List of mathematics lists
Encyclopedia
This article itemizes the various lists 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...
topics. Some of these lists link to hundreds of articles; some link only to a few. The extremely long list of mathematics articles contains all mathematical articles in alphabetical order. This article brings together the same content organised in a manner better suited to browsing.
The purpose of this list is not similar to that of the Mathematics Subject Classification
Mathematics Subject Classification
The Mathematics Subject Classification is an alphanumerical classification scheme collaboratively produced by staff of and based on the coverage of the two major mathematical reviewing databases, Mathematical Reviews and Zentralblatt MATH...
formulated by 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...
. Many mathematics journals ask authors of research papers and expository articles to list subject codes from the Mathematics Subject Classification in their papers. The subject codes so listed are used by the two major reviewing databases, Mathematical Reviews
Mathematical Reviews
Mathematical Reviews is a journal and online database published by the American Mathematical Society that contains brief synopses of many articles in mathematics, statistics and theoretical computer science.- Reviews :...
and Zentralblatt MATH
Zentralblatt MATH
Zentralblatt MATH is a service providing reviews and abstracts for articles in pure and applied mathematics, published by Springer Science+Business Media. It is a major international reviewing service which covers the entire field of mathematics...
. This list has some items that would not fit in such a classification, such as list of exponential topics and list of factorial and binomial topics, which may surprise the reader with the diversity of their coverage.
Areas of basic mathematics
These lists include topics typically taught in secondary education or in the first year of university.
- Outline of discrete mathematics
- List of calculus topics
- List of geometry topics
- List of topics in logic
- List of trigonometry topics
- Outline of trigonometry
- List of trigonometric identities
Areas of advanced mathematics
See also Areas of mathematicsAreas of mathematics
Mathematics has become a vastly diverse subject over history, and there is a corresponding need to categorize the different areas of mathematics. A number of different classification schemes have arisen, and though they share some similarities, there are differences due in part to the different...
.
As a rough guide this list is divided into pure and applied sections although in reality these branches are overlapping and intertwined.
Algebra
AlgebraAlgebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
includes the study of algebraic structures, which are sets and operations defined on these sets satisfying certain axioms. The field of algebra is further divided according to which structure is studied; for instance, group theory concerns an algebraic structure called group.
- List of abstract algebra topics
- List of algebraic structures
- List of Boolean algebra topics
- List of category theory topics
- List of commutative algebra topics
- List of homological algebra topics
- List of group theory topics
- List of representation theory topics
- List of linear algebra topics
- Glossary of field theoryGlossary of field theoryField theory is the branch of mathematics in which fields are studied. This is a glossary of some terms of the subject. -Definition of a field:...
- Glossary of group theoryGlossary of group theoryA group is a set G closed under a binary operation • satisfying the following 3 axioms:* Associativity: For all a, b and c in G, • c = a • ....
- Glossary of linear algebra
- Glossary of ring theoryGlossary of ring theoryRing theory is the branch of mathematics in which rings are studied: that is, structures supporting both an addition and a multiplication operation. This is a glossary of some terms of the subject.-Definition of a ring:...
- List of cohomology theories
Calculus and analysis
CalculusCalculus
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...
studies the computation of limits, derivatives, and integrals of functions of real numbers, and in particular studies instantaneous rates of change. Analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
studies the same subjects, but on a more rigorous level, and also topics that evolved from calculus.
- List of complex analysis topics
- List of functional analysis topics
- List of integration and measure theory topics
- List of harmonic analysis topics
- List of multivariable calculus topics
- List of real analysis topics
- List of variational topics
- Glossary of tensor theoryGlossary of tensor theoryThis is a glossary of tensor theory. For expositions of tensor theory from different points of view, see:* Tensor* Tensor * Application of tensor theory in engineering science...
- List of mathematical series
- See also Dynamical systems and differential equations section below.
