The theory of eleven dimensions (11D) actually was first postulated nearly 60 years ago using the Standard Model. ( http://en.wikipedia.org/wiki/Standard_Model
) It sat there as a possibility until it was pushed into prominence with String over 20 years ago when String ideas started to prove themselves as the only possible way of expanding the Standard Model to encompass everything. Since the 11 D Standard matched 11 D String this has become the key for advanced theories during the last 20 years. So we are referring to an idea that is half a century old and has survived decades of scientific debate and has only gotten stronger support. The Wired article
has been based on incomplete data. This is common with popular journalism. Even journalists in technical magazines don't have the required background to have followed fully the debate.
The idea that main stream science doesn't consider String strong enough is invalid. Everyone of the top theoretical physicists in the world use String. Hawking is not alone in his use of the theory.
Here is how we get the 11 plus dimensions. Consider a shadow on the ground. You don't have to look at the object making the shadow to calculate its size and shape because you know how light is projected and the angles that the light has traveled. So from a two dimensional object you can calculate what the three dimensional object looks like that projected the 2D shadow (you can take this up to 3D shadow and 4D object if you measure over time). Doing the same type of measurements on our 4 D universe you can calculate that 11 Ds or more project themselves onto our 4 D universe by the way those shadows caused by the 11D make themselves felt on our 4D.
Both the General theory and String come up with at least 11-dimensions. Since the 11-D General theory was developed in the 1950s this is a relatively old physics concept. There are just enough gaps in the real world that require more than 4-D to get the mathematics explaining them to work.
Consider this: You have a shadow moving on the 2-D ground. You use mathematics to explain how it moves and distorts during the day. The math becomes very complicated. Now instead of using the 2-D math you create a 4-D world where there is a stationary tree that doesn't change directions or size and project a shadow onto the ground as a light source (sun) moves. The math is much easier and you have rendered the 4-D world into a 3-D event (motion across a 2-D ground with time the third dimension). This is what is happening with the 11-D universe and our 4-D ability to see it. The math tells us that there is a projection from more dimensions into our 4-D shadow world. We are now in the realm of CSI. We get clues about the crime, or in this case the way the universe works. We then build up what has to happen for these events to occur. Blood on the ground means that someone was bleeding. Typing the blood tells us about the person or persons who bled. We have never and can not physically see the event but the clues tell us that it happened. We can not see the 11-D but the physical clues tell us that they are there.
M-Theory is not a theory in the mold that most people think of. It does little to explain a specific physical event. It is a framework that explains how the math describing something such as Quarks and the math explaining something such as a super nova relate to each other and how to pull the overlap between the two extremely different events together. It sets the parameters on how these different equations have to be framed so there can be a passing of information between the completely different events. M-theory is a theory that sets the conditions that all of the other, more specific, theories have to meet.