As it turns out, contemporary theory contradicts the traditionally view that Neanderthals were bulky oafs; rather, as they had larger craniums, it is actually more likely that they were more intelligent than modern man. So, if they were so smart, why did they die out?
They answer?: They didn't network well.
Due to the shape and position of the Neanderthal larynx, they could emit only a very limited range of sounds. Communicating complicated ideas would have been difficult; and as this article points out, although intelligence foments inventiveness, it is the ability to share that information that allows societies to flourish:
Studying the inventiveness of Homo Sapiens scientists have found that literally all the major innovations that have changed the way we live, from the use of fire, to agriculture, to writing etc., have developed only in a few places. For example agriculture appeared independently only in around seven places on the entire planet. All the rest of human populations that engaged in farming did it because they had learned it from somebody. Therefore, the most important aspect of inventiveness is not the ability to invent, but the ability to transmit and to preserve innovations.Neanderthals couldn't spread ideas efficiently; on the other hand, one of our biggest assets as a Homo Sapiens is the ability to learn from others - to absorb innovation and improve upon it. Try to remember that next time you're stuck in a rut. Rather than sit there waiting for that Eureka moment, trying going to a few of those places where you know innovation is happening (meet ups, events, conventions).
Get out of the cave! ;-)