two states, East Germany and West Germany. In 1990 Germany was reunified.
  
  wn.com/Germany

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  Archimedes
  Archimedes of Syracuse (Ancient Greek: Ἀρχιμήδης; c. 287 BC – c. 212 BC) was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an explanation of the principle of the lever. He is credited with designing innovative machines, including siege engines and the screw pump that bears his name. Modern experiments have tested claims that Archimedes designed machines capable of lifting attacking ships out of the water and setting ships on fire using an array of mirrors.
  Archimedes is generally considered to be the greatest mathematician of antiquity and one of the greatest of all time. He used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave a remarkably accurate approximation of pi. He also defined the spiral bearing his name, formulae for the volumes of surfaces of revolution and an ingenious system for expressing very large numbers.
  
  wn.com/Archimedes
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  Aryabhata
  Aryabhata (IAST: Āryabhaṭa, Sanskrit: आर्यभट) (476–550 CE) was the first in the line of great mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy. His most famous works are the Āryabhaṭīya (499 CE, when he was 23 years old) and the Arya-siddhanta.
  While there is a tendency to misspell his name as "Aryabhatta" by analogy with other names having the "bhatta" suffix, his name is properly spelled Aryabhata: every astronomical text spells his name thus, including Brahmagupta's references to him "in more than a hundred places by name". Furthermore, in most instances "Aryabhatta" does not fit the metre either.
  Aryabhata mentions in the Aryabhatiya that it was composed 3,630 years into the Kali Yuga, when he was 23 years old. This corresponds to 499 CE, and implies that he was born in 476
  Aryabhata was born in Taregna (literally, song of the stars), which is a small town in Bihar, India, about 30 km (19 mi) from Patna (then known as Pataliputra), the capital city of Bihar State. Evidences justify his birth there. In Taregna Aryabhata set up an Astronomical Observatory in the Sun Temple 6th century.
  
  wn.com/Aryabhata
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  Brook Taylor
  Brook Taylor FRS (18 August 1685 – 29 December 1731) was an English mathematician who is best known for Taylor's theorem and the Taylor series.
  Brook Taylor was born in Edmonton (at that time in Middlesex) to John Taylor of Bifrons House, Kent, and Olivia Tempest, daughter of Sir Nicholas Tempest, Bart., of Durham.^{[citation needed]} Brook entered St John's College, Cambridge as a fellow-commoner in 1701, and took degrees of LL.B. and LL.D. in 1709 and 1714, respectively. Having studied mathematics under John Machin and John Keill, in 1708 he obtained a remarkable solution of the problem of the "centre of oscillation," which, however, remained unpublished until May 1714, when his claim to priority was disputed by Johann Bernoulli. Taylor's Methodus Incrementorum Directa et Inversa (1715) added a new branch to the higher mathematics, now designated the "calculus of finite differences." This work is available in translation on the web [1]. Among other ingenious applications, he used it to determine the form of movement of a vibrating string, by him first successfully reduced to mechanical principles. The same work contained the celebrated formula known as Taylor's theorem, the importance of which remained unrecognised until 1772, when J. L. Lagrange realized its powers and termed it "le principal fondement du calcul différentiel" ("the main foundation of differential calculus").
  
  wn.com/Brook_Taylor
• Carl Benjamin Boyer
  Carl Benjamin Boyer (November 3, 1906 – April 26, 1976) was a historian of sciences, and especially mathematics. David Foster Wallace called him the "Gibbon of math history". He wrote the books History of Analytic Geometry, The History of the Calculus and Its Conceptual Development, A History of Mathematics, and The Rainbow: From Myth to Mathematics. He served as book-review editor of Scripta Mathematica.
  Boyer was valedictorian of his high school class. He received an A.B. from Columbia College in 1928 and an M.A. in 1929. He received his Ph.D. in Mathematics from Columbia University in 1939.
  He was a full professor of Mathematics at Brooklyn College from 1952 until his death, although he had begun tutoring and teaching at Brooklyn College in 1928.
  Boyer was instrumental as an inspiration to the founding of The Metropolitan New York Section of the History of Science Society.
  He was a 1954 John Simon Guggenheim Memorial Foundation Fellow in History of Science & Technology.
  He died of a heart attack in New York in 1976.
  
