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.