Branches of Mathematics

Pure mathematics

• Algebra
• Calculus
• Geometry
• Topology
• Trignometry
• Combinatorics
• 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
• Linear Equations
• Applied Physics
• Nano Technology
• Engineering Sciences
• Mathematical Medicine
• Fluid dynamics
• Computational Mathematics
• Gamma Ray Optics
• Onfrared Optics
• Relative Velocity
• Iciam
• Intelligent Imaging Neuroscience
• Biomedical Engineering
• Neuroscience Research
• Quantum Cosmology
• Brain Research

• 0.999...
• 1 (number)
• 28 (number)
• 496 (number)
• 6 (number)
• 8128 (number)
• Abel–Ruffini theorem
• Abraham de Moivre
• Abraham Robinson
• Absolute value
• Abstract algebra
• Actual infinity
• Addition
• Algebraic number
• Algebraic numbers
• Algorithm
• Ancient Egyptians
• Ancient Greece
• Ancient Greeks
• Arabic numerals
• Aristotle
• Arithmetic
• Arithmetica
• Arithmetical number
• Associative
• Baker's dozen
• Base ten
• Bede
• Bernhard Riemann
• Bertrand Russell
• Bhāskara II
• Bijection
• Binary operation
• Blackboard bold
• Brahmagupta
• Byzantine Empire
• Cardinal number
• Cardinality
• Carl Friedrich Gauss
• Caspar Wessel
• Century
• Charles Hermite
• China
• Chinese language
• Chuquet
• Circa
• Circumference
• Coefficient
• Coefficients
• Comma (punctuation)
• Commutative
• Complex analysis
• Complex number
• Complex plane
• Computable number
• Computus
• Concrete number
• Continued fraction
• Continuum hypothesis
• Countable
• Countable set
• Counting
• Crelle
• Cubic equation
• Cut-the-Knot
• Cyclotomic fields
• David Eugene Smith
• De Moivre's formula
• Decimal
• Decimal fraction
• Decimal point
• Dedekind cut
• Descartes
• Determinant
• Diameter
• Dionysius Exiguus
• Diophantus
• Divisibility
• Division by zero
• Divisor
• Divisor function
• Dozen
• Druckenmüller
• Dual number
• Easter
• Eduard Heine
• Egypt
• Egyptian fraction
• Empty set
• Eratosthenes
• Eric W. Weisstein
• Ernst Kummer
• Euclid
• Euclid's Elements
• Euclidean algorithm
• Euler
• Euler's formula
• Europe
• Even number
• Exponent
• Exponentiation
• Factorization
• Felix Klein
• Fibonacci
• Field (mathematics)
• Field extension
• Figurate number
• Finance
• First-order logic
• Floating point
• Frustum
• Full stop
• Galileo
• Galois theory
• Gaussian integer
• Geometry
• Georg Cantor
• German language
• Gerolamo Cardano
• Glyph
• Goldbach conjecture
• Gottfried Leibniz
• Gotthold Eisenstein
• Great gross
• Greece
• Greek alphabet
• Greek mathematics
• Greek numerals
• Gresham College
• Gross (unit)
• Group theory
• Hebrew numerals
• Heron of Alexandria
• Hipparchus
• Hippasus
• History of infinity
• History of pi
• History of zero
• Hypercomplex number
• Hyperreal number
• Hyperreal numbers
• Hyphen
• Ideal number
• Imaginary number
• Imaginary part
• Imaginary unit
• India
• Indian mathematics
• Indian numerals
• Infinite
• Infinitesimal
• Infinity
• Integer
• Irrational number
• Isaac Newton
• ISBN
• Islamic world
• Jacques Hadamard
• Jain
• John Napier
• John Wallis
• Joseph Liouville
• Kahun Papyrus
• Karl Weierstrass
• Khmer numerals
• Kossak
• Kronecker
• Lambda calculus
• Least upper bound
• Leonhard Euler
• Liber Abaci
• List of numbers
• Logarithms
• Margin of error
• Mathematical object
• Mathematical symbol
• Mathematics
• MathWorld
• Maya calendar
• Maya numerals
• Measurement
• Mexico
• Millenium
• Minus sign
• Morris Kline
• Multiplication
• Mythical number
• Méray
• Natural number
• Negative number
• Niels Henrik Abel
• Nth root
• Number
• Number line
• Number sign
• Number system
• Number theory
• Numeral system
• Numerical cognition
• Numerical digit
• Numero sign
• Octonion
• OEIS A000396
• Olmec
• Omicron
• Ordered field
• Orders of magnitude
• Ordinal number
• P-adic number
• Paolo Ruffini
• Paper ream
• Patrick Suppes
• Paul Halmos
• Paul Tannery
• Peano Arithmetic
• Pentatopic number
• Perfect number
• Philosophy
• Physical constant
• Pi
• Place value
• Place-value system
• Polygonal number
• Polynomial
• Polynomials
• Polytope
• Positive integer
• Potential infinity
• Prehistoric times
• Prime number
• Prime number theorem
• Projective geometry
• Proper subset
• Ptolemy
• Pyramid
• Pythagoras
• Pythagoreanism
• Quadratic formula
• Quartic equation
• Quaternion
• Quintic equation
• Quotient
• Radix
• Rational number
• Real closed field
• Real number
• Real numbers
• Real part
• Rectangle
• Relation number
• Renaissance
• René Descartes
• Repeating decimal
• Richard Dedekind
• Riemann hypothesis
• Ring (mathematics)
• Ring of periods
• Roman numeral
• Roman numerals
• Roots of unity
• Rounding
• Salvatore Pincherle
• Sanskrit
• Sedenion
• Serial number
• Set (mathematics)
• Set theory
• Significant digits
• Square root of 2
• Square root of two
• Sthananga Sutra
• Subset
• Subtraction
• Successor ordinal
• Sulba Sutras
• Supernatural numbers
• Superreal number
• Surreal number
• Tally marks
• Telephone number
• Tetrahedral number
• Tobias Dantzig
• Total order
• Transfer principle
• Transfinite number
• Triangular number
• Trichotomy property
• Truncate
• Turing machines
• Two New Sciences
• Unary operation
• Uncountable
• Vacuum
• Yajur Veda
• Zeno of Elea
• Zeno's paradoxes
• Évariste Galois
• 
  

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  China
  China (ⁱ/ˈtʃaɪnə/; Chinese: 中国; pinyin: Zhōngguó; see also Names of China), officially the People's Republic of China (PRC), is the world's most-populous country, with a population of over 1.3 billion. Covering approximately 9.6 million square kilometres, the East Asian state is the world's second-largest country by land area, and the third- or fourth-largest in total area, depending on the definition of total area.
  The People's Republic of China is a single-party state governed by the Communist Party of China. It exercises jurisdiction over 22 provinces, five autonomous regions, four directly controlled municipalities (Beijing, Tianjin, Shanghai, and Chongqing), and two mostly self-governing special administrative regions (Hong Kong and Macau). Its capital city is Beijing. The PRC also claims Taiwan—which is controlled by the Republic of China (ROC), a separate political entity—as its 23rd province, a claim controversial due to the complex political status of Taiwan and the unresolved Chinese Civil War. The PRC government denies the legitimacy of the ROC.
  