  wn.com/Carl_Benjamin_Boyer
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  Colin Maclaurin
  Colin Maclaurin (February 1698 – 14 June 1746) was a Scottish mathematician who made important contributions to geometry and algebra. The Maclaurin series, a special case of the Taylor series, are named after him.
  Owing to changes in orthography since that time (his name was originally rendered as e.g. "M'Laurine"), his surname is alternatively written MacLaurin. In Gaelic the name is "Cailean MacLabhruinn", which is literally 'Colin, the son of Laurence.'
  Maclaurin was born in Kilmodan, Argyll. His father, Reverend and Minister of Glendaruel John Maclaurin, died when Maclaurin was in infancy, and his mother died before he reached nine years of age. He was then educated under the care of his uncle, the Reverend Daniel Maclaurin, minister of Kilfinnan.
  At eleven, Maclaurin entered the University of Glasgow. He graduated MA three years later by defending a thesis on the Power of Gravity, and remained at Glasgow to study divinity until he was 19, when he was elected professor of mathematics in a ten-day competition at the Marischal College in the University of Aberdeen. He would hold the record as the world's youngest professor until March 2008, when the record was officially given to Alia Sabur.
  
  wn.com/Colin_Maclaurin
• Eli Maor
  Eli Maor, an Israel-born historian of mathematics, is the author of several books about the history of mathematics. Eli Maor received his PhD at the Technion – Israel Institute of Technology. He teaches the history of mathematics at Loyola University Chicago. Maor was the editor of the article on trigonometry for the Encyclopædia Britannica.
  
  
  
  wn.com/Eli_Maor
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  Euclid
  Euclid ( /ˈjuːklɪd/ EWK-lid; Ancient Greek: Εὐκλείδης Eukleidēs), fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I (323–283 BC). His Elements is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century. In the Elements, Euclid deduced the principles of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory and rigor.
  "Euclid" is the anglicized version of the Greek name Εὐκλείδης, meaning "Good Glory".
  Little is known about Euclid's life, as there are only a handful of references to him. The date and place of Euclid's birth and the date and circumstances of his death are unknown, and only roughly estimated in proximity to contemporary figures mentioned in references. No likeness or description of Euclid's physical appearance made during his lifetime survived antiquity. Therefore, Euclid's depiction in works of art is the product of the artist's imagination.
  
  wn.com/Euclid
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  Gemma Frisius
  Gemma Frisius (born Jemme Reinerszoon) (December 9, 1508–May 25, 1555), was a physician, mathematician, cartographer, philosopher, and instrument maker. He created important globes, improved the mathematical instruments of his day and applied mathematics in new ways to surveying and navigation.
  Frisius was born in Dokkum, Friesland (present-day Netherlands) of poor parents, who died when he was young. He moved to Groningen and studied at the University in Leuven beginning in 1525. He received the degree of MD in 1536 and remained on the faculty of medicine in Leuven for the rest of his life. His oldest son, Cornelius Gemma, edited a posthumous volume of his work and continued to work with Ptolemaic astrological models.
  While still a student, Frisius set up a workshop to produce globes and mathematical instruments. He became noted for the quality and accuracy of his instruments, which were praised by Tycho Brahe, among others. In 1533, he described for the first time the method of triangulation still used today in surveying. Twenty years later, he was the first to describe how an accurate clock could be used to determine longitude. Jean-Baptiste Morin (1583–1656) did not believe that Frisius' method for calculating longitude would work, remarking, "I do not know if the Devil will succeed in making a longitude timekeeper but it is folly for man to try."
  
  wn.com/Gemma_Frisius
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  Hipparchus
  Hipparchus/hɪˈpɑːrkəs/, or more correctly Hipparchos (Greek: Ἵππαρχος, Hipparkhos; c. 190 BC – c. 120 BC), was a Greek astronomer, geographer, and mathematician of the Hellenistic period. He is considered the founder of trigonometry.
  Hipparchus was born in Nicaea (now Iznik, Turkey), and probably died on the island of Rhodes. He is known to have been a working astronomer at least from 162 to 127 BC. Hipparchus is considered the greatest ancient astronomical observer and, by some, the greatest overall astronomer of antiquity. He was the first whose quantitative and accurate models for the motion of the Sun and Moon survive. For this he certainly made use of the observations and perhaps the mathematical techniques accumulated over centuries by the Chaldeans from Babylonia. He developed trigonometry and constructed trigonometric tables, and he solved several problems of spherical trigonometry. With his solar and lunar theories and his trigonometry, he may have been the first to develop a reliable method to predict solar eclipses. His other reputed achievements include the discovery of Earth's precession, the compilation of the first comprehensive star catalog of the western world, and possibly the invention of the astrolabe, also of the armillary sphere, which he used during the creation of much of the star catalogue. It would be three centuries before Claudius Ptolemaeus' synthesis of astronomy would supersede the work of Hipparchus; it is heavily dependent on it in many areas.
  