Geometry and topology
GeometryGeometry
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 ....
is initially the study of spatial figures like circles and cubes, though it has been generalized considerably. 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...
developed from geometry; it looks at those properties that do not change even when the figures are deformed by stretching and bending, like dimension.
- List of geometry topics
- List of geometric shapes
- List of curve topics
- List of triangle topics
- List of circle topics
- List of topics related to pi
- List of general topology topics
- List of differential geometry topics
- List of algebraic geometry topics
- List of algebraic topology topics
- List of geometric topology topics
- List of knot theory topics
- List of Lie group topics
- Glossary of differential geometry and topologyGlossary of differential geometry and topologyThis is a glossary of terms specific to differential geometry and differential topology.The following two glossaries are closely related:*Glossary of general topology*Glossary of Riemannian and metric geometry.See also:*List of differential geometry topics...
- Glossary of general topology
- List of points
- Glossary of Riemannian and metric geometryGlossary of Riemannian and metric geometryThis is a glossary of some terms used in Riemannian geometry and metric geometry — it doesn't cover the terminology of differential topology....
- Glossary of scheme theoryGlossary of scheme theoryThis is a glossary of scheme theory. For an introduction to the theory of schemes in algebraic geometry, see affine scheme, projective space, sheaf and scheme. The concern here is to list the fundamental technical definitions and properties of scheme theory...
Combinatorics
CombinatoricsCombinatorics
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 ,...
concerns the study of discrete
Countable set
In mathematics, a countable set is a set with the same cardinality as some subset of the set of natural numbers. A set that is not countable is called uncountable. The term was originated by Georg Cantor...
(and usually finite) objects. Aspects include "counting" the objects satisfying certain criteria (enumerative combinatorics
Enumerative combinatorics
Enumerative combinatorics is an area of combinatorics that deals with the number of ways that certain patterns can be formed. Two examples of this type of problem are counting combinations and counting permutations...
), deciding when the criteria can be met, and constructing and analyzing objects meeting the criteria (as in combinatorial design
Combinatorial design
Combinatorial design theory is the part of combinatorial mathematics that deals with the existence and construction of systems of finite sets whose intersections have specified numerical properties....
s and matroid
Matroid
In combinatorics, a branch of mathematics, a matroid or independence structure is a structure that captures the essence of a notion of "independence" that generalizes linear independence in vector spaces....
theory), finding "largest", "smallest", or "optimal" objects (extremal combinatorics
Extremal combinatorics
Extremal combinatorics is a field of combinatorics, which is itself a part of mathematics. Extremal combinatorics studies how large or how small a collection of finite objects can be, if it has to satisfy certain restrictions.For example, how many people can we invite to a party where among each...
and combinatorial optimization
Combinatorial optimization
In applied mathematics and theoretical computer science, combinatorial optimization is a topic that consists of finding an optimal object from a finite set of objects. In many such problems, exhaustive search is not feasible...
), and finding algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
ic structures these objects may have (algebraic combinatorics
Algebraic combinatorics
Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algebra....
).
- Outline of combinatorics
- List of graph theory topics
- Glossary of graph theoryGlossary of graph theoryGraph theory is a growing area in mathematical research, and has a large specialized vocabulary. Some authors use the same word with different meanings. Some authors use different words to mean the same thing. This page attempts to keep up with current usage....
Logic
LogicLogic
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...
is the foundation which underlies mathematical logic
Mathematical logic
Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...
and the rest of mathematics. It tries to formalize valid reasoning. In particular, it attempts to define what constitutes a proof.
- List of Boolean algebra topics
- List of first-order theories
- List of large cardinal properties
- List of mathematical logic topics
- Glossary of order theoryGlossary of order theoryThis is a glossary of some terms used in various branches of mathematics that are related to the fields of order, lattice, and domain theory. Note that there is a structured list of order topics available as well...
