A recent advance in geometry makes heavy use of Ramsey’s theorem, an important idea in another field — graph theory. Ramsey’s theorem states that in any graph where all points are connected by either ...

The Pythagorean theorem, a cornerstone of mathematics for millennia, provides a method for determining unknown sides in right-angled triangles using the formula a² + b² = c². Its applications extend ...

A brief and simple proof of Siegel's celebrated theorem that h(d) ≫ d 1/2-ε, as d → ∞ , is given. Here h(d) denotes the class number of the quadratic field Q($\sqrt{-d}$). Simple proofs that do not ...

Blair, C., and A. E. Roth. "An Extension and Simple Proof of a Constrained Lattice Fix-Point Theorem." Algebra Universalis 9 (1979): 131–132.