Mathematician

# Mathematician

Overview

A mathematician is a person
Person
A person is a human being, or an entity that has certain capacities or attributes strongly associated with being human , for example in a particular moral or legal context...

whose primary area of study is the field of mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

. Mathematicians are concerned with quantity
Quantity
Quantity is a property that can exist as a magnitude or multitude. Quantities can be compared in terms of "more" or "less" or "equal", or by assigning a numerical value in terms of a unit of measurement. Quantity is among the basic classes of things along with quality, substance, change, and relation...

, structure
Structure
Structure is a fundamental, tangible or intangible notion referring to the recognition, observation, nature, and permanence of patterns and relationships of entities. This notion may itself be an object, such as a built structure, or an attribute, such as the structure of society...

, space
Space
Space is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum...

, and change
Calculus
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...

.

Some scientists who research other fields, such as theoretical physics, are also considered mathematicians if their research provides insights into mathematics. Conversely, some mathematicians may provide insights into other fields of research—these people are known as applied mathematicians
Applied mathematics
Applied mathematics is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge...

.

Mathematicians usually cover breadth of topics within mathematics in their undergraduate education, and then proceed to specialize in topics of their own choice at the graduate level.
Discussion

Recent Discussions
Encyclopedia

A mathematician is a person
Person
A person is a human being, or an entity that has certain capacities or attributes strongly associated with being human , for example in a particular moral or legal context...

whose primary area of study is the field of mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

. Mathematicians are concerned with quantity
Quantity
Quantity is a property that can exist as a magnitude or multitude. Quantities can be compared in terms of "more" or "less" or "equal", or by assigning a numerical value in terms of a unit of measurement. Quantity is among the basic classes of things along with quality, substance, change, and relation...

, structure
Structure
Structure is a fundamental, tangible or intangible notion referring to the recognition, observation, nature, and permanence of patterns and relationships of entities. This notion may itself be an object, such as a built structure, or an attribute, such as the structure of society...

, space
Space
Space is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum...

, and change
Calculus
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...

.

Some scientists who research other fields, such as theoretical physics, are also considered mathematicians if their research provides insights into mathematics. Conversely, some mathematicians may provide insights into other fields of research—these people are known as applied mathematicians
Applied mathematics
Applied mathematics is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge...

.

## Education

Mathematicians usually cover breadth of topics within mathematics in their undergraduate education, and then proceed to specialize in topics of their own choice at the graduate level. In some universities, a qualifying exam serves to test both the breadth and depth of a student's understanding of mathematics; the students who pass are permitted to work on a doctoral dissertation.
There are notable cases where mathematicians have failed to reflect their ability in their university education, but have nevertheless become remarkable mathematicians. Fermat, for example, is known for having been "Prince of Amateurs", because of his extraordinary achievements with little formal mathematics training.

## Motivation

Mathematicians do research in fields such as logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...

, set theory
Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...

, category theory
Category theory
Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows , where these collections satisfy certain basic conditions...

, abstract algebra
Abstract algebra
Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras...

, number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...

, analysis
Analysis
Analysis is the process of breaking a complex topic or substance into smaller parts to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle , though analysis as a formal concept is a relatively recent development.The word is...

, geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...

, dynamical systems, combinatorics
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...

, game theory
Game theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...

, information theory
Information theory
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...

, numerical analysis
Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....

, optimization
Optimization (mathematics)
In mathematics, computational science, or management science, mathematical optimization refers to the selection of a best element from some set of available alternatives....

, computation
Computation
Computation is defined as any type of calculation. Also defined as use of computer technology in Information processing.Computation is a process following a well-defined model understood and expressed in an algorithm, protocol, network topology, etc...

, probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

and statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

. These fields comprise both pure mathematics
Pure mathematics
Broadly speaking, pure mathematics is mathematics which studies entirely abstract concepts. From the eighteenth century onwards, this was a recognized category of mathematical activity, sometimes characterized as speculative mathematics, and at variance with the trend towards meeting the needs of...

and applied mathematics
Applied mathematics
Applied mathematics is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge...

and establish links between the two. Some fields, such as the theory of dynamical systems, or game theory, are classified as applied mathematics due to the relationships they possess with physics, economics and the other sciences. Whether probability theory and statistics are of theoretical nature, applied nature, or both, is quite controversial among mathematicians. Other branches of mathematics, however, such as logic, number theory, category theory or set theory are accepted to be a part of pure mathematics, although they do indeed find applications in other sciences (predominantly computer science
Computer science
Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...

and physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

). Likewise, analysis, geometry and topology, although considered pure mathematics, do find applications in theoretical physics - string theory
String theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...

, for instance.

Although it is true that mathematics finds diverse applications in many areas of research, a mathematician does not determine the value of an idea by the diversity of its applications. Mathematics is interesting in its own right, and a majority of mathematicians investigate the diversity of structures studied in mathematics itself. Furthermore, a mathematician is not someone who merely manipulates formulas, numbers or equations—the diversity of mathematics allows for research concerning how concepts in one area of mathematics can be used in other areas too. For instance, if one graphs a set of solutions of an equation in some higher dimensional space, he may ask about the geometric properties of the graph. Thus one can understand equations by a pure understanding of abstract topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...

or geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

—this idea is of importance in algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...

. Similarly, a mathematician does not restrict his study of numbers to the integer
Integer
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...

s; rather he considers more abstract structures such as rings
Ring (mathematics)
In mathematics, a ring is an algebraic structure consisting of a set together with two binary operations usually called addition and multiplication, where the set is an abelian group under addition and a semigroup under multiplication such that multiplication distributes over addition...

, and in particular number rings in the context of algebraic number theory
Algebraic number theory
Algebraic number theory is a major branch of number theory which studies algebraic structures related to algebraic integers. This is generally accomplished by considering a ring of algebraic integers O in an algebraic number field K/Q, and studying their algebraic properties such as factorization,...

. This exemplifies the abstract nature of mathematics and how it is not restricted to questions one may ask in daily life.

In a different direction, mathematicians ask questions about space and transformations, but which are not restricted to geometric figures such as squares and circles. For instance, an active area of research within the field of differential topology
Differential topology
In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. It is closely related to differential geometry and together they make up the geometric theory of differentiable manifolds.- Description :...

concerns itself with the ways in which one can "smooth" higher dimensional figures. In fact, whether one can smooth certain higher dimensional spheres remains open—it is known as the smooth Poincaré conjecture
Poincaré conjecture
In mathematics, the Poincaré conjecture is a theorem about the characterization of the three-dimensional sphere , which is the hypersphere that bounds the unit ball in four-dimensional space...

. Another aspect of mathematics, set-theoretic topology
Set-theoretic topology
In mathematics, set-theoretic topology is a subject that combines set theory and general topology. It focuses on topological questions that are independent of ZFC. A famous problem is the normal Moore space question, a question in general topology that was the subject of intense research. The...

and point-set topology, concerns objects of a different nature from objects in our universe, or in a higher dimensional analogue of our universe. These objects behave in a rather strange manner under deformations, and the properties they possess are completely different from those of objects in our universe. For instance, the "distance" between two points on such an object, may depend on the order in which you consider the pair of points. This is quite different from ordinary life, in which it is accepted that the straight line distance from person A to person B is the same as that between person B and person A.

Another aspect of mathematics, often referred to as "foundational mathematics", consists of the fields of logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...

and set theory
Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...

. Here, various ideas regarding the ways in which one can prove certain claims are explored. This theory is far more complex than it seems, in that the truth of a claim depends on the context in which the claim is made, unlike basic ideas in daily life where truth is absolute. In fact, although some claims may be true, it is impossible to prove or disprove them in rather natural contexts.

Category theory, another field within "foundational mathematics", is rooted on the abstract axiomatization of the definition of a "class of mathematical structures", referred to as a "category". A category intuitively consists of a collection of objects, and defined relationships between them. While these objects may be anything (such as "tables" or "chairs"), mathematicians are usually interested in particular, more abstract, classes of such objects. In any case, it is the relationships between these objects, and not the actual objects which are predominantly studied.

