The
bare summary of the Science article.

The even barer
video.

What their math can't apparently tell them is why so many
different bike designs tend to stay upright. "Why does this bicycle steer the
proper amounts at the proper times to assure self-stability?" They muse. "We
have found no simple physical explanation equivalent to the mathematical
statement that all eigenvalues must have negative real parts." In other words,
they can see why the math works out the way it does, but can't figure out what
physical properties correspond to that.

The best they can surmise is that the stability is related to the ability of the
bike to steer into a fall if it starts to lean, and that there are multiple ways
of constructing a bike that does this.

Thanks to Ron Gleason.