- List of set theory topics
Number theory
Number theoryNumber theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
studies the natural, or whole, numbers. One of the central concepts in number theory is that of the prime number
Prime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...
, and there are many questions about primes that appear simple but whose resolution continues to elude mathematicians.
- List of algebraic number theory topics
- List of number theory topics
- List of recreational number theory topics
- Glossary of arithmetic and Diophantine geometryGlossary of arithmetic and Diophantine geometryThis is a glossary of arithmetic and Diophantine geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry...
- List of prime numbers—not just a table, but a list of various kinds of prime numbers (each with an accompanying table)
Dynamical systems and differential equations
A differential equationDifferential equation
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...
is an equation involving an unknown function and its derivatives.
In a dynamical system
Dynamical system
A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a...
, a fixed rule describes the time dependence of a point in a geometrical space. The mathematical models used to describe the swinging of a clock pendulum, the flow of water in a pipe, or the number of fish each spring in a lake are examples of dynamical systems.
- List of dynamical systems and differential equations topics
- List of partial differential equation topics
- List of nonlinear partial differential equations
Mathematical physics
Mathematical physicsMathematical physics
Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...
is concerned with "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories".
- List of mathematical topics in classical mechanics
- List of mathematical topics in quantum theory
- List of mathematical topics in relativity
- List of string theory topics
- List of wave topics
Computing
The fields of mathematics and computing intersect both in computer scienceComputer 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...
, the study of algorithms and data structures, and in scientific computing, the study of algorithmic methods for solving problems in mathematics, science and engineering.
- List of algorithm general topics
- List of computability and complexity topics
- Lists for computational topics in geometry and graphics
- List of computer vision topics
- List of formal language and literal string topics
- List of numerical analysis topics
- List of terms relating to algorithms and data structures
Information theory and signal processing
Information theoryInformation 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...
is a branch of 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 electrical engineering
Electrical engineering
Electrical engineering is a field of engineering that generally deals with the study and application of electricity, electronics and electromagnetism. The field first became an identifiable occupation in the late nineteenth century after commercialization of the electric telegraph and electrical...
involving the quantification of information
Information
Information in its most restricted technical sense is a message or collection of messages that consists of an ordered sequence of symbols, or it is the meaning that can be interpreted from such a message or collection of messages. Information can be recorded or transmitted. It can be recorded as...
. Historically, information theory was developed to find fundamental limits on compressing and reliably communicating
Communication
Communication is the activity of conveying meaningful information. Communication requires a sender, a message, and an intended recipient, although the receiver need not be present or aware of the sender's intent to communicate at the time of communication; thus communication can occur across vast...
data.
Signal processing
Signal processing
Signal processing is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time...
is the analysis, interpretation, and manipulation of signal
Signal (electrical engineering)
In the fields of communications, signal processing, and in electrical engineering more generally, a signal is any time-varying or spatial-varying quantity....
s. Signals of interest include sound
Audio signal processing
Audio signal processing, sometimes referred to as audio processing, is the intentional alteration of auditory signals, or sound. As audio signals may be electronically represented in either digital or analog format, signal processing may occur in either domain...
, images
Image processing
In electrical engineering and computer science, image processing is any form of signal processing for which the input is an image, such as a photograph or video frame; the output of image processing may be either an image or, a set of characteristics or parameters related to the image...
, biological signals such as ECG, radar
Radar
Radar is an object-detection system which uses radio waves to determine the range, altitude, direction, or speed of objects. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain. The radar dish or antenna transmits pulses of radio...
signals, and many others. Processing of such signals includes filtering
Filter (signal processing)
In signal processing, a filter is a device or process that removes from a signal some unwanted component or feature. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal...
, storage and reconstruction, separation of information from noise
Noise
In common use, the word noise means any unwanted sound. In both analog and digital electronics, noise is random unwanted perturbation to a wanted signal; it is called noise as a generalisation of the acoustic noise heard when listening to a weak radio transmission with significant electrical noise...
