I'm not sure if this is the right forum for this topic, so apologies if I got it wrong. I've been reading the Feynman Lectures on Physics. In it, Feynman states that though Quantum Electrodynamics is highly successful, it is still extremely difficult to evaluate the equations to obtain a theoretical result to compare to experiment. I believe he said it was the integrals that were the difficult part(I imagine this would indeed be the case). The Feynman lecture were written/given in the sixties I believe, but I've also seen videos of Feynman in Auckland University in 1979, where he again reiterate this fact, and even states that there are experiments for which no-one has been able to evaluate a theoretical result. The question I would like to ask is; what progress has been made on evaluating such integrals in the last 25-30 years. Specifically, have computers and computer algebra systems helped to tame this task? Can anyone give an example of the integrals QED theorists are faced with, if indeed it is the integrals that are giving the trouble. Is this aspect of QED still a serious problem, or is it simply a question of throwing more CPU cycles at the problem. Naive I know, but my real question is can the equations nowadays be beaten into submission?