Will Carington, works for Noodle
My advice would be to think about whether you could finish the sentence with a verb, as in "He is more alert than I [am]." If you can, then using the subject pronoun "I" is generally considered correct.
That said, there is actually a whole debate surrounding the usage of "than" as a preposition, in which case the object pronoun "me" could also be considered correct. But again, "I" is probably the safe choice in this case.
For general grammar and usage questions, I'd recommend consulting the following resources:
- University of Chicago Grammar Resources
- University of Illinois Center for Writing Studies Grammar Handbook