To a student who just solved a difficult math problem

1. That’s a brilliant deduction.
2. You’re as smart as a whip.
3. You’re really catching on.
4. That’s a step in the right direction.
5. You’ve got that down pat.
6. Nobody can do it better.
7. You should be proud of yourself.
8. You’re a pretty smart cookie.
9. I’ll be happy/glad to write a letter of recommendation for you.

To a student who just solved a difficult math problem