This article Bumblebees finally cleared for takeoff is a good summary of a Cornell physicist's research in the year 2000 mathematically demonstrating and simulating why bees and similar insects can fly.
> The computer-modeling accomplishment - which is expected to aid the future design of tiny insect-like flying machines and should dispel the longstanding myth that "bumblebees cannot fly, according to conventional aerodynamics"
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> The old bumblebee myth simply reflected our poor understanding of unsteady viscous fluid dynamics... Unlike fixed-wing aircraft with their steady, almost inviscid (without viscosity) flow dynamics, insects fly in a sea of vortices, surrounded by tiny eddies and whirlwinds that are created when they move their wings.