A question that has been bothering me for a while, is why are we as a physics community so fine with remormalization in QFT? Experimentally (QED especially) the field is VERY precise, however, looking at the mathematical side of renormalization, it doesn't look... very logical. We get divergent integrals, but then say that we weren't measuring the right process, or our constants need to normalized, etc, etc. Where can I find work being done to make QFT more mathematically consistent? I'm just a newbie when it comes to research in QG (and like GR more than QFT), but this question has been bothering me for months, and I'm sure either missing something, or will have to just learn to 'accept' the mathematically inconsistencies of QFT!