Full disclosure: I don't work in particles but have solved Feynman integrals for class work. Renormalization is indeed 'black magic'. But I don't think it is d

Full disclosure: I don't work in particles but have solved Feynman integrals for class work. Renormalization is indeed 'black magic'. But I don't think it is due to our limited mathematical knowledge. In my experience in mathematical physics, singularities appear when you have incomplete modeling ansatz, and so in this sense renormalization would just be a 'hack' that is necessary because of writing down imperfect equations. In other words, formulating the problem a different (and closer to truth) way would eliminate these infinities. I know some extensions of the standard model (string theory, in particular) do not have cutoff scales. But that is largely beyond my knowledge base.