  wn.com/China
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  Egypt
  Egypt ⁱ/ˈiːdʒɪpt/ (Arabic: مصر, Miṣr, Egyptian Arabic: [mɑsˤɾ] ; Coptic: Ⲭⲏⲙⲓ, Kīmi ; Sahidic Coptic: ⲕⲏⲙⲉ, Kēme), officially the Arab Republic of Egypt, Arabic:  جمهوريّة مصر العربيّة (help·info), is a country mainly in North Africa, with the Sinai Peninsula forming a land bridge in Southwest Asia. Egypt is thus a transcontinental country, and a major power in Africa, the Mediterranean Basin, the Middle East and the Muslim world. Covering an area of about 1,010,000 square kilometers (390,000 sq mi), Egypt is bordered by the Mediterranean Sea to the north, the Gaza Strip and Israel to the northeast, the Red Sea to the east, Sudan to the south and Libya to the west.
  Egypt is one of the most populous countries in Africa and the Middle East. The great majority of its over 81 million people live near the banks of the Nile River, in an area of about 40,000 square kilometers (15,000 sq mi), where the only arable land is found. The large areas of the Sahara Desert are sparsely inhabited. About half of Egypt's residents live in urban areas, with most spread across the densely populated centres of greater Cairo, Alexandria and other major cities in the Nile Delta.
  
  wn.com/Egypt
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  Greece
  Greece ⁱ/ˈɡriːs/ (Greek: Ελλάδα, Ellada, IPA: [eˈlaða] ( listen) historically in Katharevousa and Ancient Greek: Ἑλλάς, Hellas, IPA: [eˈlas] and [helːás] respectively), officially the Hellenic Republic (Ελληνική Δημοκρατία, Elliniki Dimokratia, IPA: [eliniˈci ðimokraˈtia]), is a country in Southern Europe, politically considered part of Western Europe.Athens is the capital and the largest city in the country (its urban area also including Piraeus). The population of the country is around 11 million.
  Greece has land borders with Albania, the Republic of Macedonia and Bulgaria to the north, and Turkey to the east. The Aegean Sea lies to the east of mainland Greece, the Ionian Sea to the west, and the Mediterranean Sea to the south. Greece has the 11th longest coastline in the world at 13,676 km (8,498 mi) in length, featuring a vast number of islands (approximately 1,400, of which 227 are inhabited), including Crete, the Dodecanese, the Cyclades, and the Ionian Islands among others. Eighty percent of Greece consists of mountains, of which Mount Olympus is the highest at 2,917 m (9,570 ft).
  
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  Gresham College
  Coordinates: 51°31′04″N 0°06′35″W / 51.5177°N 0.1098°W / 51.5177; -0.1098
  Gresham College is an institution of higher learning located at Barnard's Inn Hall off Holborn in central London, England. It was founded in 1597 under the will of Sir Thomas Gresham and today it hosts over 140 free public lectures every year within the City of London.
  Sir Thomas Gresham, founder of the Royal Exchange, left his estate jointly to the City of London Corporation and to the Mercers' Company, which today support the college through the Joint Grand Gresham Committee under the presidency of the Lord Mayor of London. Gresham's will provided for the setting up of the College—in Gresham's mansion in Bishopsgate, on the site now occupied by Tower 42, the former NatWest Tower—and endowed it with the rental income from shops sited around the Royal Exchange, which Gresham had established.
  The early success of the College led to the incorporation of the Royal Society in 1663, which pursued its activities at the College in Bishopsgate before moving to its own premises in Crane Court in 1710. The College remained in Gresham's mansion in Bishopsgate until 1768, and moved about London thereafter until the construction in 1842 of its own buildings in Gresham Street EC2. Gresham College did not become part of the University of London on the founding of the University in the 19th century, although a close association between the College and the University persisted for many years. Since 1991, the College has operated at Barnard’s Inn Hall, Holborn EC1.
  
  wn.com/Gresham_College
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  India
  India (ⁱ/ˈɪndiə/), officially the Republic of India (Bhārat Gaṇarājya), is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world. Bounded by the Indian Ocean on the south, the Arabian Sea on the south-west, and the Bay of Bengal on the south-east, it shares land borders with Pakistan to the west;China, Nepal, and Bhutan to the north-east; and Burma and Bangladesh to the east. In the Indian Ocean, India is in the vicinity of Sri Lanka and the Maldives; in addition, India's Andaman and Nicobar Islands share a maritime border with Thailand and Indonesia.
  Home to the ancient Indus Valley Civilisation and a region of historic trade routes and vast empires, the Indian subcontinent was identified with its commercial and cultural wealth for much of its long history. Four of the world's major religions—Hinduism, Buddhism, Jainism, and Sikhism—originated here, whereas Zoroastrianism, Christianity, and Islam arrived in the 1st millennium CE and also helped shape the region's diverse culture. Gradually annexed by and brought under the administration of the British East India Company from the early 18th century and administered directly by the United Kingdom from the mid-19th century, India became an independent nation in 1947 after a struggle for independence that was marked by non-violent resistance led by Mahatma Gandhi.
  
  wn.com/India
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  Mexico
  Mexico (ⁱ/ˈmɛksɨkoʊ/; Spanish: México, IPA: [ˈmexiko] ( listen)), officially the United Mexican States (Spanish:  Estados Unidos Mexicanos (help·info)), is a federal constitutional republic in North America. It is bordered on the north by the United States of America; on the south and west by the Pacific Ocean; on the southeast by Guatemala, Belize, and the Caribbean Sea; and on the east by the Gulf of Mexico. Covering almost two million square kilometres (over 760,000 sq mi), Mexico is the fifth largest country in the Americas by total area and the thirteenth largest independent nation in the world. With an estimated population of over 113 million, it is the eleventh most populous country and the most populous Spanish-speaking country. Mexico is a federation comprising thirty-one states and a Federal District, the capital city.
  In Pre-Columbian Mexico many cultures matured into advanced civilizations such as the Olmec, the Toltec, the Teotihuacan, the Zapotec, the Maya and the Aztec before the first contact with Europeans. In 1521, Spain conquered and colonized the territory from its base in México-Tenochtitlan, which was administered as the Viceroyalty of New Spain. This territory would eventually become Mexico as the colony's independence was recognized in 1821. The post-independence period was characterized by economic instability, the Mexican-American War and territorial cession to the United States, a civil war, two empires and a domestic dictatorship. The latter led to the Mexican Revolution in 1910, which culminated with the promulgation of the 1917 Constitution and the emergence of the country's current political system. Elections held in July 2000 marked the first time that an opposition party won the presidency from the Institutional Revolutionary Party.
  
  wn.com/Mexico

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  Abraham de Moivre
  Abraham de Moivre (26 May 1667 in Vitry-le-François, Champagne, France – 27 November 1754 in London, England; French pronunciation: [abʁaam də mwavʁ]) was a French mathematician famous for de Moivre's formula, which links complex numbers and trigonometry, and for his work on the normal distribution and probability theory. He was a friend of Isaac Newton, Edmund Halley, and James Stirling. Among his fellow Huguenot exiles in England, he was a colleague of the editor and translator Pierre des Maizeaux.
  De Moivre wrote a book on probability theory, The Doctrine of Chances, said to have been prized by gamblers. De Moivre first discovered Binet's formula, the closed-form expression for Fibonacci numbers linking the nth power of φ to the nth Fibonacci number.
  Abraham de Moivre was born in Vitry in Champagne on May 26, 1667. His father, Daniel de Moivre, was a surgeon who, though middle class, believed in the value of education. Though Abraham de Moivre's parents were Protestant, he first attended Christian Brothers' Catholic school in Vitry, which was unusually tolerant given religious tensions in France at the time. When he was eleven, his parents sent him to the Protestant Academy at Sedan, where he spent four years studying Greek under Jacques du Rondel. The Protestant Academy of Sedan had been founded in 1579 at the initiative of Françoise de Bourbon, widow of Henri-Robert de la Marck; in 1682 the Protestant Academy at Sedan was suppressed and de Moivre enrolled to study logic at Saumur for two years. Although mathematics was not part of his course work, de Moivre read several mathematical works on his own including Elements de mathematiques by Father Prestet and a short treatise on games of chance, De Ratiociniis in Ludo Aleae, by Christiaan Huygens. In 1684 he moved to Paris to study physics and for the first time had formal mathematics training with private lessons from Jacques Ozanam.
  
