It was once postulated that a bee is an absurdity; mathematically it can't produce the lift necessary to fly. However, this statement in itself was nonsensical to the obvious proof that bees do fly, because they can and therefore there must be something wrong with the math, not the insect. This simple understanding of flight was derived from what was known about aerodynamics, but applying the mathematics of flight of an aeroplane to that in an insect is very much a question of scale, as well as evolutionary ingenuity.
If one applies the mathematics of a rotating disk (such as in a helicopter) to that of an insect, it becomes apparent that the wing size of an insect (such as a bumblebee) is not large enough to generate the downward thrust of air, despite their incredible speeds.
Experiments during the 1970s discovered that bees as well as other insects were pushing down 10 times more air than the mathematics would assume they could. This principle arose because of the viscosity and inertia effects applicable at this small scale.
In many respects, air is more of a viscous fluid at this small scale, rather than in the way we perceive it. Every slight movement produces tiny vortices that alter the fluid dynamics of the immediate environment and the insects use this to generate lift and thrust.
Bees' wings move in a 'figure of 8' motion around their thorax. This produces both clockwise and anticlockwise vortices; these inevitably produce the thrust of the bumblebee. Furthermore, the viscosity at this level causes more air to be sucked into the vortices thus increasing the size and therefore the lift and thrust generated from the flight motion of bumblebees. This viscosity was overlooked in the original maths as viscosity plays a negligible part to plane and helicopter flight.
Lastly, by tilting the tips of the wings, bumblebees can alter the pitch of their flight. In other words, they can move up and down and around corners. This means that they do not need a tail to stabilize the eddies that are produced around the vortex.
As a result of the advent in technology and the power of high-resolution digital cameras as well as the power of modern computers, flight within the insects can be viewed at up to 7000 fps and modelled. This has enabled researches to understand the biomechanics of flight to a degree never envisaged by those that once criticized such an organism as an absurdity.