Etiquette for whether to send a follow-up email to a professor who will not have a reliable internet connection?

First, I am an undergraduate student in math who started working under a professor last Fall.

Congratulations!

During January I sent him an email with a question though I did not expect a response until he got back. Given that he has presumably been back for 2 weeks, is it appropriate for me to send him another email with a follow-up or should I wait for a response.

That is a long time to wait for a response to an email! Definitely you should send a follow-up.

Old emails often get lost in professors' email inboxes. In general, anything that has been sent at least 2 weeks ago is probably lost forever unless you send it again (and in this case it sounds like it was 3 months ago).

I usually send follow-ups 1 week later.

I am sorry if this is a ridiculous question.

Not a ridiculous question, but you are overthinking it :) Professors are just human; they aren't usually sitting around cursing anyone who sends them an email. Any question or concern you have you should go ahead and send -- as long as you can keep it polite and try to make it as easy as possible for them to understand and respond.

And since they are your advisor for your research, you need their feedback in order to progress successfully. Therefore, it is especially important to email them often (or connect through other means if email is not the best way with this individual).

There is no harm in sending an e-mail again under the pretext that the e-mail you sent in January may not have gone because of poor internet connection.