  wn.com/Abraham_de_Moivre
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  Abraham Robinson
  Abraham Robinson (born Robinsohn; October 6, 1918 – April 11, 1974) was a mathematician who is most widely known for development of non-standard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were incorporated into mathematics.
  He was born to a Jewish family with strong Zionist beliefs, in Waldenburg, Germany, which is now Wałbrzych, in Poland. In 1933, he emigrated to British Mandate of Palestine, where he earned a first degree from the Hebrew University. Robinson was in France when the Nazis invaded during World War II, and escaped by train and on foot, being alternately questioned by French soldiers suspicious of his German passport and asked by them to share his map, which was more detailed than theirs. While in London, he joined the Free French Air Force and contributed to the war effort by teaching himself aerodynamics and becoming an expert on the airfoils used in the wings of fighter planes.
  After the war, Robinson worked in London, Toronto, and Jerusalem, but ended up at University of California, Los Angeles in 1962.
  
  wn.com/Abraham_Robinson
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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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  Bede
  Bede ( /ˈbiːd/ BEED; Old English: Bǣda or Bēda; 672/673 – 26 May 735), also referred to as Saint Bede or the Venerable Bede (Latin: Bēda Venerābilis), was an English monk at the Northumbrian monastery of Saint Peter at Monkwearmouth and of its companion monastery, Saint Paul's, in modern Jarrow (see Monkwearmouth-Jarrow), both in the Kingdom of Northumbria. Bede's monastery had access to a superb library which included works by Eusebius and Orosius among many others.
  He is well known as an author and scholar, and his most famous work, Historia ecclesiastica gentis Anglorum (The Ecclesiastical History of the English People) gained him the title "The Father of English History". In 1899, Bede was made a Doctor of the Church by Leo XIII, a position of theological significance; he is the only native of Great Britain to achieve this designation (Anselm of Canterbury, also a Doctor of the Church, was originally from Italy). Bede was moreover a skilled linguist and translator, and his work with the Latin and Greek writings of the early Church Fathers contributed significantly to English Christianity, making the writings much more accessible to his fellow Anglo-Saxons.
  
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  Bernhard Riemann
  Georg Friedrich Bernhard Riemann [ˈʁiːman] ( listen) (September 17, 1826 – July 20, 1866) was an influential German mathematician who made lasting contributions to analysis, number theory and differential geometry, some of them enabling the later development of general relativity.
  Riemann was born in Breselenz, a village near Dannenberg in the Kingdom of Hanover in what is the Federal Republic of Germany today. His father, Friedrich Bernhard Riemann, was a poor Lutheran pastor in Breselenz who fought in the Napoleonic Wars. His mother, Charlotte Ebell, died before her children had reached adulthood. Riemann was the second of six children, shy, and suffered from numerous nervous breakdowns. Riemann exhibited exceptional mathematical skills, such as fantastic calculation abilities, from an early age but suffered from timidity and a fear of speaking in public.
  During 1840, Riemann went to Hanover to live with his grandmother and attend lyceum (middle school). After the death of his grandmother in 1842, he attended high school at the Johanneum Lüneburg. In high school, Riemann studied the Bible intensively, but he was often distracted by mathematics. His teachers were amazed by his adept ability to solve complicated mathematical operations, in which he often outstripped his instructor's knowledge. In 1846, at the age of 19, he started studying philology and theology in order to become a priest and help with his family's finances.
  
  wn.com/Bernhard_Riemann
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  Bertrand Russell
  Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970) was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these in any profound sense. He was born in Monmouthshire, into one of the most prominent aristocratic families in Britain.
  Russell led the British "revolt against idealism" in the early 20th century. He is considered one of the founders of analytic philosophy along with his predecessor Gottlob Frege and his friend Ludwig Wittgenstein, and is widely held to be one of the 20th century's premier logicians. He co-authored, with A. N. Whitehead, Principia Mathematica, an attempt to ground mathematics on logic. His philosophical essay "On Denoting" has been considered a "paradigm of philosophy." His work has had a considerable influence on logic, mathematics, set theory, linguistics, computer science (see type theory and type system), and philosophy, especially philosophy of language, epistemology, and metaphysics.
  
  wn.com/Bertrand_Russell
• Bhāskara II
  Bhāskara ( (1114–1185), also known as Bhāskara II and Bhāskarāchārya ("Bhāskara the teacher")), was an Indian mathematician and astronomer. He was born near Vijjadavida (Bijāpur in modern Karnataka). Bhāskara is alleged to have been the head of an astronomical observatory at Ujjain, the leading mathematical center of ancient India. He lived in the Sahyadri region.
  Bhāskara and his works represent a significant contribution to mathematical and astronomical knowledge in the 12th century. He has been called the greatest mathematician of medieval India. His main work Siddhānta Shiromani, (Sanskrit for "Crown of treatises,") is divided into four parts called Lilāvati, Bijaganita, Grahaganita and Golādhyāya. These four sections deal with arithmetic, algebra, mathematics of the planets, and spheres respectively. He also wrote another treatise named Karan Kautoohal.
  Bhāskara's work on calculus predates Newton and Leibniz by half a millennium. He is particularly known in the discovery of the principles of differential calculus and its application to astronomical problems and computations. While Newton and Leibniz have been credited with differential and integral calculus, there is strong evidence to suggest that Bhāskara was a pioneer in some of the principles of differential calculus. He was perhaps the first to conceive the differential coefficient and differential calculus.
  
  wn.com/Bhāskara_II
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  Brahmagupta
  Brahmagupta (Sanskrit: ब्रह्मगुप्त;  listen (help·info)) (598–668 CE) was an Indian mathematician and astronomer who wrote many important works on mathematics and astronomy. His best known work is the Brāhmasphuṭasiddhānta (Correctly Established Doctrine of Brahma), written in 628 in Bhinmal. Its 25 chapters contain several unprecedented mathematical results.
  Brahmagupta is believed to have been born in 598 AD in Bhinmal city in the state of Rajasthan of Northwest India. In ancient times Bhillamala was the seat of power of the Gurjars. His father was Jisnugupta. He likely lived most of his life in Bhillamala (modern Bhinmal in Rajasthan) during the reign (and possibly under the patronage) of King Vyaghramukha. As a result, Brahmagupta is often referred to as Bhillamalacarya, that is, the teacher from Bhillamala. He was the head of the astronomical observatory at Ujjain, and during his tenure there wrote four texts on mathematics and astronomy: the Cadamekela in 624, the Brahmasphutasiddhanta in 628, the Khandakhadyaka in 665, and the Durkeamynarda in 672. The Brahmasphutasiddhanta (Corrected Treatise of Brahma) is arguably his most famous work. The historian al-Biruni (c. 1050) in his book Tariq al-Hind states that the Abbasid caliph al-Ma'mun had an embassy in India and from India a book was brought to Baghdad which was translated into Arabic as Sindhind. It is generally presumed that Sindhind is none other than Brahmagupta's Brahmasphuta-siddhanta.
  
  wn.com/Brahmagupta
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  Carl Friedrich Gauss
  Johann Carl Friedrich Gauss ( /ˈɡaʊs/; German: Gauß  listen (help·info), Latin: Carolus Fridericus Gauss) (30 April 1777 – 23 February 1855) was a German mathematician and physical scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.
  Sometimes referred to as the Princeps mathematicorum (Latin, "the Prince of Mathematicians" or "the foremost of mathematicians") and "greatest mathematician since antiquity", Gauss had a remarkable influence in many fields of mathematics and science and is ranked as one of history's most influential mathematicians. He referred to mathematics as "the queen of sciences".
  Carl Friedrich Gauss was born on 30 April 1777 in Braunschweig, in the duchy of Braunschweig-Wolfenbüttel, now part of Lower Saxony, Germany, as the son of poor working-class parents. Indeed, his mother was illiterate and never recorded the date of his birth, remembering only that he had been born on a Wednesday, eight days before the Feast of the Ascension, which itself occurs 40 days after Easter. Gauss would later solve this puzzle for his birthdate in the context of finding the date of Easter, deriving methods to compute the date in both past and future years. He was christened and confirmed in a church near the school he attended as a child.
  
