A
mathematician is a person whose primary area of study and/or research is the field of
mathematicsMathematics is the science and study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions....
. Mathematicians are concerned with particular problems related to
logicLogic, from the Greek λογική is the art and science of reasoning. More specifically, it is defined by the Penguin Encyclopedia to be "The formal systematic study of the principles of valid inference and correct reasoning". As a discipline, logic dates back to Aristotle, who established its...
,
spaceSpace 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 the boundless four-dimensional...
, transformations,
numbersA number is a concept used to describe and assess quantity.Number may also refer to:* Number , a number-guessing computer game* Number , a Japanese sports magazine* Number , a manga by Tsubaki Kawori...
and more general ideas which encompass these concepts. Some scientists who research other fields are also considered mathematicians if their research provides insights into mathematics - one notable example is
Edward WittenEdward Witten is an American theoretical physicist and professor at the Institute for Advanced Study, who is widely known as “the most brilliant physicist of his generation”, and "one of the world's greatest living physicists, perhaps even Einstein's successor". He is a leading researcher in...
. Conversly, some mathematicians may provide insights into other fields of research - these people are known as
applied mathematiciansApplied mathematics is a branch of mathematics that concerns itself with the mathematical techniques typically used in the application of mathematical knowledge to other domains.-Divisions of applied mathematics:...
.
Some notable mathematicians include Sir Isaac Newton, Johann Carl Friedrich Gauss, Archimedes of Syracuse, Leonhard Paul Euler, Georg Friedrich Bernhard Riemann, Euclid of Alexandria, Jules Henri Poincaré,
David HilbertDavid Hilbert was a German mathematician, recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. He discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry...
, Joseph-Louis Lagrange, and
Pierre de FermatPierre 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 modern calculus...
.
Education
A mathematician usually covers a breadth of topics within mathematics in their undergraduate education, and then proceeds to specialize in topics of their choice at the graduate level. In some universities, a qualifying exam serves to test both the breadth and depth of a person's understanding in mathematics; should they pass, they 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. A majority of these cases were those of
child prodigiesA child prodigy is someone who at an early age masters one or more skills at an adult level. One heuristic for classifying prodigies is: a prodigy is a child, typically younger than 15 years old, who is performing at the level of a highly trained adult in a very demanding field of endeavor...
.
Problems in Mathematics
The publication of new discoveries in mathematics continues at an immense rate in hundreds of
scientific journalIn academic publishing, a scientific journal is a periodical publication intended to further the progress of science, usually by reporting new research. There are thousands of scientific journals in publication, and many more have been published at various points in the past...
s. In particular,
mathematicsMathematics is the science and study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions....
is not a closed system, in that there is no shortage of open problems; in fact, at any given time, there are infinitely many potential open problems which mathematicians have not stumbled upon. The diversity of mathematics also allows for problems, which, in certain contexts, may not be solved or are undecidable in particular theories!
Recently, an important problem in the field of
number theoryNumber theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study....
was resolved by the mathematician
Andrew WilesSir Andrew John Wiles KBE FRS is a British mathematician and a professor at Princeton University, specializing in number theory...
; this is known as
Fermat's Last TheoremIn number theory, Fermat's Last Theorem states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two...
(or "Fermat's Last Conjecture" prior to the discovery of its proof). The problem remained open for approximately 350 years making it one of the oldest problems in the history of mathematics.
Another recently resolved important problem, in the field of
differential topologyIn 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 :...
, is the
Poincaré conjectureIn mathematics, the Poincaré conjecture is a theorem about the characterization of the three-dimensional sphere among three-dimensional manifolds. It began as a popular, important conjecture, but is now considered a theorem to the satisfaction of the awarders of the Fields medal...
. Like Fermat's Last Theorem, this conjecture withstood 100 years of attempts at its solution, but was eventually resolved by Russian mathematician
Grigori PerelmanGrigori Yakovlevich Perelman , born 13 June 1966 in Leningrad, USSR , sometimes known as Grisha Perelman, is a Russian mathematician who has made landmark contributions to Riemannian geometry and geometric topology. In particular, he proved Thurston's geometrization conjecture...
in 2003. A
peer reviewPeer review is the process of subjecting an author's scholarly work, research, or ideas to the scrutiny of others who are experts in the same field. Peer review requires a community of experts in a given field, who are qualified and able to perform impartial review...
was completed in 2006, and the proof was accepted as valid.
The Poincaré conjecture belonged to a larger class of open problems (prior to its proof) known as the
Millennium Prize ProblemsThe Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000. Currently, six of the problems remain unsolved. A correct solution to any of the problems results in a US$1,000,000 prize being awarded by the institute...
