It's often occurred to me it might be possible to resolve some of the more difficult problems in physics such as infinities and renormalization in QED if we had

It's often occurred to me it might be possible to resolve some of the more difficult problems in physics such as infinities and renormalization in QED if we had some other form of mathematics that treated the 1/0 matter differently. Other than posing the question I've never pushed my brain any further on the matter as I've just assumed that those with much greater mathematical brainpower than I have have either ruled it out or considered it not worth pursuing.