  wn.com/Carl_Friedrich_Gauss
• Caspar Wessel
  Caspar Wessel (June 8, 1745, Vestby – March 25, 1818, Copenhagen) was a Norwegian-Danish mathematician and cartographer. In 1799, Wessel was the first person to describe the geometrical interpretation of complex numbers as points in the complex plane. He was the younger brother of poet and playwright Johan Herman Wessel.
  Wessel was born in Jonsrud, Vestby, Akershus, Norway. In 1763, having completed secondary school, he went to Denmark for further studies. He attended the University of Copenhagen and acquired the degree of candidatus juris in 1778. From 1794, however, he was employed as a surveyor (from 1798 as Royal inspector of Surveying).
  It was the mathematical aspect of surveying that led him to exploring the geometrical significance of complex numbers. His fundamental paper, Om directionens analytiske betegning, was published in 1799 by the Royal Danish Academy of Sciences and Letters. Since it was in Danish, it passed almost unnoticed, and the same results were later independently rediscovered by Argand in 1806 and Gauss in 1831.
  
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  Charles Hermite
  Charles Hermite (French pronunciation: [ʃaʁl ɛʁˈmit]) (December 24, 1822 – January 14, 1901) was a French mathematician who did research on number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra.
  Hermite polynomials, Hermite interpolation, Hermite normal form, Hermitian operators, and cubic Hermite splines are named in his honor. One of his students was Henri Poincaré.
  He was the first to prove that e, the base of natural logarithms, is a transcendental number. His methods were later used by Ferdinand von Lindemann to prove that π is transcendental.
  In a letter to Thomas Stieltjes in 1893, Hermite famously remarked: "I turn with terror and horror from this lamentable scourge of continuous functions with no derivatives."
  Born at Dieuze, Moselle, 24 December 1822 he was the son of a salt mine engineer, Ferdinand Hermite. His mother was Madeleine Lallemand. The family moved to run a drapers business in Nancy in 1828 and his father also pursued ambitions as an artist. Charles was the sixth of his parents' seven children.
  
  wn.com/Charles_Hermite
• David Eugene Smith
  David Eugene Smith, Ph.D., LL.D. (January 21, 1860 in Cortland, New York – July 29, 1944 in New York) was an American mathematician, educator, and editor.
  
  
  David Eugene Smith is considered one of the founders of the field of mathematics education. Smith was born in Cortland, New York, to Abram P. Smith, attorney and surrogate judge, and Mary Elizabeth Bronson, who taught her young son Latin and Greek. He attended Syracuse University, graduating in 1881 (Ph. D., 1887; LL.D., 1905). He studied to be a lawyer concentrating in arts and humanities, but accepted an instructorship in mathematics at the Cortland Normal School in 1884. He became a professor at the Michigan State Normal College in 1891 (later Eastern Michigan University), the principal at the State Normal School in Brockport, New York (1898), and a professor of mathematics at Teachers College, Columbia University (1901) where he remained until his retirement in 1926.
  Smith became president of the Mathematical Association of America in 1920. He also wrote a large number of publications of various types. He was editor of the Bulletin of the American Mathematical Society; contributed to other mathematical journals; published a series of textbooks; translated Klein's Famous Problems of Geometry, Fink's History of Mathematics, and the Treviso Arithmetic. He edited Augustus De Morgan's Budget of Paradoxes (1915) and wrote many books on Mathematics which are listed below.
  
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  Dionysius Exiguus
  Dionysius Exiguus (Dennis the Small, Dennis the Little or Dennis the Short, meaning humble) (c. 470 – c. 544) was a 6th-century monk born in Scythia Minor, modern Dobruja shared by Romania and Bulgaria. He was a member of the Scythian monks community concentrated in Tomis, the major city of Scythia Minor. Dionysius is best known as the inventor of the Anno Domini (AD) era, which is used to number the years of both the Gregorian calendar and the (Christianized) Julian calendar.
  From about 500 he lived in Rome, where, as a learned member of the Roman Curia, he translated from Greek into Latin 401 ecclesiastical canons, including the apostolical canons and the decrees of the councils of Nicaea, Constantinople, Chalcedon and Sardis, and also a collection of the decretals of the popes from Siricius to Anastasius II. These collections had great authority in the West and still guide church administrations. Dionysius also wrote a treatise on elementary mathematics.
  The author of a continuation of Dionysius's Computus, writing in 616, described Dionysius as a "most learned abbot of the city of Rome", and the Venerable Bede accorded him the honorific abbas, which could be applied to any monk, especially a senior and respected monk, and does not necessarily imply that Dionysius ever headed a monastery; indeed, Dionysius's friend Cassiodorus stated in Institutiones that he was still only a monk late in life.
  
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  Diophantus
  Diophantus of Alexandria (Ancient Greek: Διόφαντος ὁ Ἀλεξανδρεύς. b. between A.D. 200 and 214, d. between 284 and 298 at age 84), sometimes called "the father of algebra", was an Alexandrian Greek mathematician and the author of a series of books called Arithmetica. These texts deal with solving algebraic equations, many of which are now lost. In studying Arithmetica, Pierre de Fermat concluded that a certain equation considered by Diophantus had no solutions, and noted without elaboration that he had found "a truly marvelous proof of this proposition," now referred to as Fermat's Last Theorem. This led to tremendous advances in number theory, and the study of Diophantine equations ("Diophantine geometry") and of Diophantine approximations remain important areas of mathematical research. Diophantus was the first Greek mathematician who recognized fractions as numbers; thus he allowed positive rational numbers for the coefficients and solutions. In modern use, Diophantine equations are usually algebraic equations with integer coefficients, for which integer solutions are sought. Diophantus also made advances in mathematical notation.
  
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  Eduard Heine
  Heinrich Eduard Heine (March 16, 1821, Berlin–October 21, 1881, Halle) was a German mathematician.
  Heine became known for results on special functions and in real analysis. In particular, he authored an important treatise on spherical harmonics and Legendre functions (Handbuch der Kugelfunctionen). He also investigated basic hypergeometric series. He introduced the Mehler–Heine formula.
  Heinrich Eduard Heine was born on 16 March 1821 in Berlin, as the eighth child of banker Karl Heine and his wife Henriette Märtens. Eduard was initially home schooled, then studied at the Friedrichswerdersche Gymnasium and Köllnische Gymnasium in Berlin. In 1838, after graduating from gymnasium, he enrolled at the University of Berlin, but transferred to the University of Göttingen to attended the mathematics lectures of Carl Friedrich Gauss and Moritz Stern. In 1840 Heine returned to Berlin, where he studied mathematics under Gustav Lejeune Dirichlet, while also attending classes of Jakob Steiner and Johann Franz Encke. In 1842 he was a awarded a Ph.D. by the University of Berlin for a thesis on differential equations submitted with Enno Dirksen and Martin Ohm as advisors. Heine dedicated the doctoral thesis to his professor Gustav Dirichlet. Next he went to the University of Königsberg to participate in the mathematical seminar of Carl Gustav Jacobi, while also following mathematical physics classes of Franz Ernst Neumann. In Königsberg Heine got in contact with fellow students Gustav Kirchhoff and Philipp Ludwig von Seidel.
  
