Stereotypes simply are not, and never will be true. It's simple. "Black people like chicken." If there is a single black person that doesn't, the stereotype is false.
People hate the truth, and deny history, and therefor repeat it.
The thing is because it's a stereotype people run into the problem of whenever you see that stereotype play out it reinforces them seeing the stereotype as true while when it doesn't happen they just don't pay any attention to it. Take the stereotype that all British people have bad teeth well you see a British person with bad teeth and it just proved the stereotype true. But in 2009 a study was done and it found Great Britain is one of the highest ranked countries for healthy teeth.
You realize the very definition of a stereotype is a sweeping generalization or cultural misconceptions, right?
I mean do black people eat fried chicken 95% of the time? Do white people fuck horses (yes this is a stereotype in America) 95% of the time? Are those of the Jewish faith greedy 95% of the time?
Stereotypes are often based in reality, and do hold some degree of accuracy.
The issue with them is that they are not a 100% representation of every person you meet who fits the type.
Even if it is the case that a disproportionately high amount of Asians are good at math compared to other demographics, that doesn't mean you can just walk up to any Asian and expect them to be an expert mathematician. Many Asians are not great at math, so you cannot expect a particular individual Asian to be good just because they are Asian. You have to verify that information.
Even if 95% of Asians are in fact good at math, you cannot guarantee that a particular random Asian individual that you encounter is, so it's unfair to judge them as such.
Not fair to the exceptions to judge them instantly.
This is the problem.
Stereotypes are often true, and that's why they exist. It's a natural function of the human brain to associate things into different categories based on certain sensory cues. That's extremely useful in the animal kingdom for survival and such.
However, when it comes to humans, we can be so much more complex, that this system isn't good for categorizing us. I think in general, stereotypes have like a higher chance of being right than wrong, otherwise they wouldn't truly exist, but when a human is categorized or predetermined to be a certain way just because of a superficial characteristic, it can be offensive as it degrades the person as a whole. No one human should be reduced to a simple prominent aesthetic feature.
in today's online and multimedia world there is an argument for stereotypes not being true at all but they became stereotypes simply because that's how news/TV/movies continually portray the same trope.
I mean, there's the "asians are good at math" example in the OP. If you think about it, it's really only "transfer students or wealthy immigrants or native born asians are potentially good at math." I mean if you really think about it, the vast majority of Asian's globally have barely had 4(or less) years of education total.