On my dark days, I suspect that that’s exactly what string theory boils down to…
Physicists please help explain: jewel-like geometric object that dramatically simplifies calculation
Agreed. The circuitousness doesn’t bother me – as if some explorer slogged through rain forest and over mountaintops to reach a remote destination only to discover a secret airstrip that he could have flown into – but it is noteworthy. Whether the generalization angle bears fruit, time will tell.
You should go play a little arXiv vs. snarXiv to drive that feeling home. 
Let me try to break it down to a simpler level. We wish to study interactions between particles. In particular, we ultimately wish to answer practical questions like “How long will this particle typically last before decaying into something else?”, or “If I shoot a beam of this kind of particle at a beam of this other kind of particle, how likely am I to get one of this other kind of particle coming out?”. To do this, we come up with mathematical models that describe all of the kinds of particles we know of, and their known interactions.
Sometimes, we also come up with what’s called toy models: mathematical models of particles or interactions which, so far as we know, do not exist. We do this not for their own sake, but to give us practice on using the relevant mathematical techniques, and to facilitate teaching these techniques to other physicists (the toy models are generally simpler than the real-world models).
But just having the mathematical model isn’t enough, either. You also have to do the calculations involved in those models. This is, in general, really hard. The most common approach is to use something called Feynman diagrams: You draw a bunch of pictures with squiggly lines, subject to some rules, and then you convert each picture into a relatively straightforward calculation according to some other rules, and then you add up the results of all of those calculations. Unfortunately, this is only ever an approximation: To get the right answer, you need to add up the results of all of the diagrams, and there are an infinite number of them. In practice, what people do is to just take the few most significant diagrams, add up those, and call it a day, but for some situations, you might need a very large number of diagrams, and for others, sometimes no number of diagrams is enough.
These people have found another way of doing the calculations, that gives the exact answer directly, without approximations and much more easily than the Feynman diagrams. The catch is that the method they’ve found only works for one of those toy models, that doesn’t describe the real world. What makes it exciting is the thought that maybe, they’ll be able to come up with a similar method, that will work on the real models. That would be really great, but they haven’t done it yet.
Thanks Chronos, that’s a nice summary.
And just to be absolutely clear my facetious comments weren’t meant to suggest you guys were making it all up, far from it, merely that whenever any of us drift into “shop-talk” it can get quite abstract and exclusive quite quickly and even more so in your area seeing as you deal with some uber-abstract concepts from the get-go.
That probably explains why we revere the great physicist educators so. Their genius lies as much in their ability to simplify for us mortals as it does in their arcane flights of mathematical fancy.