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  Eratosthenes
  Eratosthenes of Cyrene (Ancient Greek: Ἐρατοσθένης, IPA: [eratostʰénɛːs]; English /ɛrəˈtɒsθəniːz/; c. 276 BC – c. 195 BC) was a Greek mathematician, geographer, poet, athlete, astronomer, and music theorist.
  He was the first person to use the word "geography" and invented the discipline of geography as we understand it. He invented a system of latitude and longitude.
  He was the first person to calculate the circumference of the earth by using a measuring system using stades, or the length of stadiums during that time period (with remarkable accuracy). He was the first to calculate the tilt of the Earth's axis (also with remarkable accuracy). He may also have accurately calculated the distance from the earth to the sun and invented the leap day. He also created the first map of the world incorporating parallels and meridians within his cartographic depictions based on the available geographical knowledge of the era. In addition, Eratosthenes was the founder of scientific chronology; he endeavored to fix the dates of the chief literary and political events from the conquest of Troy.
  
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• Ernst Kummer
  Ernst Eduard Kummer (29 January 1810 – 14 May 1893) was a German mathematician. Skilled in applied mathematics, Kummer trained German army officers in ballistics; afterwards, he taught for 10 years in a gymnasium, the German equivalent of high school, where he inspired the mathematical career of Leopold Kronecker.
  Kummer was born in Sorau, Brandenburg (then part of Prussia). Kummer was first married to Ottilie Mendelssohn, daughter of Nathan Mendelssohn and Henriette Itzig. Ottilie was a cousin of Felix Mendelssohn and his sister Rebecca Mendelssohn Bartholdy, the wife of the mathematician Peter Gustav Lejeune Dirichlet. His second wife, Bertha was a maternal cousin of Ottilie. Overall, he had 13 children. His daughter Marie married the mathematician Hermann Schwarz. Kummer retired from teaching and from mathematics in 1890 and died three years later in Berlin.
  Kummer made several contributions to mathematics in different areas; he codified some of the relations between different hypergeometric series, known as contiguity relations. The Kummer surface results from taking the quotient of a two-dimensional abelian variety by the cyclic group {1, −1} (an early orbifold: it has 16 singular points, and its geometry was intensively studied in the nineteenth century). See also Kummer's function, Kummer ring and Kummer sum.
  
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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.
  
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  Felix Klein
  Christian Felix Klein (25 April 1849 – 22 June 1925) was a German mathematician, known for his work in group theory, complex analysis, non-Euclidean geometry, and on the connections between geometry and group theory. His 1872 Erlangen Program, classifying geometries by their underlying symmetry groups, was a hugely influential synthesis of much of the mathematics of the day.
  Klein was born in Düsseldorf, to Prussian parents; his father was a Prussian government official's secretary stationed in the Rhine Province. He attended the Gymnasium in Düsseldorf, then studied mathematics and physics at the University of Bonn, 1865–1866, intending to become a physicist. At that time, Julius Plücker held Bonn's chair of mathematics and experimental physics, but by the time Klein became his assistant, in 1866, Plücker's interest was geometry. Klein received his doctorate, supervised by Plücker, from the University of Bonn in 1868.
  Plücker died in 1868, leaving his book on the foundations of line geometry incomplete. Klein was the obvious person to complete the second part of Plücker's Neue Geometrie des Raumes, and thus became acquainted with Alfred Clebsch, who had moved to Göttingen in 1868. Klein visited Clebsch the following year, along with visits to Berlin and Paris. In July 1870, at the outbreak of the Franco-Prussian War, he was in Paris and had to leave the country. For a short time, he served as a medical orderly in the Prussian army before being appointed lecturer at Göttingen in early 1871.
  
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  Fibonacci
  Leonardo Pisano Bigollo (c. 1170 – c. 1250) also known as Leonardo of Pisa, Leonardo Pisano, Leonardo Bonacci, Leonardo Fibonacci, or, most commonly, simply Fibonacci, was an Italian mathematician, considered by some "the most talented western mathematician of the Middle Ages."
  Fibonacci is best known to the modern world for the spreading of the Hindu–Arabic numeral system in Europe, primarily through the publication in 1202 of his Liber Abaci (Book of Calculation), and for a number sequence named the Fibonacci numbers after him, which he did not discover but used as an example in the Liber Abaci.
  Leonardo Fibonacci was born around 1170 to Guglielmo Bonacci, a wealthy Italian merchant. Guglielmo directed a trading post (by some accounts he was the consultant for Pisa) in Bugia, a port east of Algiers in the Almohad dynasty's sultanate in North Africa (now Bejaia, Algeria). As a young boy, Leonardo traveled with him to help; it was there he learned about the Hindu–Arabic numeral system.
  Recognizing that arithmetic with Hindu–Arabic numerals is simpler and more efficient than with Roman numerals, Fibonacci traveled throughout the Mediterranean world to study under the leading Arab mathematicians of the time. Leonardo returned from his travels around 1200. In 1202, at age 32, he published what he had learned in Liber Abaci (Book of Abacus or Book of Calculation), and thereby popularized Hindu–Arabic numerals in Europe.
  
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  Georg Cantor
  Georg Ferdinand Ludwig Philipp Cantor ( /ˈkæntɔr/ KAN-tor; German: [ɡeˈɔʁk ˈfɛʁdinant ˈluːtvɪç ˈfiːlɪp ˈkantɔʁ]; March 3 [O.S. February 19] 1845 – January 6, 1918) was a German mathematician, best known as the inventor of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are "more numerous" than the natural numbers. In fact, Cantor's method of proof of this theorem implies the existence of an "infinity of infinities". He defined the cardinal and ordinal numbers and their arithmetic. Cantor's work is of great philosophical interest, a fact of which he was well aware.
  
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  Gerolamo Cardano
  Gerolamo (or Girolamo, or Geronimo) Cardano (French Jérôme Cardan; Latin Hieronymus Cardanus) (24 September 1501 – 21 September 1576) was an Italian Renaissance mathematician, physician, astrologer and gambler. His gambling led him to formulate elementary rules in probability, making him one of the founders of the field.
  He was born in Pavia, Lombardy, the illegitimate child of Fazio Cardano, a mathematically gifted lawyer, who was a friend of Leonardo da Vinci. In his autobiography, Cardano claimed that his mother had attempted to abort him. Shortly before his birth, his mother had to move from Milan to Pavia to escape the Plague; her three other children died from the disease.
  In 1520, he entered the University of Pavia and later in Padua studied medicine. His eccentric and confrontational style did not earn him many friends and he had a difficult time finding work after his studies ended. In 1525, Cardano repeatedly applied to the College of Physicians in Milan, but was not admitted owing to his combative reputation and illegitimate birth.
  
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• Gotthold Eisenstein
  Ferdinand Gotthold Max Eisenstein (16 April 1823 – 11 October 1852) was a German mathematician. He specialized in number theory and analysis, and proved several results that eluded even Gauss. Like Galois and Abel before him, Eisenstein died before the age of 30. He was born and died in Berlin, Prussia.
  He was born into Jewish family. Gotthold Eisenstein's father was Johan Konstantin Eisenstein and his mother was Helene Pollack. Before Gotthold, who was their first child, was born they had converted from Judaism to become Protestants. From an early age, he demonstrated talent in mathematics, and also in music. As a young child he learned to play piano, and he continued to play and compose for the instrument throughout his life.
  He suffered various health problems throughout his life, including meningitis as an infant, a disease which took the lives of all five of his brothers and sisters. In 1837, at the age of 14, he enrolled at Friedrich Wilhelm Gymnasium, and soon thereafter at Friedrich Werder Gymnasium in Berlin. His teachers recognized his talents in mathematics, but by 15 years of age he had already learned all the material taught at the school, and he began to study differential calculus from the works of Euler and Lagrange.
  
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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.
  
