First of all, I have a pretty specific story about my rec letters, so if you don't feel like reading all of it, then please just answer this - how important are recommendation letters from people other than your teacher and counselor (like a research mentor), and can they actually have an impact on the decision at top schools like MIT?
Now, my actual story. This summer, I contacted a professor at University of Michigan, and he gave me a pretty interesting assignment - I had to research asteroid movement (and by that, I mean all the math that goes into calculating the exact position - it's a lot more difficult that you'd imagine), and then I had to write a computer program that would calculate planetary position based on some input parameters (orbital elements), and display an animation of these planets and asteroids and predict any close encounters in the future. I've put a ton of work into this program, and I'm actually still working on it, and the professor is going to use it to teach his graduate class once I'm done. Of course, I've included this project in my app and even submitted the program through SlideRoom to several colleges, like MIT and Harvard. My question is - do you guys think it's a good idea to ask the professor for a rec letter? He's a really busy guy (like most college profs, I'm assuming) and on top of that, he doesn't really know me that well - we've communicated mainly through email, and it was mostly just me explaining my progress. However, he does know that I've put a ton of work into this project and that I'm *pretty good* at comp sci. So, would his rec letter add anything to my app, and is it worth bothering him? Or is it possible that he'll just write a really generic one that'll actually hurt my chances?
Thanks for any responses, even if you didn't read the whole story - any feedback is greatly appreciated.