. These problems concern such diverse fields of mathematics such as
algebraic geometryAlgebraic geometry is a branch of mathematics which, as the name suggests, combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such...
,
algebraic number theoryIn mathematics, algebraic number theory is a major branch of number theory which studies algebraic structures related to algebraic integers. This is generally accomplished by considering a ring of algebraic integers O in an algebraic number field K/Q, and studying their algebraic properties such as...
, differential geometry,
theoretical computer scienceTheoretical computer science is the collection of topics of computer science that focuses on the more abstract, logical and mathematical aspects of computing, such as the theory of computation, analysis of algorithms, and semantics of programming languages...
and so forth. For any one of these problems, there is a
US$The United States dollar is the unit of currency of the United States. The U.S. dollar is normally abbreviated as the dollar sign, $, or as USD or US$ to distinguish it from other dollar-denominated currencies and from others that use the $ symbol. It is divided into 100 cents .The U.S...
1,000,000 award for its solution. However, many mathematicians consider the prestige to be of a greater value than the actual sum of money.
Motivation
Mathematicians do research in fields such as
logicLogic, from the Greek λογική is the art and science of reasoning. More specifically, it is defined by the Penguin Encyclopedia to be "The formal systematic study of the principles of valid inference and correct reasoning". As a discipline, logic dates back to Aristotle, who established its...
,
set theoryThe modern study of set theory was initiated by Cantor and Dedekind in the 1870s. After the discovery of paradoxes in informal set theory, numerous axiom systems were proposed in the early twentieth century, of which the Zermelo–Fraenkel axioms, with the axiom of choice, are the best-known.The...
,
category theoryIn mathematics, category theory deals in an abstract way with mathematical structures and relationships between them: it abstracts from sets and functions to objects linked in diagrams by morphisms or arrows....
, modern algebra,
number theoryNumber theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study....
,
analysisAnalysis 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 a...
,
geometryGeometry 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....
,
topologyTopology is a major area of mathematics concerned with spatial properties that are preserved under continuous deformations of objects, for example deformations that involve stretching, but no tearing or gluing...
, dynamical systems,
combinatoricsCombinatorics is a branch of pure mathematics concerning the study of discrete objects. It is related to many other areas of mathematics, such as algebra, probability theory, ergodic theory and geometry, as well as to applied subjects in computer science and statistical physics...
,
game theoryGame theory is a branch of applied mathematics that is used in the social sciences, most notably in economics, as well as in biology, engineering, political science, international relations, computer science, and philosophy...
,
information theoryInformation theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Historically, information theory was developed by Claude E. Shannon to find fundamental limits on compressing and reliably storing and communicating data...
,
numerical analysisNumerical analysis is the study of algorithms for the problems of continuous mathematics .One of the earliest mathematical writings is the Babylonian tablet YBC 7289, which gives a sexagesimal numerical approximation of , the length of the diagonal in a unit square.Being able to compute the sides...
,
optimizationOptimization or optimality may refer to:Relating to improving performance:* Optimization , the process of finding function extrema to solve problems...
,
computationComputation is a general term for any type of information processing. This includes phenomena ranging from human thinking to calculations with a more narrow meaning. Computation is a process following a well-defined model that is understood and can be expressed in an algorithm, protocol, network...
,
probabilityProbability is a way of expressing knowledge or belief that an event will occur or has occurred. In mathematics the concept has been given an exact meaning in probability theory, that is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy...
and
statisticsStatistics is a branch of mathematics concerned with collecting and interpreting data. According to other definitions, it is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. Statisticians improve the quality of data with the...
. These fields comprise both
pure mathematicsBroadly speaking, pure mathematics is mathematics motivated entirely for reasons other than application. It is distinguished by its rigour, abstraction, and beauty...
and
applied mathematicsApplied mathematics is a branch of mathematics that concerns itself with the mathematical techniques typically used in the application of mathematical knowledge to other domains.-Divisions of applied mathematics:...
, as well as 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 scienceComputer science is the study of the theoretical foundations of information and computation, and of practical techniques for their implementation and application in computer systems. It is frequently described as the systematic study of algorithmic processes that create, describe and transform...
and
physicsPhysics is a natural science; it is the study of matter and its motion through spacetime and all that derives from these, such as energy and force...
). Likewise, analysis, geometry and topology, although considered pure mathematics, do find applications in theoretical physics -
string theoryString theory is a developing branch of theoretical physics that combines quantum mechanics and general relativity into a quantum theory of gravity...
