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In a 1847 talk to the Académie des Sciences in Paris, Gabriel Lamé (1795-1870) claimed to have proven Fermat's last theorem. However, Joseph Liouville immediately pointed out ...

Let A be a unital C^*-algebra, then an element u in A is called an isometry if u^*u=1.

Let A = [B D; E C] (1) A^(-1) = [W X; Y Z], (2) where B and W are k×k matrices. Then det(Z)det(A)=det(B). (3) The proof follows from equating determinants on the two sides of ...

Let A be a matrix with the elementary divisors of its characteristic matrix expressed as powers of its irreducible polynomials in the field F[lambda], and consider an ...

If f_1,...,f_m:R^n->R are exponential polynomials, then {x in R^n:f_1(x)=...f_n(x)=0} has finitely many connected components.

The manipulation of Dehn surgery descriptions by a certain set of operations.

The numbers B_(n,k)(1!,2!,3!,...)=(n-1; k-1)(n!)/(k!), where B_(n,k) is a Bell polynomial.

A distinct (including reflections and rotations) arrangement of adjacent squares on a grid, also called a fixed polyomino.

The Lebesgue identity is the algebraic identity (Nagell 1951, pp. 194-195).

A lens space L(p,q) is the 3-manifold obtained by gluing the boundaries of two solid tori together such that the meridian of the first goes to a (p,q)-curve on the second, ...