Quantum mechanics
Classical physics uses the mathematical methods of Joseph Fourier to make a math picture of the physical world,  It uses collections of smooth curves that go together to make one smooth curve that gives, in this case, intensities for light of all frequencies from some light. But it is not right because that smooth curve only appears at higher frequencies. At lower frequencies, there are always isolated points and nothing connects the dots. So, to make a map of the real world, Heisenberg had to make a big change. He had to do something to pick out only the numbers that would match what was seen in nature. Sometimes people say he "guessed" these equations, but he was not making blind guesses. He found what he needed. The numbers that he calculated would put dots on a graph, but there would be no line drawn between the dots. And making one "graph" just of dots for every set of calculations would have wasted lots of paper and not have gotten anything done. Heisenberg found a way to efficiently predict the intensities for different frequencies and to organize that information in a helpful way.