[dron57]

Your example of looking at a problem from more than one angle made me think of the problem of finding the Hubble constant that describes the rate of expansion of the universe. There are two recent methods which have different estimates for this rate of expansion.

PBS Space time has an excellent video on the topic: https://www.youtube.com/watch?v=72cM_E6bsOs

[analog31]

Indeed, one of the things that's possible in physics is to nail down the experimental results to the point where, if two results disagree, you know that they really disagree, and that it's not just a statistical fluke. Then it gets interesting.

In physics, when a result raises more questions than it answers, we call it "job security." ;-)