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• Hippasus
  Hippasus (Ancient Greek: Ἵππασος, Híppasos; 5th century BC) of Metapontum in Magna Graecia, was a Pythagorean philosopher. Little is known about his life or his beliefs, but he is sometimes credited with the discovery of the existence of irrational numbers. The discovery of irrational numbers is said to have been shocking to the Pythagoreans, and Hippasus is supposed to have drowned at sea (apparently as a punishment from the gods). However, the few ancient sources which describe this story either do not mention Hippasus by name or alternatively tell us that Hippasus drowned because he revealed how to construct a dodecahedron inside a sphere. The discovery of irrationality is not specifically ascribed to Hippasus by any ancient writer. Some modern scholars though have suggested that he discovered the irrationality of √2, which it is believed was discovered around the time that he lived.
  Little is known about the life of Hippasus. He may have lived in the late 5th century BC, about a century after the time of Pythagoras. He probably came from Metapontum in Italy (Magna Graecia), although the nearby city of Croton is also mentioned as his birthplace.Iamblichus states that he was the founder of a sect of the Pythagoreans called the Mathematici (Greek: μαθηματικοί) in opposition to the Acusmatici (Greek: ἀκουσματικοί); but elsewhere he makes him the founder of the Acusmatici in opposition to the Mathematici.
  
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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.
  
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  Jacques Hadamard
  Jacques Salomon Hadamard FRS (8 December 1865 – 17 October 1963) was a French mathematician who made major contributions in number theory, complex function theory, differential geometry and partial differential equations.
  
  
  The son of a teacher, Amédée Hadamard, of Jewish descent, and Claire Marie Jeanne Picard, Hadamard was born in Versailles, France and attended the Lycée Charlemagne and Lycée Louis-le-Grand, where his father taught. In 1884 Hadamard entered the École Normale Supérieure, having been placed first in the entrance examinations both there and at the École Polytechnique. His teachers included Tannery, Hermite, Darboux, Appell, Goursat and Picard. He obtained his doctorate in 1892 and in the same year was awarded the Grand Prix des Sciences Mathématiques for his essay on the Riemann zeta function.
  In 1892 Hadamard married Louise-Anna Trénel, also of Jewish descent, with whom he had three sons and two daughters. The following year he took up a lectureship in the University of Bordeaux, where he proved his celebrated inequality on determinants, which led to the discovery of Hadamard matrices when equality holds. In 1896 he made two important contributions: he proved the prime number theorem, using complex function theory (also proved independently by Charles Jean de la Vallée-Poussin); and he was awarded the Bordin Prize of the French Academy of Sciences for his work on geodesics in the differential geometry of surfaces and dynamical systems. In the same year he was appointed Professor of Astronomy and Rational Mechanics in Bordeaux. His foundational work on geometry and symbolic dynamics continued in 1898 with the study of geodesics on surfaces of negative curvature. For his cumulative work, he was awarded the Prix Poncelet in 1898.
  
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  John Napier
  John Napier of Merchiston (1550 – 4 April 1617) – also signed as Neper, Nepair – named Marvellous Merchiston, was a Scottish landowner known as a mathematician, physicist, astronomer and astrologer. He was the 8th Laird of Merchistoun.
  John Napier is best known as the discoverer of logarithms. He was also the inventor of the so-called "Napier's bones". Napier also made common the use of the decimal point in arithmetic and mathematics.
  Napier's birthplace, the Merchiston Tower in Edinburgh, Scotland, is now part of the facilities of Edinburgh Napier University. After his death from the effects of gout, Napier's remains were buried in St Cuthbert's Church, Edinburgh.
  Napier's father was Sir Archibald Napier of Merchiston Castle, and his mother was Janet Bothwell, daughter of a member of the Estates of Parliament, and a sister of Adam Bothwell who became the Bishop of Orkney. Archibald Napier was 16 years old when John Napier was born.
  As was the common practice for members of the nobility at that time, John Napier did not enter schools until he was 13. He did not stay in school very long, however. It is believed that he dropped out of school in Scotland and perhaps travelled in mainland Europe to better continue his studies. Little is known about those years, where, when, or with whom he might have studied, although his uncle Adam Bothwell wrote a letter to John's father on 5 December 1560, saying "I pray you, sir, to send John to the schools either to France or Flanders, for he can learn no good at home", and it is believed that this advice was followed.
  
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  John Wallis
  John Wallis (23 November 1616 – 28 October 1703) was an English mathematician who is given partial credit for the development of infinitesimal calculus. Between 1643 and 1689 he served as chief cryptographer for Parliament and, later, the royal court. He is also credited with introducing the symbol Failed to parse (Missing texvc executable; please see math/README to configure.): {\infty}
  John Brehaut Wallis was born in Ashford, Kent, the third of five children of Reverend John Wallis and Joanna Chapman. He was initially educated at a local Ashford school, but moved to James Movat's school in Tenterden in 1625 following an outbreak of plague. Wallis was first exposed to mathematics in 1631, at Martin Holbeach's school in Felsted; he enjoyed maths, but his study was erratic, since: "mathematics, at that time with us, were scarce looked on as academical studies, but rather mechanical" (Scriba 1970).
  As it was intended that he should be a doctor, he was sent in 1632 to Emmanuel College, Cambridge. While there, he kept an act on the doctrine of the circulation of the blood; that was said to have been the first occasion in Europe on which this theory was publicly maintained in a disputation. His interests, however, centred on mathematics. He received his Bachelor of Arts degree in 1637, and a Master's in 1640, afterwards entering the priesthood. From 1643–49, he served as a non-voting scribe at the Westminster Assembly. Wallis was elected to a fellowship at Queens' College, Cambridge in 1644, which he however had to resign following his marriage.
  
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  Joseph Liouville
  Joseph Liouville (French pronunciation: [ʒɔzɛf ljuvil], English pronunciation: /ˈdʒoʊzəf ˌliuˈvɪl/; 24 March 1809 – 8 September 1882) was a French mathematician.
  Liouville graduated from the École Polytechnique in 1827. After some years as an assistant at various institutions including the Ecole Centrale Paris, he was appointed as professor at the École Polytechnique in 1838. He obtained a chair in mathematics at the Collège de France in 1850 and a chair in mechanics at the Faculté des Sciences in 1857.
  Besides his academic achievements, he was very talented in organisational matters. Liouville founded the Journal de Mathématiques Pures et Appliquées which retains its high reputation up to today, in order to promote other mathematicians' work. He was the first to read, and to recognize, the importance of the unpublished work of Évariste Galois which appeared in his journal in 1846. Liouville was also involved in politics for some time, and he became member of the Constituting Assembly in 1848. However, after his defeat in the legislative elections in 1849, he turned away from politics.
  
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  Karl Weierstrass
  Karl Theodor Wilhelm Weierstrass (German: Weierstraß; 31 October 1815 – 19 February 1897) was a German mathematician who is often cited as the "father of modern analysis".
  Weierstrass was born in Ostenfelde, part of Ennigerloh, Province of Westphalia.
  Weierstrass was the son of Wilhelm Weierstrass, a government official, and Theodora Vonderforst. His interest in mathematics began while he was a Gymnasium student at Theodorianum in Paderborn. He was sent to the University of Bonn upon graduation to prepare for a government position. Because his studies were to be in the fields of law, economics, and finance, he was immediately in conflict with his hopes to study mathematics. He resolved the conflict by paying little heed to his planned course of study, but continued private study in mathematics. The outcome was to leave the university without a degree. After that he studied mathematics at the University of Münster (which was even at this time very famous for mathematics) and his father was able to obtain a place for him in a teacher training school in Münster. Later he was certified as a teacher in that city. During this period of study, Weierstrass attended the lectures of Christoph Gudermann and became interested in elliptic functions. In 1843 he taught in Deutsch-Krone in Westprussia and since 1848 he taught at the Lyceum Hosianum in Braunsberg. Besides mathematics he also taught physics, botanics and gymnastics.
  
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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."
  