, compression
Data compression
In computer science and information theory, data compression, source coding or bit-rate reduction is the process of encoding information using fewer bits than the original representation would use....
, and feature extraction
Feature extraction
In pattern recognition and in image processing, feature extraction is a special form of dimensionality reduction.When the input data to an algorithm is too large to be processed and it is suspected to be notoriously redundant then the input data will be transformed into a reduced representation...
.
- List of information theory topics
- List of algebraic coding theory topics
- List of cryptography topics
Probability and statistics
Probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
is the formalization and study of the mathematics of uncertain events or knowledge. The related field of mathematical statistics
Mathematical statistics
Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and analysis...
develops statistical theory
Statistical theory
The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that...
with mathematics. 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....
, the science concerned with collecting and analyzing data, is an autonomous discipline (and not a subdiscipline of 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...
).
- List of probability topics
- List of stochastic processes topics
- List of probability distributions
- Catalog of articles in probability theoryCatalog of articles in probability theoryThis page lists articles related to Probability theory. In particular, it lists many articles corresponding to specific probability distributions. Such articles are marked here by a code of the form , which refers to number of random variables involved and the type of the distribution. For example ...
- List of statistics topics
- Outline of regression analysisOutline of regression analysisIn statistics, regression analysis includes any technique for learning about the relationship between one or more dependent variables Y and one or more independent variables X....
Game theory
Game theoryGame 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...
is a branch 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...
that uses models to study interactions with formalized incentive structures ("games"). It has applications in a variety of fields, including economics
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
, evolutionary biology, political science
Political science
Political Science is a social science discipline concerned with the study of the state, government and politics. Aristotle defined it as the study of the state. It deals extensively with the theory and practice of politics, and the analysis of political systems and political behavior...
, social psychology
Social psychology
Social psychology is the scientific study of how people's thoughts, feelings, and behaviors are influenced by the actual, imagined, or implied presence of others. By this definition, scientific refers to the empirical method of investigation. The terms thoughts, feelings, and behaviors include all...
and military strategy
Military strategy
Military strategy is a set of ideas implemented by military organizations to pursue desired strategic goals. Derived from the Greek strategos, strategy when it appeared in use during the 18th century, was seen in its narrow sense as the "art of the general", 'the art of arrangement' of troops...
.
Operations research
Operations researchOperations research
Operations research is an interdisciplinary mathematical science that focuses on the effective use of technology by organizations...
is the study and use of mathematical models, statistics and algorithms to aid in decision-making, typically with the goal of improving or optimizing performance of real-world systems.
Methodology
Mathematical statements
A mathematical statement amounts to a proposition or assertion of some mathematical fact, formula, or construction. Such statements include axioms and the theorems that may be proved from them, conjectures that may be unproven or even unprovable, and also algorithms for computing the answers to questions that can be expressed mathematically.- List of algorithms
- List of axioms
- List of conjectures
- Erdős conjecture — a list of conjectures by Paul ErdősPaul ErdosPaul 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...
- Erdős conjecture — a list of conjectures by Paul Erdős
- Combinatorial principlesCombinatorial principlesIn proving results in combinatorics several useful combinatorial rules or combinatorial principles are commonly recognized and used.The rule of sum, rule of product, and inclusion-exclusion principle are often used for enumerative purposes. Bijective proofs are utilized to demonstrate that two sets...
