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The only Wiedersehen surfaces are the standard round spheres. The conjecture was proven by combining the Berger-Kazdan comparison theorem with A. Weinstein's results for n ...

Relates invariants of a curve defined over the integers. If this inequality were proven true, then Fermat's last theorem would follow for sufficiently large exponents. ...

Qualitatively, a deep theorem is a theorem whose proof is long, complicated, difficult, or appears to involve branches of mathematics which are not obviously related to the ...

Dual pairs of linear programs are in "strong duality" if both are possible. The theorem was first conceived by John von Neumann. The first written proof was an Air Force ...

Let A be a matrix and x and b vectors. Then the system Ax=b, x>=0 has no solution iff the system A^(T)y>=0, b^(T)y<0 has a solution, where y is a vector (Fang and Puthenpura ...

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 ...

The correspondence which relates the Hanoi graph to the isomorphic graph of the odd binomial coefficients in Pascal's triangle, where the adjacencies are determined by ...

Every graph with n vertices and maximum vertex degree Delta(G)<=k is (k+1)-colorable with all color classes of size |_n/(k+1)_| or [n/(k+1)], where |_x_| is the floor ...

The difference between the sum of the angles A, B, and C of a spherical triangle and pi radians (180 degrees), E=A+B+C-pi. The notation Delta is sometimes used for spherical ...

Based on a problem in particle physics, Dyson (1962abc) conjectured that the constant term in the Laurent series product_(1<=i!=j<=n)(1-(x_i)/(x_j))^(a_i) is the multinomial ...