## Differences with scientists

Mathematics differs from natural science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...

s in that physical theories in the sciences are tested by experiments, while mathematical statements are supported by proofs that may be verified objectively. If a certain statement is believed to be true by mathematicians (typically because special cases have been confirmed to some degree) but has neither been proved nor disproved, it is called a conjecture
Conjecture
A conjecture is a proposition that is unproven but is thought to be true and has not been disproven. Karl Popper pioneered the use of the term "conjecture" in scientific philosophy. Conjecture is contrasted by hypothesis , which is a testable statement based on accepted grounds...

, as opposed to the ultimate goal: a theorem that has been proved. Physical theories may be expected to change whenever new information about our physical world is discovered. Mathematics changes in a different way: new ideas do not falsify old ones but rather are used to generalize what was known before to capture a broader range of phenomena. For instance, calculus
Calculus
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...

(in one variable) generalizes to multivariable calculus
Multivariable calculus
Multivariable calculus is the extension of calculus in one variable to calculus in more than one variable: the differentiated and integrated functions involve multiple variables, rather than just one....

, which generalizes to analysis on manifold
Manifold
In mathematics , a manifold is a topological space that on a small enough scale resembles the Euclidean space of a specific dimension, called the dimension of the manifold....

s. The development of algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...

from its classical to modern forms is a particularly striking example of the way an area of mathematics can change radically in its viewpoint without making what was proved before in any way incorrect. While a theorem, once proved, is true forever, our understanding of what the theorem really means gains in profundity as the mathematics around the theorem grows. A mathematician feels that a theorem is better understood when it can be extended to apply in a broader setting than previously known. For instance, Fermat's little theorem
Fermat's little theorem
Fermat's little theorem states that if p is a prime number, then for any integer a, a p − a will be evenly divisible by p...

for the nonzero integers modulo a prime generalizes to Euler's theorem for the invertible numbers modulo any nonzero integer, which generalizes to Lagrange's theorem for finite groups.

## Women in mathematics

While the majority of mathematicians are male, there have been some demographic changes since World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...

. Some prominent female mathematicians are Hypatia of Alexandria
Hypatia of Alexandria
Hypatia was an Egyptian Neoplatonist philosopher who was the first notable woman in mathematics. As head of the Platonist school at Alexandria, she also taught philosophy and astronomy...

Augusta Ada King, Countess of Lovelace , born Augusta Ada Byron, was an English writer chiefly known for her work on Charles Babbage's early mechanical general-purpose computer, the analytical engine...

(1815–1852), Maria Gaetana Agnesi
Maria Gaetana Agnesi
Maria Gaetana Agnesi was an Italian linguist, mathematician, and philosopher. Agnesi is credited with writing the first book discussing both differential and integral calculus. She was an honorary member of the faculty at the University of Bologna...

(1718–1799), Emmy Noether
Emmy Noether
Amalie Emmy Noether was an influential German mathematician known for her groundbreaking contributions to abstract algebra and theoretical physics. Described by David Hilbert, Albert Einstein and others as the most important woman in the history of mathematics, she revolutionized the theories of...

(1882–1935), Sophie Germain
Sophie Germain
Marie-Sophie Germain was a French mathematician, physicist, and philosopher. Despite initial opposition from her parents and difficulties presented by a gender-biased society, she gained education from books in her father's library and from correspondence with famous mathematicians such as...

(1776–1831), Sofia Kovalevskaya
Sofia Kovalevskaya
Sofia Vasilyevna Kovalevskaya , was the first major Russian female mathematician, responsible for important original contributions to analysis, differential equations and mechanics, and the first woman appointed to a full professorship in Northern Europe.She was also one of the first females to...

(1850–1891), Alicia Boole Stott
Alicia Boole Stott
Alicia Boole Stott was the third daughter of George Boole and Mary Everest Boole, born in Cork, Ireland. Before marrying Walter Stott, an actuary, in 1890, she was known as Alicia Boole...