, 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 permits for researchers in other areas too. In fact, the theory of equations and numbers (formulas to a lesser extent in theoretical mathematics, but to some extent in applied mathematics), can lead to deep questions. For instance, if one graphs a set of solutions of an equation in some higher dimensional space, he may ask of the geometric properties of the graph. Thus one can understand equations by a pure understanding of abstract
topologyTopology is a major area of mathematics concerned with spatial properties that are preserved under continuous deformations of objects, for example deformations that involve stretching, but no tearing or gluing...
or
geometryGeometry 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 geometryAlgebraic geometry is a branch of mathematics which, as the name suggests, 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...
. Similarly, a mathematican does not restrict his study of numbers to the
integerThe integers are natural numbers including 0 and their negatives . They are numbers that can be written without a fractional or decimal component, and fall within the set {.....
s; rather he considers more abstract structures such as
ringsIn mathematics, a ring is an algebraic structure consisting of a set together with two binary operations , where each operation combines two elements to form a third element...
, and in particular number rings in the context of
algebraic number theoryIn mathematics, 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...
. 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 topologyIn 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 "smoothen" higher dimensional figures. In fact, whether one can smoothen certain higher dimensional spheres remains open - it is known as the
smooth Poincaré conjectureIn mathematics, the Poincaré conjecture is a theorem about the characterization of the three-dimensional sphere among three-dimensional manifolds. It began as a popular, important conjecture, but is now considered a theorem to the satisfaction of the awarders of the Fields medal...
. Another aspect of mathematics,
set-theoretic topologyIn mathematics, set-theoretic topology is a subject that combines set theory and general topology. It focuses on topological questions that are independent of ZFC....
and point-set topology, concerns objects of a different nature to those 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 to those objects in our universe. For instance, the "distance" between one point on such an object, and another point, may depend on the order in which you consider the pair of points. This is quite different to ordinary life, in which it is accepted that the straight line distance from person A to person B is the same (and not different to!) that between person B and person A.
Another aspect of mathematics, often referred to as "foundational mathematics", consists of the fields of
logicLogic, from the Greek λογική is the art and science of reasoning. More specifically, it is defined by the Penguin Encyclopedia to be "The formal systematic study of the principles of valid inference and correct reasoning". As a discipline, logic dates back to Aristotle, who established its...
and
set theoryThe modern study of set theory was initiated by Cantor and Dedekind in the 1870s. After the discovery of paradoxes in informal set theory, numerous axiom systems were proposed in the early twentieth century, of which the Zermelo–Fraenkel axioms, with the axiom of choice, are the best-known.The...
. 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.
The Nobel Prize is never awarded for work in the field of theoretical mathematics. Instead, the most prestigious award in mathematics is the
Fields MedalThe Fields Medal 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 years. The Fields Medal is often viewed as the top honor a mathematician can receive. It...
, sometimes referred to as the "Nobel Prize of Mathematics". The Fields Medal is considered more of a prestige than a mere reward in that it is only awarded every four years, and the amount of money awarded is small in comparison to that of the Nobel Prize. Furthermore, the recipient of the Fields Medal must be (roughly) under 40 years of age at the time the medal is awarded. Other prominent prizes in mathematics include the
Abel PrizeThe 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 been often described as the "mathematician's Nobel" prize and is among the most prestigious...
, the Nemmers Prize, the
Wolf PrizeThe Wolf Prize is an international award, that has been presented annually since 1978 to living scientists and artists for "achievements in the interest of mankind and friendly relations among peoples ... irrespective of nationality, race, colour, religion, sex or political views."The prize is...
, the
Schock PrizeThe 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 PrizeThe 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:...
.
Differences
Mathematics differs from natural
scienceScience is in its broadest sense to any systematic knowledge-base or prescriptive practice that is capable of resulting in a prediction or predictable type of outcome...
s in that physical theories in the sciences are tested by experiments, while mathematical statements are supported by proofs which may be verified objectively by mathematicians. 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 proven nor dis-proven, it is called a
conjectureA conjecture is a proposition which is presumed to be real, true, or genuine, mostly based on inconclusive grounds. 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 is proven true. Physical theories may be expected to change whenever new information about our physical world is discovered. Mathematics changes in a different way: new ideas don't falsify old ones but rather are used to
generalize what was known before to capture a broader range of phenomena. For instance,
calculusCalculus is a discipline in 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...
(in one variable) generalizes to
multivariable calculusMultivariable calculus is the extension of calculus in one variable to calculus in several variables: the functions which are differentiated and integrated involve several variables rather than one variable....
, which generalizes to analysis on
manifoldIn mathematics, more specifically in differential geometry and topology, a manifold is a mathematical space that on a small enough scale resembles the Euclidean space of a certain dimension, called the dimension of the manifold....
s. The development of
algebraic geometryAlgebraic geometry is a branch of mathematics which, as the name suggests, 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...
