Combinatorics

Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.

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Quotes

Combinatorics and Algebraic Geometry have enjoyed a fruitful interplay since the nineteenth century. Classical interactions include invariant theory, theta functions, and enumerative geometry.
- Aldo Conca; Sandra Di Rocco; Jan Draisma; June Huh; Bernd Sturmfels; Filippo Viviani (15 May 2014). Combinatorial Algebraic Geometry: Levico Terme, Italy 2013. Springer. p. 5. ISBN 978-3-319-04870-3.

The result of a counting process is independent of the way in which it is done. This is really an assumption about what counting is. It would be senseless to try to prove it, because it is so basic; either you see it or you don't—but in the latter case, a proof won't help you a bit.
- Douglas Hofstadter. Gödel, Escher, Bach. p. 55.

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Combinatorics

Mathematics
Mathematicians (by country)	Abel • Anaxagoras • Archimedes • Aristarchus of Samos • Aryabhata • Averroes • Arnold • Banach • Bhāskara I • Bhāskara II • Brahmagupta • Cantor • Cartan • Chern • Cohen • Descartes • Diophantus • Erdős • Euclid • Euler • Fourier • Gauss • Gödel • Grassmann • Grothendieck • Hamilton • Hilbert • Hypatia • Lagrange • Laplace • Leibniz • Milnor • Newton • von Neumann • Noether • Penrose • Perelman • Poincaré • Pólya • Pythagoras • Ramanujan • Riemann • Russell • Schwartz • Serre • Tao • Tarski • Thales • Turing • Weil • Weyl • Wiles • Witten
Numbers	1 • 23 • 360 • e • π • Fibonacci numbers • Fraction • Irrational number • Negative number • Number • Prime number • Quaternion • Octonion • Sedenion
Concepts	Abstraction • Algorithms • Axiomatic system • Completeness • Deductive reasoning • Differential equation • Dimension • Ellipse • Elliptic curve • Exponential growth • Infinity • Integration • Geodesic • Induction • Proof • Partial differential equation • Principle of least action • Prisoner's dilemma • Probability • Randomness • Theorem • Topological space • Wave equation
Results	Euler's identity • Fermat's Last Theorem
Pure math	Abstract algebra • Algebra • Analysis • Algebraic geometry (Sheaf theory) • Algebraic topology • Arithmetic • Calculus • Category theory • Combinatorics • Commutative algebra • Complex analysis • Differential calculus • Differential geometry • Differential topology • Ergodic theory • Foundations of mathematics • Functional analysis • Game theory • Geometry • Global analysis • Graph theory • Group theory • Harmonic analysis • Homological algebra • Invariant theory • Logic • Non-Euclidean geometry • Nonstandard analysis • Number theory • Numerical analysis • Operations research • Representation theory • Ring theory • Set theory • Sheaf theory • Statistics • Symplectic geometry • Topology
Applied math	Computational fluid dynamics • Econometrics • Fluid mechanics • Mathematical physics • Science
History of math	Algorism • Ancient Greek mathematics • Euclid's Elements • Hindu–Arabic numeral system • History of algebra • History of calculus • History of logarithms • Indian mathematics • Principia Mathematica
Other	Mathematics and mysticism • Mathematical Platonism • Mathematics education • Mathematics, from the points of view of the Mathematician and of the Physicist • Philosophy of mathematics • Unification in science and mathematics