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I've seen internet jokes (at least more than 1) between mathematicians like this one here about someone studying a set (or another object such as a group) with interesting properties. And then, after a lot of research (presumably after some years of work), find out such set couldn't be other than the empty set, making the work of years useless (or at least disappointing), I guess.

Is this something that happens commonly? Do you know any real examples of this?

EDIT: I like how someone interpreted this question in the comments as "are there verifiably true examples of this well-known 'urban legend template'?"

I've seen internet jokes (at least more than 1) between mathematicians like this one here about someone studying a set with interesting properties. And then, after a lot of research (presumably after some years of work), find out such set couldn't be other than the empty set, making the work of years useless (or at least disappointing), I guess.

Is this something that happens commonly? Do you know any real examples of this?

EDIT: I like how someone interpreted this question in the comments as "are there verifiably true examples of this well-known 'urban legend template'?"

I've seen internet jokes (at least more than 1) between mathematicians like this one here about someone studying a set (or another object such as a group) with interesting properties. And then, after a lot of research (presumably after some years of work), find out such set couldn't be other than the empty set, making the work of years useless (or at least disappointing), I guess.

Is this something that happens commonly? Do you know any real examples of this?

P.S. Honestly I don't known which tags to use, or even if this question fits here, so feel free to add/remove tags as needed.

I've seen internet jokes (at least more than 1) between mathematicians like this one here about someone studying a set (or another object such as a group) with interesting properties. And then, after a lot of research (presumably after some years of work), find out such set couldn't be other than the empty set, making the work of years useless (or at least disappointing), I guess.

Is this something that happens commonly? Do you know any real examples of this?

EDIT: I like how someone interpreted this question in the comments as "are there verifiably true examples of this well-known 'urban legend template'?"