Oh, c'mon on. Even I know that... you pedal it.
Lol, I know it sounds out there and it humored me when I came across it also. For real though, all attempts by modern science to conclusively prove how a bicycle works and remains stable have failed thus far.
(The bicycle conundrum is found on page 6)
7 Simple Questions with No Answers | Open Science Questions
It is rather humorous, but also a good example of how modern science has more questions than it has answers.