1. However brilliant she is, she won't be able to solve this math problem.

Question

2. However brilliant she may be, she won't be able to solve this math problem.

3. No mater how brilliant she is, she won't be able to solve this math problem.

4. No matter how brilliant she may be, she won't be able to solve this math problem.

(What expressions are grammatical? Are all grammatical and the same? Then which ones are commonly used? Thank you for your help.)

Answer 1

All sentences are fine and all mean about the same thing. The only correction needed is the spelling of "matter" in #3.