In math/physics, or generally in science, there are many moments where the success and the triumph come from the accidental, unplanned attempts. Moreover, there are some cases that originally having attempts for one specific question or a goal, but solve another seemly unrelated problems, or reach seemly the opposite goals. There are these kinds of moments leading to breakthrough of math or science.
[Question]: Can any of the readers here list more and others in the subject of math? To give us some inspiration and high motivations to be subconsciously aware of those random accidental moments.