Lorentz and Fitzgerald offered within the framework of Lorentz ether theory a more elegant solution to how the motion of an absolute aether could be undetectable ( length contraction ), but if their equations were correct, the new special theory of relativity ( 1905 ) could generate the same mathematics without referring to an aether at all.

In mathematics, the Banach fixed-point theorem ( also known as the contraction mapping theorem or contraction mapping principle ) is an important tool in the theory of metric spaces ; it guarantees the existence and uniqueness of fixed points of certain self-maps of metric spaces, and provides a constructive method to find those fixed points.

Hendrik Lorentz and George Francis FitzGerald offered within the framework of Lorentz ether theory a more elegant solution to how the motion of an absolute aether could be undetectable ( length contraction ), but if their equations were correct, Albert Einstein's 1905 special theory of relativity could generate the same mathematics without referring to an aether at all.

In mathematics, more particularly in the fields of dynamical systems and geometric topology, an Anosov map on a manifold M is a certain type of mapping, from M to itself, with rather clearly marked local directions of ' expansion ' and ' contraction '.

In category theory, a branch of mathematics, a functor is a special type of mapping between categories.

In mathematics, a linear map, linear mapping, linear transformation, or linear operator ( in some contexts also called linear function ) is a function between two modules ( including vector spaces ) that preserves the operations of module ( or vector ) addition and scalar multiplication.

The Julia set of a function ƒ is commonly denoted J ( ƒ ), and the Fatou set is denoted F ( ƒ ).< ref > Note that for other areas of mathematics the notation can also represent the Jacobian matrix of a real valued mapping between smooth manifolds .</ ref > These sets are named after the French mathematicians Gaston Julia and Pierre Fatou whose work began the study of complex dynamics during the early 20th century.

* Contraction mapping, in mathematics, a type of function on a metric space

* Injective function in mathematics, a function mapping distinct arguments to distinct values

But generative art can also be made using systems of chemistry, biology, mechanics and robotics, smart materials, manual randomization, mathematics, data mapping, symmetry, tiling, and more.

* Bilinear transform, a complex conformal mapping in mathematics

In mathematics, the cokernel of a linear mapping of vector spaces f: X → Y is the quotient space Y / im ( f ) of the codomain of f by the image of f. The dimension of the cokernel is called the corank of f.

In mathematics, a mapping from a complex vector space to another is said to be antilinear ( or conjugate-linear or semilinear, though the latter term is more general ) if

In mathematics, a reflection ( also spelled reflexion ) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as set of fixed points ; this set is called the axis ( in dimension 2 ) or plane ( in dimension 3 ) of reflection.

Since then this mapping has become an avenue to higher mathematics.

Quantization, in mathematics and digital signal processing, is the process of mapping a large set of input values to a smaller set – such as rounding values to some unit of precision.

Analytic methods typically use the structure of mathematics to arrive at a simple, elegant solution, but the required derivation for all but the simplest domain geometries can be quite complex ( involving non-standard coordinates, conformal mapping, etc .).

* Operator ( mathematics ), a mapping from one vector space or module to another

In mathematics, a bilinear form on a vector space V is a bilinear mapping V × V → F, where F is the field of scalars.

In mathematics, the ( field ) norm is a mapping defined in field theory, to map elements of a larger field into a smaller one.

In most of mathematics and in some related technical fields, the term mapping, usually shortened to map, is either a synonym for function, or denotes a particular kind of function which is important in that branch, or denotes something conceptually similar to a function.

In mathematics, the Lefschetz fixed-point theorem is a formula that counts the fixed points of a continuous mapping from a compact topological space X to itself by means of traces of the induced mappings on the homology groups of X.

In mathematics, an invariant subspace of a linear mapping

In mathematics, a Tschirnhaus transformation, also known as Tschirnhausen transformation, is a type of mapping on polynomials developed by Ehrenfried Walther von Tschirnhaus in 1683.

In mathematics, in the sub-field of geometric topology, the mapping class group

In mathematics, shear mapping or transvection is a particular kind of linear mapping.

Scientists say that the world and everything in it are based on mathematics.

But because science is based on mathematics doesn't mean that a hot rodder must necessarily be a mathematician.

Pythagoras believed that behind the appearance of things, there was the permanent principle of mathematics, and that the forms were based on a transcendental mathematical relation.

Ethics cannot be based on the authoritative certainty given by mathematics and logic, or prescribed directly from the empirical findings of science.

In mathematics, a binary relation R on a set X is antisymmetric if, for all a and b in X

He used his time in Bourg to research mathematics, producing Considérations sur la théorie mathématique de jeu ( 1802 ; “ Considerations on the Mathematical Theory of Games ”), a treatise on mathematical probability that he sent to the Paris Academy of Sciences in 1803.

Two aspects of this attitude deserve to be mentioned: 1 ) he did not only study science from books, as other academics did in his day, but actually observed and experimented with nature ( the rumours starting by those who did not understand this are probably at the source of Albert's supposed connections with alchemy and witchcraft ), 2 ) he took from Aristotle the view that scientific method had to be appropriate to the objects of the scientific discipline at hand ( in discussions with Roger Bacon, who, like many 20th century academics, thought that all science should be based on mathematics ).

The axiom of regularity is arguably the least useful ingredient of Zermelo – Fraenkel set theory, since virtually all results in the branches of mathematics based on set theory hold even in the absence of regularity ( see chapter 3 of ).

Though respected for their contributions to various academic disciplines ( respectively mathematics, linguistics, and literature ), the three men became known to the general public only by making often-controversial and disputed pronouncements on politics and public policy that would not be regarded as noteworthy if offered by a medical doctor or skilled tradesman.

" The Four Books on Measurement " were published at Nuremberg in 1525 and was the first book for adults on mathematics in German, as well as being cited later by Galileo and Kepler.

By focusing consciously on an idea, feeling or intention the meditant seeks to arrive at pure thinking, a state exemplified by but not confined to pure mathematics.

On the Infinite was Hilbert ’ s most important paper on the foundations of mathematics, serving as the heart of Hilbert's program to secure the foundation of transfinite numbers by basing them on finite methods.

Abstraction in mathematics is the process of extracting the underlying essence of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.

In mathematics, a binary relation on a set A is a collection of ordered pairs of elements of A.

In mathematics, a binary operation on a set is a calculation involving two elements of the set ( called operands ) and producing another element of the set ( more formally, an operation whose arity is two ).

Following Desargues ' thinking, the sixteen-year-old Pascal produced, as a means of proof, a short treatise on what was called the " Mystic Hexagram ", Essai pour les coniques (" Essay on Conics ") and sent it — his first serious work of mathematics — to Père Mersenne in Paris ; it is known still today as Pascal's theorem.

The first person to describe the mathematics behind Brownian motion was Thorvald N. Thiele in a paper on the method of least squares published in 1880.

Calculus ( Latin, calculus, a small stone used for counting ) is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series.

On November 29, 1921, the trustees declared it to be the express policy of the Institute to pursue scientific research of the greatest importance and at the same time " to continue to conduct thorough courses in engineering and pure science, basing the work of these courses on exceptionally strong instruction in the fundamental sciences of mathematics, physics, and chemistry ; broadening and enriching the curriculum by a liberal amount of instruction in such subjects as English, history, and economics ; and vitalizing all the work of the Institute by the infusion in generous measure of the spirit of research.

* nLab, a wiki project on mathematics, physics and philosophy with emphasis on the n-categorical point of view