(1860–1940), Rózsa Péter
Rózsa Péter
Rózsa Péter , Hungarian name Péter Rózsa, was a Hungarian mathematician. She is best known for her work with recursion theory....

(1905–1977), Julia Robinson
Julia Robinson
Julia Hall Bowman Robinson was an American mathematician best known for her work on decision problems and Hilbert's Tenth Problem.-Background and education:...

(1919–1985), Olga Taussky-Todd (1906–1995), Émilie du Châtelet
Émilie du Châtelet
-Early life:Du Châtelet was born on 17 December 1706 in Paris, the only daughter of six children. Three brothers lived to adulthood: René-Alexandre , Charles-Auguste , and Elisabeth-Théodore . Her eldest brother, René-Alexandre, died in 1720, and the next brother, Charles-Auguste, died in 1731...

(1706–1749), Mary Cartwright
Mary Cartwright
Dame Mary Lucy Cartwright DBE FRS was a leading 20th-century British mathematician. She was born in Aynho, Northamptonshire where her father was the vicar and died in Cambridge, England...

Olga Aleksandrovna Ladyzhenskaya was a Soviet and Russian mathematician. She was known for her work on partial differential equations and fluid dynamics...

(1922–2004).

The Association for Women in Mathematics
Association for Women in Mathematics
The Association for Women in Mathematics is a professional society whose mission is to encourage women and girls to study and to have active careers in the mathematical sciences. Equal opportunity and the equal treatment of women and girls in the mathematical sciences are promoted. The AWM was...

is a professional society whose purpose is "to encourage women and girls to study and to have active careers in the mathematical sciences, and to promote equal opportunity and the equal treatment of women and girls in the mathematical sciences."
The American Mathematical Society
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...

and other mathematical societies offer several prizes aimed at increasing the representation of women and minorities in the future of mathematics.

## Prizes in mathematics

There is no Nobel Prize in mathematics, though sometimes mathematicians have won the Nobel Prize in a different field, such as economics. Prominent prizes in mathematics include the Abel Prize
Abel Prize
The Abel Prize is an international prize presented annually by the King of Norway to one or more outstanding mathematicians. The prize is named after Norwegian mathematician Niels Henrik Abel . It has often been described as the "mathematician's Nobel prize" and is among the most prestigious...

, the Chern Medal, the Fields Medal
Fields Medal
The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union , a meeting that takes place every four...

, the Gauss Prize, the Nemmers Prize, the Balzan Prize
Balzan Prize
The International Balzan Prize Foundation awards four annual monetary prizes to people or organisations who have made outstanding achievements in the fields of humanities, natural sciences, culture, as well as for endeavours for peace and the brotherhood of man.-Rewards and assets:Each year the...

, the Crafoord Prize
Crafoord Prize
The Crafoord Prize is an annual science prize established in 1980 by Holger Crafoord, a Swedish industrialist, and his wife Anna-Greta Crafoord...

, the Shaw Prize
Shaw Prize
The Shaw Prize is an annual award first presented by the Shaw Prize Foundation in 2004. Established in 2002 in Hong Kong, it honours living "individuals, regardless of race, nationality and religious belief, who have achieved significant breakthrough in academic and scientific research or...

, the Wolf Prize, the Schock Prize
Schock prize
The Rolf Schock Prizes were established and endowed by bequest of philosopher and artist Rolf Schock . The prizes were first awarded in Stockholm, Sweden, in 1993 and have been awarded every two years since...

, and the Nevanlinna Prize
Nevanlinna Prize
The Rolf Nevanlinna Prize is awarded once every 4 years at the International Congress of Mathematicians, for outstanding contributions in Mathematical Aspects of Information Sciences including:...

.

The following are quotations about mathematicians, or by mathematicians.
A mathematician is a device for turning coffee into theorems.
—Attributed to both Alfréd Rényi
Alfréd Rényi
Alfréd Rényi was a Hungarian mathematician who made contributions in combinatorics, graph theory, number theory but mostly in probability theory.-Life:...

and Paul Erdős
Paul Erdos
Paul Erdős was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory...