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• Morris Kline
  Morris Kline (May 1, 1908 – June 10, 1992) was a Professor of Mathematics, a writer on the history, philosophy, and teaching of mathematics, and also a popularizer of mathematical subjects.
  Kline grew up in Brooklyn and in Jamaica, Queens. After graduating from Boys High School in Brooklyn, he studied mathematics at New York University, earning a bachelor's degree in 1930, a master's degree in 1932, and a doctorate in 1936. He continued at NYU as an instructor until 1942.
  During World War II, Kline was posted to the Signal Corps (United States Army) stationed at Belmar, New Jersey. Designated a physicist, he worked in the engineering lab where RADAR was developed. After the war he continued investigating electromagnetism, and from 1946 to 1966 was director of the division for electromagnetic research at the Courant Institute of Mathematical Sciences.
  Kline resumed his mathematical teaching at NYU, becoming a full professor in 1952. He taught at New York University until 1975, and wrote many papers and more than a dozen books on various aspects of mathematics and particularly mathematics teaching. He repeatedly stressed the need to teach the applications and usefulness of mathematics rather than expecting students to enjoy it for its own sake. Similarly, he urged that mathematical research concentrate on solving problems posed in other fields rather than building structures of interest only to other mathematicians. One can get a sense of Kline's views on teaching from the following:
  
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  Niels Henrik Abel
  Niels Henrik Abel (5 August 1802 – 6 April 1829) was a Norwegian mathematician who proved the impossibility of solving the quintic equation by radicals. The Abel Prize is named for him.
  Niels Henrik Abel was born in Nedstrand, Norway, as second child to Søren Georg Abel and Anne Marie Simonsen. When he was born, the family was living at the rectory at Finnøy. Much suggests that Niels Henrik was born in the neighboring parish, as his parents were guests of the bailiff in Nedstrand in July / August of his year of birth.
  Niels Henrik Abel's father, Søren Georg Abel, had a degree in theology and philosophy and served as pastor at Finnøy. Søren's father, Niels's grandfather, Hans Mathias Abel, was also a pastor, at Gjerstad near Risør. Søren had spent his childhood at Gjerstad, and had also served as chaplain there; and after his father's death in 1804, Søren was appointed pastor at Gjerstad and the family moved there.
  Anne Marie Simonsen was from Risør; her father, Niels Henrik Saxild Simonsen, was a tradesman and merchant ship-owner, and said to be the richest person in Risør. Anne Marie had grown up with two stepmothers, in relative luxurious surroundings. At Gjerstad rectory, she enjoyed arranging balls and social gatherings. Much suggests she was early on an alcoholic and took little interest in the upbringing of the children. Niels Henrik and his brothers were given their schooling by their father, with handwritten books to read. Interestingly, an addition table in a book of mathematics reads: 1+0=0.
  
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  Olmec
  The Olmec were the first major civilization in Mexico. They lived in the tropical lowlands of south-central Mexico, in the modern-day states of Veracruz and Tabasco.
  The Olmec flourished during Mesoamerica's Formative period, dating roughly from as early as 1500 BCE to about 400 BCE. Pre-Olmec cultures had flourished in the area since about 2500 BCE, but by 1600-1500 BCE Early Olmec culture had emerged centered around the San Lorenzo Tenochtitlán site near the coast in southeast Veracruz. They were the first Mesoamerican civilization and laid many of the foundations for the civilizations that followed. Among other "firsts", the Olmec appeared to practice ritual bloodletting and played the Mesoamerican ballgame, hallmarks of nearly all subsequent Mesoamerican societies.
  The most familiar aspect of the Olmecs is their artwork, particularly the aptly named "colossal heads". The Olmec civilization was first defined through artifacts which collectors purchased on the pre-Columbian art market in the late 19th century and early 20th century. Olmec artworks are considered among ancient America's most striking.
  
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  Paolo Ruffini
  Paolo Ruffini (September 22, 1765 – May 10, 1822) was an Italian mathematician and philosopher.
  By 1788 he had earned university degrees in philosophy, medicine/surgery, and mathematics. Among his work was an incomplete proof (Abel–Ruffini theorem) that quintic (and higher-order) equations cannot be solved by radicals (1799), and Ruffini's rule which is a quick method for polynomial division. Ruffini also made contributions to group theory in addition to probability and quadrature of the circle.
  He practiced as both a professor of mathematics (University of Modena) and a doctor including scientific work on typhus.
  Ruffini’s 1799 work marked a major development for group theory. Ruffini developed Joseph Louis Lagrange's work on permutation theory, following 29 years after Lagrange’s "Réflexions sur la théorie algébrique des equations" (1770–1771) which was largely ignored until Ruffini who established strong connections between permutations and the solvability of algebraic equations. Ruffini was the first to controversially assert the unsolvability by radicals of algebraic equations higher than quartics. This angered many members of the community such as Malfatti (1731–1807). Work in this area was later carried on by those such as Gauss and Galois who succeeded in such a proof.
  
  wn.com/Paolo_Ruffini
• Patrick Suppes
  Patrick Colonel Suppes (born March 17, 1922) is an American philosopher who has made significant contributions to philosophy of science, the theory of measurement, the foundations of quantum mechanics, decision theory, psychology, and educational technology. He is currently the Lucie Stern Professor of Philosophy Emeritus at the Stanford University School of Education.
  Suppes was born on March 17, 1922, in Tulsa, Oklahoma. He grew up as an only child, later with a half brother George who was born in 1943 after Patrick had entered the army. His grandfather, C.E. Suppes, had moved to Oklahoma from Ohio. Suppes' father and grandfather were independent oil men. His mother died when he was a young boy. He was raised by his stepmother, who married his father before he was six years old. His parents did not have much formal education.
  Suppes began college at the University of Oklahoma in 1939, but transferred to the University of Chicago in his second year, citing boredom with intellectual life in Oklahoma as his primary motivation. In his third year, at the insistence of his family, Suppes attended the University of Tulsa, majoring in physics, before entering the Army Reserves in 1942. In 1943 he returned to the University of Chicago and graduated with a B.S. in meteorology, and was stationed shortly thereafter at the Solomon Islands to serve during World War II.
  
  wn.com/Patrick_Suppes
• 
  Paul Halmos
  Paul Richard Halmos (March 3, 1916 – October 2, 2006) was a Hungarian-born American mathematician who made fundamental advances in the areas of probability theory, statistics, operator theory, ergodic theory, and functional analysis (in particular, Hilbert spaces). He was also recognized as a great mathematical expositor.
  Halmos obtained his B.A. from the University of Illinois, majoring in philosophy and minoring in mathematics. He took only three years to obtain the degree, and was only 19 when he graduated. He then began a Ph.D. in philosophy, but after failing his masters' oral exams, shifted to mathematics, graduating in 1938. Joseph Doob supervised his dissertation, titled Invariants of Certain Stochastic Transformations: The Mathematical Theory of Gambling Systems. Shortly thereafter, Halmos left for the Institute for Advanced Study, lacking both job and grant money. Six months later, he was working under John von Neumann, which proved a decisive experience. While at the Institute, Halmos wrote his first book, Finite Dimensional Vector Spaces, which immediately established his reputation as a fine expositor of mathematics.
  
  wn.com/Paul_Halmos
• 
  Paul Tannery
  Paul Tannery (1843–1904) was a French mathematician and historian of mathematics. He was the older brother of mathematician Jules Tannery, to whose Notions Mathématiques he contributed an historical chapter. Though Tannery's career was in the tobacco industry, he devoted his evenings and his life to the study of mathematicians and mathematical development.
  Tannery was born on December 20, 1843, to a deeply Catholic family. He attended private school in Mantes, followed by the Lycées in Le Mans and Caen. He then entered the École Polytechnique, on whose entrance exam he excelled. His curriculum included mathematics, the sciences, and the classics, all of which would be represented in his future academic work. Tannery's life of public service began as he then entered the École d'Applications des Tabacs as an apprentice engineer.
  As an assistant engineer, Tannery spent two years in the state tobacco factory at Lille. In 1867, he moved to Paris; three years later, he served as an artillery captain in the Franco-Prussian War. Biographies of Tannery describe him as an ardent patriot and claim that he never fully accepted the humiliating Treaty of Frankfurt.
  
