“Gentlemen, that is surely true, it is absolutely paradoxical; we cannot understand it, and we don’t know what it means. But we have proved it, and therefore we know it must be the truth.” —Benjamin ...

Mathematical equations aren't just useful -- many are quite beautiful. And many scientists admit they are often fond of particular formulas not just for their function, but for their form, and the ...

What is it that makes Euler's identity, e]iPi + 1 = 0, so special? In Euler's Pioneering Equation Robin Wilson shows how this simple, elegant, and profound formula links together perhaps the five most ...

SIAM Journal on Numerical Analysis, Vol. 24, No. 3 (Jun., 1987), pp. 538-582 (45 pages) We prove the convergence of a large class of vortex methods for two-dimensional incompressible, inviscid flows ...

The compressible Euler equations form the cornerstone of fluid dynamics, describing the conservation of mass, momentum and energy in a compressible fluid. When augmented by damping effects, these ...

Quarterly of Applied Mathematics, Vol. 67, No. 2 (June 2009), pp. 327-341 (15 pages) A wide class of linear ordinary differential equations reducible to algebraic equations is studied. The method for ...