1. There's no rule that INTPs have to love math or be good at it. In my case, it turns out I was not too bad at math, it's just that I wasn't that interested in it to begin with, so I slacked off a lot in school, with the exception of geometry. Also, the way math is taught, particularly in K-12 education, seems to be in a manner that isn't well-suited for intuitive types, considering they make up roughly 15% of the general population.
2. There's plenty of INTP artists and musicians. In general, extraverted intuition can lend itself to very original and imaginative expression. Being bored by strict adherence to
ANYTHING seems to be a fairly common complaint among INTPs. If you prefer a field in the arts, you should pursue it. Find out how your logical thought process gives you a unique edge or approach in creating art.
3. INTPs are just as subject to their emotions as anyone else, it's just that they don't always do a great job expressing them, or simply prefer to not express them openly. Nor do we like to feel governed by them. INTPs can also be very empathetic--if anyone disagrees, they might consider reading Einstein's
Ideas and Opinions. It's not whether or not they are empathetic and sympathetic so much as how they approach and handle empathy/sympathy which defines them.
I used to mistype myself as INFP and INFJ, even though I would often test as INTP. I think this is partly due to the fact that I allowed myself to be misled by the stereotypes surrounding NTs in general and INTPs in particular. Keirsey is largely to blame for initially misleading me. Many of the profiles based on MBTI were just as misleading. It ultimately took communicating with people of the various types and gaining a better understanding of cognitive function theory to help me see the truth.
The overall abundance of ignorance in the online typology community certainly doesn't help either. I've seen people accused of being NT impostors in Facebook groups for having emotional outbursts or for merely discussing emotions. I thought for the longest time that such outbursts were uncharacteristic for INTP, so how could I be one? Again, deeper understanding of the function theory led me to learn that it is because of their inferior Fe that INTPs can experience these outbursts. It seems counter-intuitive at first, but developing a healthy understanding and usage of Fe can in fact help INTPs better control such outbursts.
I'd recommend this site:
http://www.intpexperience.com/whereitcamefrom.php
It dispels a lot of the myths surrounding the INTP type and has useful advice on how to better get in touch with our emotions without letting them govern us.