- List of equations
- List of formulae involving pi
- List of fundamental theorems
- List of mathematical identities
- List of inequalities
- List of lemmas
- List of mathematical proofs
- List of NP-complete problems
- List of statements undecidable in ZFC
- List of undecidable problems
- List of theorems
General concepts
- List of convexity topics
- List of dualities
- List of exceptional set concepts
- List of exponential topics
- List of factorial and binomial topics
- List of fractal topics
- List of logarithm topics
- List of numeral system topics
- List of order topics
- List of partition topics
- List of polynomial topics
- List of properties of sets of reals
- List of transforms
- List of permutation topics
Mathematical objects
Among mathematical objects are numbers, functions, sets, a great variety of things called "spaces" of one kind or another, algebraic structures such as rings, groups, or fields, and many other things.- List of mathematical examples
- List of curves
- List of complex reflection groups
- List of complexity classes
- List of examples in general topology
- List of finite simple groups
- List of Fourier-related transforms
- List of mathematical functions
- List of mathematical knots and links
- List of manifolds
- List of mathematical shapes
- List of matrices
- List of numbers
- List of polygons, polyhedra and polytopes
- List of regular polytopes
- List of simple Lie groups
- List of small groups
- List of special functions and eponyms
- List of algebraic surfaces
- List of surfaces
- Table of Lie groupsTable of Lie groupsThis article gives a table of some common Lie groups and their associated Lie algebras.The following are noted: the topological properties of the group , as well as on their algebraic properties .For more examples of Lie groups and other...
Equations named after people
- Scientific equations named after peopleScientific equations named after peopleThis is a list of scientific equations named after people .-See also:* Eponym* List of eponymous laws* List of laws in science* List of equations* Scientific constants named after people* Scientific phenomena named after people...
About mathematics
- List of mathematical societies
- List of letters used in mathematics and science
- List of mathematics competitions
- List of mathematics history topics
- List of publications in mathematics
Mathematicians
MathematicianMathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
s study and research in all the different areas of mathematics. The publication of new discoveries in mathematics continues at an immense rate in hundreds of scientific journals, many of them devoted to mathematics and many devoted to subjects to which mathematics is applied (such as theoretical 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 theoretical physics
Theoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
).
- List of geometers
- List of logicians
- List of mathematicians
- List of mathematical probabilists
- List of statisticians
Work of particular mathematicians
- List of topics named after Augustin-Louis Cauchy
- List of things named after Albert Einstein
- List of topics named after Euclid
- List of topics named after Leonhard Euler
- List of things named after Paul Erdős
- List of topics named after Fibonacci
- List of topics named after Carl Friedrich Gauss
- List of topics named after Joseph Louis Lagrange
- List of topics named after Srinivasa Ramanujan
- List of topics named after Bernhard Riemann
- List of topics named after James Joseph Sylvester
- List of topics named after Alfred Tarski
- List of topics named after Karl Weierstrass
- List of topics named after Hermann Weyl
Reference tables
- List of mathematical reference tables
- List of moments of inertia
- Table of derivatives
Integrals
In calculus, the integralIntegral
Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus...
of a function is a generalization of area, mass, volume, sum, and total. The following pages list the integrals of many different functions.
- Lists of integrals
- List of integrals of exponential functions
- List of integrals of hyperbolic functions
- List of integrals of inverse hyperbolic functions
- List of integrals of inverse trigonometric functions
- List of integrals of irrational functions
- List of integrals of logarithmic functions
- List of integrals of rational functions
- List of integrals of trigonometric functions
Meta-lists
- List of important publications in mathematics
- List of important publications in statistics
- List of mathematical theories
- List of mathematics articles
- List of mathematics categories
- Table of mathematical symbolsTable of mathematical symbolsThis is a listing of common symbols found within all branches of mathematics. Each symbol is listed in both HTML, which depends on appropriate fonts being installed, and in , as an image.-Symbols:-Variations:...
- Table of logic symbolsTable of logic symbolsIn logic, a set of symbols is commonly used to express logical representation. As logicians are familiar with these symbols, they are not explained each time they are used. So, for students of logic, the following table lists many common symbols together with their name, pronunciation and related...
External links and references
- 2000 Mathematics Subject Classification from the American Mathematical SocietyAmerican 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...
. Many research journals in mathematics ask authors to classify their papers according to this scheme; the classifications appear in the published work. - The Mathematical Atlas