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Almgren–Pitts min-max theory; Approximation theory; Arakelov theory; Asymptotic theory; Automata theory; Bass–Serre theory; Bifurcation theory; Braid theory; Brill–Noether theory; Catastrophe theory; Category theory; Chaos theory; Character theory; Choquet theory; Class field theory; Cobordism theory; Coding theory; Cohomology theory ...
List of mathematical functions; List of mathematical identities; List of mathematical proofs; List of misnamed theorems; List of scientific laws; List of theories; Most of the results below come from pure mathematics, but some are from theoretical physics, economics, and other applied fields.
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German mathematician Carl Friedrich Gauss said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theory also studies the natural, or whole, numbers. One of the central concepts in number theory is that of the prime number , and there are many questions about primes that appear simple but whose ...
The following list is meant to serve as a repository for compiling a list of such ideas. The idea of the Pythagoreans that all numbers can be expressed as a ratio of two whole numbers . This was disproved by one of Pythagoras ' own disciples, Hippasus , who showed that the square root of two is what we today call an irrational number .
Harmonic series (mathematics) divergence of the (standard) harmonic series; Highly composite number; Area of hyperbolic sector, basis of hyperbolic angle; Infinite series. convergence of the geometric series with first term 1 and ratio 1/2; Integer partition; Irrational number. irrationality of log 2 3; irrationality of the square root of 2 ...
Category theory is a unifying theory of mathematics that was initially developed in the second half of the 20th century. [4] In this respect, it is an alternative and complement to set theory. A key theme from the "categorical" point of view is that mathematics requires not only certain kinds of objects ( Lie groups , Banach spaces , etc.) but ...
This is a list of mathematical logic topics. For traditional syllogistic logic, see the list of topics in logic . See also the list of computability and complexity topics for more theory of algorithms .