Disciplines
Mathematics
Also Known As Math
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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.
Facts
Founded YearEuclid'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 QuestionSourced to the subject's own accountWhat 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 ScopeSourced to the subject's own accountMathematics 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 SignificanceSourced to the subject's own accountAround 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 Cross-Tradition Connections
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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 logicMathematics (Wikipedia)
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