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Does there exist an algorithm for deciding whether or not a specific mathematical assertion does or does not have a proof? The decision problem is also known as the ...

A set of algebraic invariants for a quantic such that any invariant of the quantic is expressible as a polynomial in members of the set. Gordan (1868) proved the existence of ...

An H-space, named after Heinz Hopf, and sometimes also called a Hopf space, is a topological space together with a continuous binary operation mu:X×X->X, such that there ...

A handle is a topological structure which can be thought of as the object produced by puncturing a surface twice, attaching a zip around each puncture travelling in opposite ...

If a subgroup H of G has a group representation phi:H×W->W, then there is a unique induced representation of G on a vector space V. The original space W is contained in V, ...

A law is a mathematical statement which always holds true. Whereas "laws" in physics are generally experimental observations backed up by theoretical underpinning, laws in ...

A proof which indirectly shows a mathematical object exists without providing a specific example or algorithm for producing an example. Nonconstructive proofs are also called ...

According to G. Pólya, the method of finding geometric objects by intersection. 1. For example, the centers of all circles tangent to a straight line s at a given point P lie ...

Two triangles DeltaABC and DeltaA^'B^'C^' are said to be perspective, or sometimes homologic, from a line if the extensions of their three pairs of corresponding sides meet ...

A polyhedron having two polygons in parallel planes as bases and triangular or trapezoidal lateral faces with one side lying in one base and the opposite polyhedron vertex or ...