  wn.com/Paul_Tannery
• 
  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
• 
  Pythagoras
  Pythagoras of Samos (Ancient Greek: Πυθαγόρας ὁ Σάμιος [Πυθαγόρης in Ionian Greek] Pythagóras ho Sámios "Pythagoras the Samian", or simply Πυθαγόρας; b. about 570 – d. about 495 BC) was an Ionian Greek philosopher, mathematician, and founder of the religious movement called Pythagoreanism. Most of the information about Pythagoras was written down centuries after he lived, so very little reliable information is known about him. He was born on the island of Samos, and might have travelled widely in his youth, visiting Egypt and other places seeking knowledge. Around 530 BC, he moved to Croton, a Greek colony in southern Italy, and there set up a religious sect. His followers pursued the religious rites and practices developed by Pythagoras, and studied his philosophical theories. The society took an active role in the politics of Croton, but this eventually led to their downfall. The Pythagorean meeting-places were burned, and Pythagoras was forced to flee the city. He is said to have ended his days in Metapontum.
  
  wn.com/Pythagoras
• 
  René Descartes
  René Descartes (French pronunciation: [ʁəne dekaʁt]; Latinized form: Renatus Cartesius; adjectival form: "Cartesian"; 31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and writer who spent most of his adult life in the Dutch Republic. He has been dubbed the 'Father of Modern Philosophy', and much subsequent Western philosophy is a response to his writings, which are studied closely to this day. In particular, his Meditations on First Philosophy continues to be a standard text at most university philosophy departments. Descartes' influence in mathematics is equally apparent; the Cartesian coordinate system — allowing algebraic equations to be expressed as geometric shapes in a two-dimensional coordinate system — was named after him. He is credited as the father of analytical geometry, the bridge between algebra and geometry, crucial to the discovery of infinitesimal calculus and analysis. Descartes was also one of the key figures in the Scientific Revolution and has been described as an example of genius.
  
  wn.com/René_Descartes
• 
  Richard Dedekind
  Julius Wilhelm Richard Dedekind (October 6, 1831 – February 12, 1916) was a German mathematician who did important work in abstract algebra (particularly ring theory), algebraic number theory and the foundations of the real numbers.
  Dedekind's father was Julius Levin Ulrich Dedekind, an administrator at Collegium Carolinum in Braunschweig. Dedekind had three older siblings. As an adult, he never employed the names Julius Wilhelm. He was born, lived most of his life, and died in Braunschweig (often called "Brunswick" in English).
  He first attended the Collegium Carolinum in 1848 before moving to the University of Göttingen in 1850. There, Dedekind studied number theory under Moritz Stern. Gauss was still teaching, although mostly at an elementary level, and Dedekind became his last student. Dedekind received his doctorate in 1852, for a thesis titled Über die Theorie der Eulerschen Integrale ("On the Theory of Eulerian integrals^{[disambiguation needed ]}"). This thesis did not display the talent evident in Dedekind's subsequent publications.
  
  wn.com/Richard_Dedekind
• 
  Salvatore Pincherle
  Salvatore Pincherle (March 11, 1853 — July 10, 1936) was an Italian mathematician. He contributed significantly to (and arguably helped to found) the field of functional analysis, established the Italian Mathematical Union (Italian: "Unione Matematica Italiana"), and was president of the Third International Congress of Mathematicians. The Pincherle derivative is named after him.
  Pincherle was born into a Jewish family in Trieste (then part of the Austrian Littoral) and spent his childhood in Marseille, France. After completing his basic schooling in Marseille, he left in 1869 to study mathematics at the University of Pisa, where he was a student under both Enrico Betti and Ulisse Dini. After he graduated in 1874, he taught at a school in Pavia until he received a scholarship in 1877.
  After winning the scholarship and studying abroad at the University of Berlin, Pincherle met Karl Weierstrass. Pincherle contributed to Weierstrass' theory of analytic functions, and in 1880, influenced by Weierstrass, he wrote an expository paper in the Giornale di Matematiche, which proved to be a significant paper in the field of analysis. Throughout his life, Pincherle's work greatly reflected the influence that Weierstrass had on him. He later collaborated with Vito Volterra and explored Laplace transforms and other parts of functional analysis.
  
  wn.com/Salvatore_Pincherle
• Tobias Dantzig
  Tobias Dantzig (February 19, 1884 – August 9, 1956) was a Baltic German Russian American mathematician, the father of George Dantzig, and the author of Number: The Language of Science (A critical survey written for the cultured non-mathematician) (1930) and Aspects of Science (New York, Macmillan, 1937).
  Born in Latvia, Dantzig studied mathematics with Henri Poincaré in Paris. Tobias married a fellow Sorbonne University student, Anja Ourisson, and the couple emigrated to the United States in 1910. Working for a time as a lumberjack in Oregon, Dantzig received his Ph.D. in mathematics from Indiana University in 1917. He taught at Johns Hopkins, Columbia University, and the University of Maryland. Dantzig died in Los Angeles in 1956. He was the father of George Dantzig, a key figure in the development of linear programming.
  Memorable Quotation:
  "The harmony of the universe knows only one musical form - the legato; while the symphony of number knows only its opposite - the staccato. All attempts to reconcile this discrepancy are based on the hope that an accelerated staccato may appear to our senses as a legato."^{[citation needed]}
  
  wn.com/Tobias_Dantzig
• 
  Zeno of Elea
  Zeno of Elea ( /ˈziːnoʊ əv ˈɛliə/; Greek: Ζήνων ὁ Ἐλεάτης; ca. 490 BC – ca. 430 BC) was a pre-Socratic Greek philosopher of southern Italy and a member of the Eleatic School founded by Parmenides. Aristotle called him the inventor of the dialectic. He is best known for his paradoxes, which Bertrand Russell has described as "immeasurably subtle and profound".
  Little is known for certain about Zeno's life. Although written nearly a century after Zeno's death, the primary source of biographical information about Zeno is Plato's Parmenides dialogue. In the dialogue, Plato describes a visit to Athens by Zeno and Parmenides, at a time when Parmenides is "about 65," Zeno is "nearly 40" and Socrates is "a very young man". Assuming an age for Socrates of around 20, and taking the date of Socrates' birth as 469 BC gives an approximate date of birth for Zeno of 490 BC. Plato says that Zeno was "tall and fair to look upon" and was "in the days of his youth … reported to have been beloved by Parmenides".
  
  wn.com/Zeno_of_Elea
• 
  Évariste Galois
  Évariste Galois (French pronunciation: [evaʁist ɡalwa]) (25 October 1811 – 31 May 1832) was a French mathematician born in Bourg-la-Reine. While still in his teens, he was able to determine a necessary and sufficient condition for a polynomial to be solvable by radicals, thereby solving a long-standing problem. His work laid the foundations for Galois theory and group theory, two major branches of abstract algebra, and the subfield of Galois connections. He was the first to use the word "group" (French: groupe) as a technical term in mathematics to represent a group of permutations. A radical Republican during the monarchy of Louis Philippe in France, he died from wounds suffered in a duel under questionable circumstances at the age of twenty.
  Galois was born on 25 October 1811 to Nicolas-Gabriel Galois and Adélaïde-Marie (born Demante). His father was a Republican and was head of Bourg-la-Reine's liberal party. He became mayor of the village after Louis XVIII returned to the throne in 1814. His mother, the daughter of a jurist, was a fluent reader of Latin and classical literature and was responsible for her son's education for his first twelve years. At the age of 10, Galois was offered a place at the college of Reims, but his mother preferred to keep him at home.
  
  wn.com/Évariste_Galois

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