Traditionally, two physics phenomena were considered necessary for keeping bicycles upright. Turns out neither of them are. And humans aren't necessary either.
If anyone had gone up to their physics professors a few days ago and asked what keeps bicycles upright, they would have gotten two answers; gyroscopic stability and the trail. It was presumed for some time that bikes managed to stay so stable while rolling down a road because the fast motion of the wheels gave the bike stability. If a force acts on the top of a spinning wheel, the wheel won't topple over. Instead, it turn left or right - turning along an axis perpendicular to the force applied. And so if someone riding on a fast-moving bike starts to fall sideways, the bike won't topple, it will turn into the fall and stay upright.
The 'trail' of a bike refers to fact that, if a vector were drawn that showed the applied force of the steering mechanism on the front wheel, that vector would hit the ground before the wheel does. Trace down the bar that goes from the handlebars of a bike to its front wheel - if you continue the line, it will always hit the ground in front of point where the wheel hits the ground.
If the force were applied behind the point where the wheel hits the ground, it would be a little like trying to steer a car with 'back wheel drive'. The trail keeps the bike upright for the same reason the gyroscopic effect does. If the bike tips to the left, the trail will force the bike to steer to the left. It will steer into the fall, get its wheels back under it, and stay upright.
If anyone reading this actually did go up to their professor a few days ago, and did get those answers, they can go back now and act extremely snotty, because it turns out that those answers are not correct. Scientists have built a bike that has neither property, but not only does it stay upright, it stays upright without a rider.
First scientists took out the gyroscopic properties of their prototype bike by adding an extra set of wheels. These wheels don't touch the ground, but they are placed to spin in exactly the opposite direction of the actual useful set of wheels on the bike. So if this bike tips left, one set of wheels will feel a pull to the left, and the other will feel a pull to the right. The overall pull cancels out, and so the bike is not feeling any force making it stay upright. Scientists also designed this new bike with a steering mechanism that slants forward, a little like the handle on a toy wagon. This exerts force on the front wheels that ends behind where they touch the ground. By all rights, this bike should topple over in a second. And yet it doesn't.
This bike stays up only through speed and mass distribution. The front part of the bike, the part attached to the wheels that steer, is designed with a lower center of mass. This causes it to fall to the ground faster when tipped. (To get an intuitive sense of why, grab two wrapped lollipops. Place one so that it is standing on the tip of its stick, and the other so it is standing on its bulbous head. Let both of them go so they tip over. The one with its head on the ground - and a lower center of mass - will hit the ground first.) Since the front wheels with the steering mechanism move faster than the back back wheels, the bike once again steers into the fall, and its wheels come back under it when it tips.
This bike is definitely not better than the commercial bikes out there. And it doesn't prove that the gyroscopic effect or the trail don't help a bike stay up. In fact, regular bikes probably make use of both effects. The new prototype only proves that bikes don't need either effect to stay upright. They can just use properly distributed mass.