Portal:Mathematics

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The Mathematics Portal

Mathematics, from the Greek: μαθηματικά or mathēmatiká, is the study of patterns. Such patterns include quantities (numbers) and their operations, interrelations, combinations and abstractions; and of space configurations and their structure, measurement, transformations, and generalizations. Mathematics evolved through the use of abstraction and logical Reasoning, from Counting, Calculation, Measurement, and the systematic study of positions, Shapes and motions of abstract objects. Mathematicians explore such concepts, aiming to formulate new Conjectures and establish their truth by rigorous deduction from appropriately chosen Axioms and Definitions.

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The Pythagorean theorem, or Pythagoras' theorem, relates the lengths of the three sides of a Right triangle, and states:

In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).

There are many proofs of the theorem, dating back to Ancient Greek mathematician Pythagoras who is credited with its discovery. The above diagram shows one such geometric proof.

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General	Foundations	Number theory	Discrete mathematics
Mathematicians History of mathematics Philosophy of mathematics Mathematical notation Mathematical beauty Mathematics education Areas of mathematics List of basic mathematics topics Wikipedia Books: Mathematics	Foundations of mathematics Mathematical logic Set theory (portal) Naive set theory Axiomatic set theory Proof theory Model theory Recursion theory Category theory (portal) Topos theory Gödel's incompleteness theorems	Number theory (portal) Algebraic number theory Analytic number theory Arithmetic Numbers Natural numbers Prime numbers Rational numbers Algebraic numbers Fundamental theorem of arithmetic	Discrete mathematics (portal) Combinatorics Graph theory Game theory Discrete geometry Theoretical computer science Computability theory Complexity theory Information theory
Analysis	Algebra	Geometry and topology	Applied mathematics
Analysis (portal) Calculus Vector calculus Differential equations Calculus of variations Real analysis Complex analysis Functional analysis Measure theory Harmonic analysis Special functions Fundamental theorem of calculus	Algebra (portal) Elementary algebra Abstract algebra Group theory Ring theory Field theory Commutative algebra Geometric algebra Linear algebra Matrix theory Multilinear algebra Universal algebra Order theory Fundamental theorem of algebra	Geometry (portal) Topology (portal) General topology Algebraic topology Geometric topology Euclidean geometry Non-Euclidean geometry Affine geometry Projective geometry Differential geometry Riemannian geometry Lie groups Algebraic geometry Trigonometry	Applied mathematics Numerical analysis Mathematical biology Optimization Dynamical systems Chaos theory Financial mathematics Cryptography (portal) Mathematical physics Classical mechanics Probability Statistics (portal) Stochastic processes Operations research