Die Mathematiker sind eine Art Franzosen; redet man mit ihnen, so übersetzen sie es in ihre Sprache, und dann ist es alsobald ganz etwas anderes. (Mathematicians are [like] a sort of Frenchmen; if you talk to them, they translate it into their own language, and then it is immediately something quite different.)
Johann Wolfgang von Goethe
Johann Wolfgang von Goethe
Johann Wolfgang von Goethe was a German writer, pictorial artist, biologist, theoretical physicist, and polymath. He is considered the supreme genius of modern German literature. His works span the fields of poetry, drama, prose, philosophy, and science. His Faust has been called the greatest long...

Each generation has its few great mathematicians...and [the others'] research harms no one.
—Alfred W. Adler (1930- ), "Mathematics and Creativity"

In short, I never yet encountered the mere mathematician who could be trusted out of equal roots, or one who did not clandestinely hold it as a point of his faith that x squared + px was absolutely and unconditionally equal to q. Say to one of these gentlemen, by way of experiment, if you please, that you believe occasions may occur where x squared + px is not altogether equal to q, and, having made him understand what you mean, get out of his reach as speedily as convenient, for, beyond doubt, he will endeavor to knock you down.
Edgar Allan Poe
Edgar Allan Poe
Edgar Allan Poe was an American author, poet, editor and literary critic, considered part of the American Romantic Movement. Best known for his tales of mystery and the macabre, Poe was one of the earliest American practitioners of the short story and is considered the inventor of the detective...

, The purloined letter

A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.
G. H. Hardy
G. H. Hardy
Godfrey Harold “G. H.” Hardy FRS was a prominent English mathematician, known for his achievements in number theory and mathematical analysis....

, A Mathematician's Apology

Some of you may have met mathematicians and wondered how they got that way.
Tom Lehrer
Tom Lehrer
Thomas Andrew "Tom" Lehrer is an American singer-songwriter, satirist, pianist, mathematician and polymath. He has lectured on mathematics and musical theater...

It is impossible to be a mathematician without being a poet in soul.
Sofia Kovalevskaya
Sofia Kovalevskaya
Sofia Vasilyevna Kovalevskaya , was the first major Russian female mathematician, responsible for important original contributions to analysis, differential equations and mechanics, and the first woman appointed to a full professorship in Northern Europe.She was also one of the first females to...

Some notable mathematicians include Archimedes of Syracuse, Leonhard Euler
Leonhard Euler
Leonhard Euler 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...

, Carl Gauss, Johann Bernoulli
Johann Bernoulli
Johann Bernoulli was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family...

, Jacob Bernoulli, Aryabhatta, Brahmagupta
Brahmagupta
Brahmagupta was an Indian mathematician and astronomer who wrote many important works on mathematics and astronomy. His best known work is the Brāhmasphuṭasiddhānta , written in 628 in Bhinmal...

, Omar Khayyám
Omar Khayyám
Omar Khayyám was aPersian polymath: philosopher, mathematician, astronomer and poet. He also wrote treatises on mechanics, geography, mineralogy, music, climatology and theology....

'There is some confusion in the literature on whether al-Khwārizmī's full name is ' or '. Ibn Khaldun notes in his encyclopedic work: "The first who wrote upon this branch was Abu ʿAbdallah al-Khowarizmi, after whom came Abu Kamil Shojaʿ ibn Aslam." . 'There is some confusion in the literature on...

, Bernhard Riemann
Bernhard Riemann
Georg Friedrich Bernhard Riemann was an influential German mathematician who made lasting contributions to analysis and differential geometry, some of them enabling the later development of general relativity....

, Gottfried Leibniz
Gottfried Leibniz
Gottfried Wilhelm Leibniz was a German philosopher and mathematician. He wrote in different languages, primarily in Latin , French and German ....

, Andrei Kolmogorov, Euclid of Alexandria, Jules Henri Poincaré, Srinivasa Ramanujan
Srinivasa Ramanujan
Srīnivāsa Aiyangār Rāmānujan FRS, better known as Srinivasa Iyengar Ramanujan was a Indian mathematician and autodidact who, with almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis, number theory, infinite series and continued fractions...

