Who says mathematics papers can't be practical?  Noah T. Jafferis, Howard A. Stone, and James C. Sturm of Princeton took a theoretical shot at a flying hoverboard and made it work - except it is a 4-inch conductive plastic sheet that “flies” using transverse traveling waves so don't get dreams of Marty McFly in "Back To The Future II" about it just yet, despite my title. A hoverboard using this current technology will need to be 50 feet wide to carry you.

Basically, they applied current to the plastic sheet and it created pockets of air underneath that moved from the front to the back, moving the sheet somewhat like a stingray in water.

They use the term 'flying' in quotes but it moves about a centimeter per second and this is not a research article so I will go ahead and say this thing flies.   

What would make it more awesome?   They're working on a solar-powered version.

Citation: Noah T. Jafferis, Howard A. Stone, and James C. Sturm, 'Traveling wave-induced aerodynamic propulsive forces using piezoelectrically deformed substrates', Appl. Phys. Lett. 99, 114102 (2011); doi:10.1063/1.3637635