A good rule of thumb I always use if a science article title has the word "breakthrough"in it, then it's probably not a breakthrough.
If the title does nothing to describe the actual discovery made and solely consist of "Breakthrough in [Field]" then it's definitely not a breakthrough.
A good rule that could be refined by applying it only to topics that the general public cares about. A breakthrough in analytic number theory or international accounting standards is probably genuine, one in AI or battery technology probably not.
Why is that? I suppose complex maths is harder for the science journalist to understand, and doesn’t get as many clicks, so if they are reporting on it it’s because it’s substantial?
Any rule that reduces the posterior of a breakthrough is generally going to be an improvement. Unless your definition of "breakthrough" is extremely generous.
If the title does nothing to describe the actual discovery made and solely consist of "Breakthrough in [Field]" then it's definitely not a breakthrough.