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Discipline

Mathematics

Also Known As Math
Formal Sciences

Mathematics is the study of numbers, quantities, shapes, and the logical relationships between them, built up from definitions and proof rather than observation alone. It has been developed independently in many civilizations, from Babylonian and Egyptian arithmetic through Greek geometry and Indian and Islamic algebra to modern analysis, and it supplies the language in which every other science states and tests its theories. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/

Facts
Founded Year
300 BCE 1
Euclid's Elements (c. 300 BCE) systematized geometry and number theory into the axiomatic, proof-based form that defines mathematics as a discipline rather than a scattered set of practical techniques; the same landmark-publication convention this atlas already uses for physics (Newton's Principia, 1687) and chemistry (Lavoisier's Traite, 1789). The exact year is not recorded; MacTutor and the wider historiography place it circa 300 BCE.
Central Question
What can be proven true from a given set of axioms, and which of the field's enduring unsolved problems, such as whether P equals NP, will yield to that method? 2
Scope
Mathematics studies abstract concepts such as numbers, geometric shapes, sets, functions and probabilities, using logical reasoning and proof to establish their properties as theorems, formulas and equations. 2
Significance
Around 300 BC Euclid organized the mathematical knowledge of his day by way of postulates and first principles, originating the axiomatic method that still defines mathematical proof today. The more than sixty first level branches recognized now, from number theory and geometry to discrete mathematics and mathematical logic, all still build proof on that same foundation. 2
Connections

Associated With

Fields Medal, Institutions

The Fields Medal is awarded to mathematicians at the International Congress of Mathematicians.

Source Fields Medal (Wikipedia)
London Mathematical Society, Institutions
Source London Mathematical Society (Wikipedia)

Founded By

Euclid, Scientists
Source Wikipedia: Mathematics

Has Scientist

Ada Lovelace, Scientists
Adrien-Marie Legendre, Scientists
Source Adrien-Marie Legendre (Wikipedia)
Alan Turing, Scientists
Al-Biruni, Scientists
Alexander Grothendieck, Scientists
Al-Khwarizmi, Scientists
Andrew Wiles, Scientists
Andrey Kolmogorov, Scientists
Andrey Markov, Scientists
Archimedes, Scientists
Aryabhata, Scientists
Augustin-Louis Cauchy, Scientists
Bernhard Riemann, Scientists
Carl Friedrich Gauss, Scientists
Source Carl Friedrich Gauss (MacTutor)
Claude Shannon, Scientists
David Hilbert, Scientists
Source David Hilbert (MacTutor)
Emmy Noether, Scientists
Source Emmy Noether (MacTutor)
Euclid, Scientists
Evangelista Torricelli, Scientists
Source Evangelista Torricelli (Wikipedia)
Evariste Galois, Scientists
Felix Hausdorff, Scientists
Georg Cantor, Scientists
Gottfried Wilhelm Leibniz, Scientists
Source Gottfried Wilhelm Leibniz (MacTutor)
Grigori Perelman, Scientists
Henri Poincare, Scientists
Hypatia, Scientists
Isaac Newton, Scientists
Source Isaac Newton (Britannica)
John Nash, Scientists
Joseph-Louis Lagrange, Scientists
Kurt Godel, Scientists
Leonhard Euler, Scientists
Source Leonhard Euler (MacTutor)
Maryam Mirzakhani, Scientists
Niels Henrik Abel, Scientists
Pafnuty Chebyshev, Scientists
Paul Cohen, Scientists
Paul Erdos, Scientists
Pierre de Fermat, Scientists
Pierre-Simon Laplace, Scientists
Rene Descartes, Scientists
Shing-Tung Yau, Scientists
Sofia Kovalevskaya, Scientists
Srinivasa Ramanujan, Scientists
Source Srinivasa Ramanujan (MacTutor)
Stanislaw Ulam, Scientists
Stefan Banach, Scientists
Terence Tao, Scientists
Thales of Miletus, Scientists
Source Thales of Miletus (Wikipedia)
Yitang Zhang, Scientists

Has Theory

Calculus, Theories
Source The Rise of Calculus (MacTutor)
Central Limit Theorem, Theories
Fermat's Last Theorem, Theories
Fundamental Theorem of Algebra, Theories
Game Theory, Theories
Information Theory, Theories
Non-Euclidean Geometry, Theories
Source Non-Euclidean Geometry (MacTutor)
Prime Number Theorem, Theories
Pythagorean Theorem, Theories
Ramsey Theory, Theories
Set Theory, Theories
Source Set Theory (Stanford Encyclopedia of Philosophy)

Long-Form Articles

The Postulate Euclid Could Not Prove, Articles

Open Questions

Does P equal NP?, Open Questions
Source Wikipedia: Mathematics
When did mathematics become a discipline rather than a scattered set of practical and philosophical techniques?, Open Questions

Studies

Axiom, Concepts
Source Euclid (MacTutor)
Number Theory, Concepts
Source Disquisitiones Arithmeticae (1801)Carl Friedrich Gauss
Proof, Concepts
Source Euclid (MacTutor)
Theorem, Concepts
Source Euclid (MacTutor)
Sources
1. Euclid (MacTutor)
MacTutor History of Mathematics, University of St Andrews
2. Wikipedia: Mathematics
Wikipedia
  • Lead section
    Mathematics is a field of knowledge concerned with abstract concepts such as numbers, geometric shapes, sets, functions, and probabilities. It uses logical reasoning and proof to study and establish their properties, often expressed as theorems, formulas, and equations.
  • Founded By: Euclid
View the Source
Evangelista Torricelli (Wikipedia)
WikipediaHas Scientist: Evangelista TorricelliView the Source
Statistics (Wikipedia)
WikipediaEncompasses: StatisticsView the Source
Fields Medal (Wikipedia)
WikipediaAssociated With: Fields MedalView the Source
London Mathematical Society (Wikipedia)
WikipediaAssociated With: London Mathematical SocietyView the Source
Thales of Miletus (Wikipedia)
WikipediaHas Scientist: Thales of Miletus, Lead section, second paragraph
Quote, Has Scientist: Thales of Miletus, Lead section, second paragraph
He is thus otherwise referred to as the first to have engaged in mathematics, science, and deductive reasoning.
View the Source
Adrien-Marie Legendre (Wikipedia)
WikipediaHas Scientist: Adrien-Marie Legendre, Lead section, second sentence
Quote, Has Scientist: Adrien-Marie Legendre, Lead section, second sentence
Well-known and important concepts such as the Legendre polynomials and Legendre transformation are named after him.
View the Source
Open Questions (1 open question)
Does P equal NP?

The P versus NP problem asks whether every problem whose solution can be quickly checked can also be quickly solved. It has resisted proof or disproof since it was formalized in the early 1970s and is one of the seven Millennium Prize Problems; a solution in either direction would reshape cryptography, optimization and much of theoretical computer science.

What would resolve this A rigorous proof that P equals NP, exhibiting a general fast algorithm for an NP-complete problem, or a proof that P does not equal NP, most likely by establishing a genuine computational barrier no such algorithm can cross.
Theoretical computer science and mathematical logicWikipedia: Mathematics
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