7. EM Drive
In 2015, news of an "impossible engine" hit the headlines. The RF resonant cavity thruster is a controversial type of EM drive that could, theoretically, power a ship to Mars in just 10 weeks without rocket fuel and could even enable us to reach the edge of the solar system in a matter of months, not years. If it works, that is. The thing is that an engine like this actually breaks some of the most fundamental laws of physics, the conservation of momentum, and yet there have been hints of an experimental engine of this kind actually working. It could be an error in the readings or some kind of contamination, but if the reports are to believed then there's an engine in a lab somewhere that is producing thrust and no one can figure out why. If we can figure out how this works and why this works, even if it's not quite the same as our initial thoughts, then this kind of engine could potentially power the human race out towards the stars. We could seen massive advancements in our exploration of the solar system and understanding of the universe, it could even spur a space tourism industry in the near future. Fingers crossed then, eh?