Uncertainty principle
Even though many physicists said they could not figure out the various math steps in Heisenberg's breakthrough paper, one recent article that tries to explain how Heisenberg got his result uses twenty math-filled pages. Even that article is not easy to understand. The math started with some really hard stuff and would eventually produce something relatively simple that is shown at the top of this article. Getting the simpler result was not easy, and we are not going to try to show the process of getting from an outdated picture of the universe to the new quantum physics. We need just enough detail to show that almost as soon as Heisenberg made his breakthrough a part of how the universe works that nobody had ever seen before came into view.