, Alexander Grothendieck
Alexander Grothendieck
Alexander Grothendieck is a mathematician and the central figure behind the creation of the modern theory of algebraic geometry. His research program vastly extended the scope of the field, incorporating major elements of commutative algebra, homological algebra, sheaf theory, and category theory...

, David Hilbert
David Hilbert
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...

, Alan Turing
Alan Turing
Alan Mathison Turing, OBE, FRS , was an English mathematician, logician, cryptanalyst, and computer scientist. He was highly influential in the development of computer science, providing a formalisation of the concepts of "algorithm" and "computation" with the Turing machine, which played a...

, von Neumann, Kurt Godel
Kurt Gödel
Kurt Friedrich Gödel was an Austrian logician, mathematician and philosopher. Later in his life he emigrated to the United States to escape the effects of World War II. One of the most significant logicians of all time, Gödel made an immense impact upon scientific and philosophical thinking in the...

, Joseph-Louis Lagrange, Georg Cantor
Georg Cantor
Georg Ferdinand Ludwig Philipp Cantor 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,...

, William Rowan Hamilton
William Rowan Hamilton
Sir William Rowan Hamilton was an Irish physicist, astronomer, and mathematician, who made important contributions to classical mechanics, optics, and algebra. His studies of mechanical and optical systems led him to discover new mathematical concepts and techniques...

, Carl Jacobi, Évariste Galois
Évariste Galois
Évariste Galois 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...

, Nikolay Lobachevsky, Rene Descartes
René Descartes
René Descartes ; was a French philosopher 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...

, Joseph Fourier
Joseph Fourier
Jean Baptiste Joseph Fourier was a French mathematician and physicist best known for initiating the investigation of Fourier series and their applications to problems of heat transfer and vibrations. The Fourier transform and Fourier's Law are also named in his honour...

, Pierre-Simon Laplace
Pierre-Simon Laplace
Pierre-Simon, marquis de Laplace was a French mathematician and astronomer whose work was pivotal to the development of mathematical astronomy and statistics. He summarized and extended the work of his predecessors in his five volume Mécanique Céleste...

, Robert Lee Moore
Robert Lee Moore
Robert Lee Moore was an American mathematician, known for his work in general topology and the Moore method of teaching university mathematics.-Life:...

, Alonzo Church
Alonzo Church
Alonzo Church was an American mathematician and logician who made major contributions to mathematical logic and the foundations of theoretical computer science. He is best known for the lambda calculus, Church–Turing thesis, Frege–Church ontology, and the Church–Rosser theorem.-Life:Alonzo Church...

, Nikolay Bogolyubov
Nikolay Bogolyubov
Nikolay Nikolaevich Bogolyubov was a Russian and Ukrainian Soviet mathematician and theoretical physicist known for a significant contribution to quantum field theory, classical and quantum statistical mechanics, and to the theory of dynamical systems; a recipient of the Dirac Prize...

and Pierre de Fermat
Pierre de Fermat
Pierre de Fermat was a French lawyer at the Parlement of Toulouse, France, and an amateur mathematician who is given credit for early developments that led to infinitesimal calculus, including his adequality...

.

• List of amateur mathematicians
• List of female mathematicians
• List of mathematicians
• Mathematical joke
Mathematical joke
A mathematical joke is a form of humor which relies on aspects of mathematics or a stereotype of mathematicians to derive humor. The humor may come from a pun, or from a double meaning of a mathematical term. It may also come from a lay person's misunderstanding of a mathematical concept...

• Men of mathematics
Men of Mathematics
Men of Mathematics is a book on the history of mathematics written in 1937 by the mathematician E.T. Bell. After a brief chapter on three ancient mathematicians, the remainder of the book is devoted to the lives of about forty mathematicians who worked in the seventeenth, eighteenth and nineteenth...

(book)
• A Mathematician's Apology
A Mathematician's Apology
A Mathematician's Apology is a 1940 essay by British mathematician G. H. Hardy. It concerns the aesthetics of mathematics with some personal content, and gives the layman an insight into the mind of a working mathematician.-Summary:...