  wn.com/Hipparchus
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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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  Nicolaus Copernicus
  Nicolaus Copernicus (German: Nikolaus Kopernikus; Italian: Nicolò Copernico; Polish:  Mikołaj Kopernik (help·info); in his youth, Niclas Koppernigk; 19 February 1473 – 24 May 1543) was a Renaissance astronomer and the first person to formulate a comprehensive heliocentric cosmology which displaced the Earth from the center of the universe.
  Copernicus' epochal book, De revolutionibus orbium coelestium (On the Revolutions of the Celestial Spheres), published just before his death in 1543, is often regarded as the starting point of modern astronomy and the defining epiphany that began the scientific revolution. His heliocentric model, with the Sun at the center of the universe, demonstrated that the observed motions of celestial objects can be explained without putting Earth at rest in the center of the universe. His work stimulated further scientific investigations, becoming a landmark in the history of science that is often referred to as the Copernican Revolution.
  Among the great polymaths of the Renaissance, Copernicus was a mathematician, astronomer, jurist with a doctorate in law, physician, quadrilingual polyglot, classics scholar, translator, artist,Catholic cleric, governor, diplomat and economist.
  
  wn.com/Nicolaus_Copernicus
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  Nubia
  Nubia is a region along the Nile river, which is located in northern Sudan and southern Egypt.
  There were a number of small Nubian kingdoms throughout the Middle Ages, the last of which collapsed in 1504, when Nubia became divided between Egypt and the Sennar sultanate resulting in the Arabization of much of the Nubian population. Nubia was again united within Ottoman Egypt in the 19th century, and within Anglo-Egyptian Sudan from 1899 to 1956.
  The name Nubia is derived from that of the Noba people, nomads who settled the area in the 4th century, with the collapse of the kingdom of Meroë. The Noba spoke a Nilo-Saharan language, ancestral to Old Nubian. Old Nubian was used in mostly religious texts dating from the 8th and 15th centuries AD. Before the 4th century, and throughout classical antiquity, Nubia was known as Kush, or, in Classical Greek usage, included under the name Ethiopia (Aithiopia).
  Historically, the people of Nubia spoke at least two varieties of the Nubian language group, a subfamily which includes Nobiin (the descendant of Old Nubian), Kenuzi-Dongola, Midob and several related varieties in the northern part of the Nuba Mountains in South Kordofan. A variety (Birgid) was spoken (at least until 1970) north of Nyala in Darfur but is now extinct.
  
  wn.com/Nubia
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  Ptolemy
  Claudius Ptolemy ( /ˈtɒləmi/; Greek: Κλαύδιος Πτολεμαῖος, Klaudios Ptolemaios; Latin: Claudius Ptolemaeus; c. AD 90 – c. AD 168), was a Greek-Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the Thebaid. This theory, proposed by Theodore Meliteniotes, could be correct, but it is late (ca. 1360) and unsupported. There is no reason to suppose that he ever lived anywhere else than Alexandria, where he died around AD 168.
  Ptolemy was the author of several scientific treatises, at least three of which were of continuing importance to later Islamic and European science. The first is the astronomical treatise now known as the Almagest (in Greek, Ἡ Μεγάλη Σύνταξις, "The Great Treatise", originally Μαθηματικὴ Σύνταξις, "Mathematical Treatise"). The second is the Geography, which is a thorough discussion of the geographic knowledge of the Greco-Roman world. The third is the astrological treatise known sometimes in Greek as the Apotelesmatika (Ἀποτελεσματικά), more commonly in Greek as the Tetrabiblos (Τετράβιβλος "Four books"), and in Latin as the Quadripartitum (or four books) in which he attempted to adapt horoscopic astrology to the Aristotelian natural philosophy of his day.
  
  wn.com/Ptolemy
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  Regiomontanus
  Johannes Müller von Königsberg (6 June 1436 – 6 July 1476), today best known by his Latin toponym Regiomontanus, was a German mathematician, astronomer, astrologer, translator, instrument maker and Catholic bishop.
  He was born in the Franconian village of Unfinden (now part of Königsberg, Bavaria) — not in the more famous East-Prussian Königsberg.
  He was also known as Johannes der Königsberger (Johannes of Königsberg). His writings were published under the toponym Joannes de Monte Regio. The name Regiomontanus was first coined by Phillip Melanchthon in 1534, fifty-eight years after his death.
  At eleven years of age, he became a student at the university in Leipzig, Saxony. In 1451 he continued his studies at Alma Mater Rudolfina, the university in Vienna, Austria. There he became a pupil and friend of Georg von Peurbach. In 1452 he graduated BA and was awarded his “magister artium” (Master of Arts) at the age of 21 in 1457 and held lectures in optics and ancient literature.
  He continued to work with Peuerbach learning and extending the then known areas of astronomy, mathematics and instrument making until Peuerbach's death in 1461.
  
  wn.com/Regiomontanus

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