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I recently got a major revision from an applied math journal. However the only change the reviewer has asked is to put a remark on some theorem in the paper (why the specified theorem will not work under some general case). According to the reviewers the rest of the paper is fine.
I am slightly confused why is it a "major revision". Any suggestion will be helpful.
It varies by journal I'm sure but sometimes the line between "minor" and "major" revision is set by whether the reviewers wish to see the changes authors make in response to their comments before recommending acceptance.
A "minor" revision would go straight back to the editor and then to production while a "major" one goes back to the reviewers first. This might not be related to the amount of work required.
In your case it's possible that the reviewer wants to be sure you include an appropriate section about the limitations of the algorithm otherwise they wouldn't recommend acceptance.
Just make the required changes and send the paper back to the editor. Don't worry about what it's called – it makes no difference to your situation whether it's called a major revision, a minor revision or a super-special changey thing.
As to why it was described as a major revision, only the editor really knows that. Maybe it was even just a mistake.
(Background disclaimer: I’ve seen this from the perspective of an author and reviewer, not an editor.)
Major/minor can refer to the importance of an edit, not just to its size.
For instance, if a key statement in the paper is inaccurate (e.g. if a theorem is incorrect as stated), then even if the changes needed to fix it are small, the reviewer may describe this as “major revisions”, and the editor may agree. So the referee is saying “you seriously need to fix this!” not just “consider adding something about this?” For some journals/conferences, it also has the practical effect that the referees get to see the revised version before it’s accepted, and check that the required changes have been made — so, again, a referee may call a revision “major” because they feel it’s essential for correctness, and want to ensure it has been made before endorsing the paper for publication.
For some journals I've seen, a minor revision means we're going to accept the paper eventually, a major revision means we're still undecided.
Umm, why not just ask them (the editor and/or the reviewer)?
Maybe some paragraph got clipped out of the email? Maybe the reviewer is over-estimating the importance of that comment, or you are under-estimating it? You can just ask - no harm, no foul. It's not like you're asking for some special favor.
PS - Better to ask when while submitting the corrected version, so it won't appear you want to evade their suggestion.
Two additions to answers given sooner.
First: in most reviewing systems, reviewers may provide a decision (eg: accept, minor, major, reject), comments for the authors AND (blind) comments to the editor. It might happen that the latter influence the editor more, especially if they exist. Very often often, reviewers go open (only comments for the authors). But, in some cases, the comments to the editor can be different, or asking for a more drastic decision.
Second: each reviewer provides a decision. There is no standardized way of producing a unique decision (editor) from several rankings. For some, three minors make a major, two majors a reject, for instance. Up to the editor or the journal rules.
Third: in mathematics (or fields using maths heavily), more than in other sciences, a tiny detail can be quite important.
Anyway, what matters most is your precise answer. The rest is not in your hands.
Did I say "Two additions" in the preamble? Let me remind you that: there are three types of mathematicians, those who can count and those who can't.
