Letter of Recommendation is very short and mostly nonspecific - What should I do? I'm an undergraduate mathematics student at a US university applying to graduate school.
I took two classes with a professor and did extremely well - he loved me, and when I asked him to write me a letter of recommendation he promised to write a very strong one. He liked me so much that he actually sent me his letter so I could see what he thought of me.

The letter is highly flattering and I am extremely grateful, but it is only two or three paragraphs long, less than half a page. This made me nervous so I looked up features that a letter might have. This letter has only a bit of specific information and mostly speaks in vague, but highly positive, generalities - i.e. "the student did well in my very rigorous class" with no supporting evidence as to what made the class rigorous.

I am very worried that an admissions panel may see it as a vague, formulaic letter and discard it. I truly believe this professor has very high confidence in my abilities and that the letter is sincere, but I don't think that it is effective. I asked for the letter pretty early on in the semester and reminded him three weeks ago so I don't think time was the issue.

What should I do? Would it be rude to ask him to rewrite the letter with details and supporting examples? I am almost tempted to seek out a different professor to avoid asking him. Any advice would be useful.
Almost all letters of recommendation for graduate program applications are short -- at my previous university, for example, there was a field that letter writers could fill in that essentially only held the equivalent of a single paragraph. Fundamentally, for current undergraduates, it is rare that a professor has spent more than a couple of hours one-on-one with you, and so it's hard to really say much of any specificity -- as would be the case if one were writing for one's own graduate student or postdocs, for example.

In other words, since almost all letters are that short, you're not suffering any harm. Go on doing what you're doing well, and don't worry about the letter too much.