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Definitions of mathematics, the Glossary

Mathematics has no generally accepted definition.^[1]

45 relations: Abstraction (mathematics), Academic discipline, Arend Heyting, Aristotle, Arithmetic, Auguste Comte, Benjamin Peirce, Bertrand Russell, Black cat analogy, Categorical proposition, Charles Darwin, Deductive reasoning, Encyclopædia Britannica, Eugene Wigner, Formalism (philosophy of mathematics), Foundations of mathematics, G. H. Hardy, Geometry, Group theory, Haskell Curry, Henri Poincaré, Ian Stewart (mathematician), Intuitionism, Intuitionistic logic, James Joseph Sylvester, L. E. J. Brouwer, Logic, Logicism, Mathematics, Oxford English Dictionary, Peripatetic school, Philosophy, Philosophy of mathematics, Plato, Platonism, Problem of universals, Projective geometry, Pythagoras, Science, Symbol, Syntax, The American Heritage Dictionary of the English Language, The Unreasonable Effectiveness of Mathematics in the Natural Sciences, Uta Merzbach, Walter Warwick Sawyer.
Definitions

Abstraction (mathematics)

Abstraction in mathematics is the process of extracting the underlying structures, patterns or properties of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.

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Academic discipline

An academic discipline or academic field is a subdivision of knowledge that is taught and researched at the college or university level.

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Arend Heyting

Arend Heyting (9 May 1898 – 9 July 1980) was a Dutch mathematician and logician.

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Aristotle

Aristotle (Ἀριστοτέλης Aristotélēs; 384–322 BC) was an Ancient Greek philosopher and polymath.

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Arithmetic

Arithmetic is an elementary branch of mathematics that studies numerical operations like addition, subtraction, multiplication, and division.

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Auguste Comte

Isidore Auguste Marie François Xavier Comte (19 January 1798 – 30 September 1857) was a French philosopher, mathematician and writer who formulated the doctrine of positivism.

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Benjamin Peirce

Benjamin Peirce (April 4, 1809 – October 6, 1880) was an American mathematician who taught at Harvard University for approximately 50 years.

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Bertrand Russell

Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, logician, philosopher, and public intellectual.

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Black cat analogy

The black cat analogy is an analogy accounting for the differences between science and religion, or in some versions also between other disciplines such as philosophy and metaphysics.

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Categorical proposition

In logic, a categorical proposition, or categorical statement, is a proposition that asserts or denies that all or some of the members of one category (the subject term) are included in another (the predicate term).

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Charles Darwin

Charles Robert Darwin (12 February 1809 – 19 April 1882) was an English naturalist, geologist, and biologist, widely known for his contributions to evolutionary biology.

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Deductive reasoning

Deductive reasoning is the process of drawing valid inferences.

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Encyclopædia Britannica

The British Encyclopaedia is a general knowledge English-language encyclopaedia.

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Eugene Wigner

Eugene Paul Wigner (Wigner Jenő Pál,; November 17, 1902 – January 1, 1995) was a Hungarian-American theoretical physicist who also contributed to mathematical physics.

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Formalism (philosophy of mathematics)

In the philosophy of mathematics, formalism is the view that holds that statements of mathematics and logic can be considered to be statements about the consequences of the manipulation of strings (alphanumeric sequences of symbols, usually as equations) using established manipulation rules. Definitions of mathematics and formalism (philosophy of mathematics) are philosophy of mathematics.

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Foundations of mathematics

Foundations of mathematics is the logical and mathematical framework that allows the development of mathematics without generating self-contradictory theories, and, in particular, to have reliable concepts of theorems, proofs, algorithms, etc. Definitions of mathematics and Foundations of mathematics are philosophy of mathematics.

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G. H. Hardy

Godfrey Harold Hardy (7 February 1877 – 1 December 1947) was an English mathematician, known for his achievements in number theory and mathematical analysis.

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Geometry

Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.

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Group theory

In abstract algebra, group theory studies the algebraic structures known as groups.

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Haskell Curry

Haskell Brooks Curry (September 12, 1900 – September 1, 1982) was an American mathematician and logician.

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Henri Poincaré

Jules Henri Poincaré (29 April 185417 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science.

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Ian Stewart (mathematician)

Ian Nicholas Stewart (born 24 September 1945) is a British mathematician and a popular-science and science-fiction writer.

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Intuitionism

In the philosophy of mathematics, intuitionism, or neointuitionism (opposed to preintuitionism), is an approach where mathematics is considered to be purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles claimed to exist in an objective reality. Definitions of mathematics and intuitionism are philosophy of mathematics.

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Intuitionistic logic

Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion of constructive proof.

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James Joseph Sylvester

James Joseph Sylvester (3 September 1814 – 15 March 1897) was an English mathematician.

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L. E. J. Brouwer

Luitzen Egbertus Jan "Bertus" Brouwer (27 February 1881 – 2 December 1966) was a Dutch mathematician and philosopher who worked in topology, set theory, measure theory and complex analysis.

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Logic

Logic is the study of correct reasoning.

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Logicism

In the philosophy of mathematics, logicism is a programme comprising one or more of the theses that – for some coherent meaning of 'logic' – mathematics is an extension of logic, some or all of mathematics is reducible to logic, or some or all of mathematics may be modelled in logic. Definitions of mathematics and logicism are philosophy of mathematics.

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Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

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Oxford English Dictionary

The Oxford English Dictionary (OED) is the principal historical dictionary of the English language, published by Oxford University Press (OUP), a University of Oxford publishing house.

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Peripatetic school

The Peripatetic school was a philosophical school founded in 335 BC by Aristotle in the Lyceum in Ancient Athens.

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Philosophy

Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, value, mind, and language.

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Philosophy of mathematics

Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship with other human activities.

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Plato

Plato (Greek: Πλάτων), born Aristocles (Ἀριστοκλῆς; – 348 BC), was an ancient Greek philosopher of the Classical period who is considered a foundational thinker in Western philosophy and an innovator of the written dialogue and dialectic forms.

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Platonism

Platonism is the philosophy of Plato and philosophical systems closely derived from it, though contemporary Platonists do not necessarily accept all doctrines of Plato.

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Problem of universals

The problem of universals is an ancient question from metaphysics that has inspired a range of philosophical topics and disputes: "Should the properties an object has in common with other objects, such as color and shape, be considered to exist beyond those objects? And if a property exists separately from objects, what is the nature of that existence?" The problem of universals relates to various inquiries closely related to metaphysics, logic, and epistemology, as far back as Plato and Aristotle, in efforts to define the mental connections a human makes when they understand a property such as shape or color to be the same in nonidentical objects.

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References

[1] https://en.wikipedia.org/wiki/Definitions_of_mathematics

Also known as Definition of mathematics.

Definitions of mathematics, the Glossary

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