If you're reading advice that's meant for students in various fields, not just mathematics, you should keep that in mind. I had lots of friends who published as undergrads. But these were people in other fields (mostly chemistry) where they worked in a lab at some point as an undergrad and had done some part of the work that led to a paper. We don't have positions analogous to those in mathematics (you can't "work in someone's lab") and so the expectations are different.
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