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I am writing this post regarding how to approach a situation I am currently in. First, I am an undergraduate student in math who started working under a professor last Fall. Prior to the start of Spring term, he let me know that he will be going on Sabbatical until early-to-mid April. Additionally, they would not have a reliable internet connection. 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. I am sorry if this is a ridiculous question.

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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).

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    Thank you for the helpful response. I was just not sure about how to proceed since I am an undergraduate student and not a graduate student.
    – Motig5753
    May 1, 2020 at 1:57
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    @Motig5753 If you like, you can ask the professor directly: how often would you like to receive email from me about this project? And is email the best way to discuss things or is another medium better? No better way to get clarity than ask. As you are doing research with him you would generally be the same as a graduate student, unless he has delegated someone else (one of his grad students) to supervise you.
    – Caleb Stanford
    May 1, 2020 at 2:01
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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.

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