The Discovery Science Channel ran an absorbing program, “Parallel Universes” which I recorded and watched with some interest. However, that is not to say I understood it. So, I wonder what kind of math do I need to truly comprehend all this heady material?
Anyway, here’s what I could delve from the program
Initially, String Theorists believed that all matter is composed of teeny tiny strings, and that their research would explain the Big Bang and everything in the Universe - i.e., the Theory of Everything.
But they were thwarted by the fact that they kept finding more and more different strings to explain the same thing. Thus, instead of a TOE they were getting a TON: a Theory of Nothing. All their strings, they said, consisted of 10 dimensions — 9 were Spatial, 1 was Time.
Meanwhile a particularly brilliant guy, Michael Duff (perhaps a Brit, judging from his accent), was working on Super Gravity, and he insisted that the string was composed not of 10, but 11 dimensions. Sadly he was pooh poohed by the know-it-all String savants and for maybe 10 years poor Duff was in the scientific equivalent of limbo.
Eventually, however, things took a change for the better when the String theorists finally realized he was right. Eleven dimensions was right on the money, and with that, they found there were not 5, but just one string after all. Those other pain in the ass “different” strings were simply manifestations of the same string and in fact were quite the same. What’s more this one string was infinitely long and just 10 to the minus 20 mm wide.
But, somewhere along the line, this 1 string morphed into a membrane, and it gets even more incomprehensible after that. In a nutshell, here’s what I think I gleaned from the program:
Our universe is a Membrane — aka Brane. There are an infinity of other Branes, other Universes, out there all sailing along in (for lack of a better word) Space. The Branes appear in variety of shapes - Donuts, Balls, Sheets, etc.
When two Branes collide some very violent stuff happens. And this, say the M-Theorists, is precisely how this Universe of ours was formed.
Imagine an outline of two ripple-shaped Branes, looking more or less like colorless, cruller-shaped clouds. If these two Branes collide, when one Brane’s cruller outcroppings touch the other’s outcroppings, a super gigantic explosion results — a Big Bang.
And since these Branes are surging endlessly through Space, such collisions probably happen regularly, resulting in ever more Big Bangs, ever more Branes, ever more Universes.
What I like about this theory, is it seems to negate the damned Singularity. I just cannot accept the fact that all the matter in this universe was compacted in a tiny mass, maybe as large as an atomic nucleus, maybe as big as a thumbnail (Carl Sagan?), maybe the size of a clenched fist. Whatever. It is inconceivable (to me) that billions upon billions of stars in untold billions of galaxies and star clusters could be contained in such a small mass.
Another pleasant aspect is that the theory looks to what happened before our Big Bang, something that some scientists (including some Dopers) have insisted is pointless.
The upshot of M-Theory is that we don’t live in a Universe, but a Multiverse. And I don’t understand any of it.
So that’s my question:
What math background do the String and M-Theorists have? And even if by some improbable show of perseverance, I should acquire such knowledge, would I have any chance of getting a hold on the subject?
Somehow, I doubt it. 
AAMOF, that’s the one I was trying to find. I remember reading some of the articles.