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 theoremFermat'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 theoremIn number theory, Euler's theorem states that if n is a positive integer and a is a positive integer coprime to n, then...
for the invertible numbers modulo any nonzero integer, which generalizes to Lagrange's theorem for finite groups.
Doctoral degree statistics for mathematicians in the United States
The number of Doctoral degrees in mathematics awarded each year in the
United StatesThe United States of America is a federal constitutional republic comprising fifty states and a federal district...
has ranged from 750 to 1230 over the past 35 years. In the early seventies, degree awards were at their peak, followed by a decline throughout the seventies, a rise through the eighties, and another peak through the nineties. Unemployment for new doctoral recipients peaked at 10.7% in 1994 but was as low as 3.3% by 2000. The percentage of female doctoral recipients increased from 15% in 1980 to 30% in 2000.
As of 2000, there are approximately 21,000 full-time faculty positions in mathematics at colleges and universities in the United States. Of these positions about 36% are at institutions whose highest degree granted in mathematics is a bachelor's degree, 23% at institutions that offer a master's degree and 41% at institutions offering a doctoral degree.
The median age for doctoral recipients in 1999-2000 was 30, and the mean age was 31.7.'
Women in mathematics
While the majority of mathematicians are male, there have been some demographic changes since
World War IIWorld War II, or the Second World War , was a global military conflict which involved a majority of the world's nations, including all great powers, organized into two opposing military alliances: the Allies and the Axis...
. Some prominent female mathematicians are
Hypatia of AlexandriaHypatia of Alexandria was a Greek scholar from Alexandria in Egypt, considered the first notable woman in mathematics, who also taught philosophy and astronomy. She lived in Roman Egypt, and was killed by a Christian mob who falsely blamed her for religious turmoil...
(ca. 400 AD), Labana of Cordoba (ca. 1000),
Ada LovelaceAugusta Ada King, Countess of Lovelace , born Augusta Ada Byron, was the only legitimate child of poet Lord Byron...
(1815–1852),
Maria Gaetana AgnesiMaria 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 NoetherAmalie Emmy Noether, , was a German-born mathematician known for her groundbreaking contributions to abstract algebra and theoretical physics. Described by Albert Einstein and others as the most important woman in the history of mathematics, she revolutionized the theories of rings, fields, and...
(1882–1935),
Sophie GermainMarie-Sophie Germain was a French mathematician who made important contributions to the fields of differential geometry and number theory, and to the study of Fermat's Last Theorem.-Biography:...
(1776–1831),
Sofia KovalevskayaSofia 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.There are some alternative...
(1850–1891),
Rózsa PéterRózsa Péter , was a Hungarian mathematician. She is best known for her work with recursion theory....
(1905–1977),
Julia RobinsonJulia Hall Bowman Robinson was an American mathematician, born in St. Louis, Missouri. She is best known for her work on decision problems and Hilbert's Tenth Problem.-Background and education:Robinson was born in St...
(1919–1985), Olga Taussky-Todd (1906–1995),
Émilie du ChâteletGabrielle Émilie Le Tonnelier de Breteuil, marquise du Châtelet was a French mathematician, physicist, and author during the Age of Enlightenment. Her crowning achievement is considered to be her translation of Isaac Newton's monumental work Principia Mathematica, with her own commentary; it is...
(1706–1749), and
Mary CartwrightDame Mary Lucy Cartwright DBE was a leading 20th-century British mathematician. She was born in Aynho, Northamptonshire where her father was the vicar and died in Cambridge, England...
(1900–1998).
The
Association for Women in MathematicsThe Association for Women in Mathematics is a non-profit organization devoted to promoting equal treatment and equal opportunity for women and girls in the mathematical sciences, and to encouraging them to enter this field.-History:...
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 SocietyThe 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.
Quotations about mathematicians
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 was a Hungarian mathematician who made contributions in combinatorics, graph theory, number theory but mostly in probability theory....
and Paul ErdősPaul Erdős was an immensely prolific and famously eccentric Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators...
- 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 was a German writer and polymath. Goethe's works span the fields of poetry, drama, literature, theology, philosophy, humanism and science. Goethe's magnum opus, lauded as one of the peaks of world literature, is the two-part drama Faust...
- 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 was an American writer, 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...
, 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 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
Thomas Andrew "Tom" Lehrer is an American singer-songwriter, satirist, pianist, and mathematician. He has lectured on mathematics and musical theater...
- It is impossible to be a mathematician without being a poet in soul.
- —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.There are some alternative...
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