Uncertainty principle
Heisenberg realized that besides squaring amplitude he would eventually want to multiply position by momentum, or multiply energy by time, and it looked like it would make a difference if he turned the order around in these new cases. Heisenberg did not think it should matter if one multiplied position by momentum or if one multiplied momentum by position. If they had been just simple numbers there would have been no problem. But they were both complicated equations, and how you got the numbers to plug into the equations turned out to be different depending on which way you got started. In nature you had to measure position and then measure momentum, or else you had to measure momentum and then measure position, and in math the same general situation prevailed. (See the English Wikipedia article Heisenberg's entryway to matrix mechanics if you want to learn the fussy details!) The tiny but pesky differences between results were going to remain, not matter how much Heisenberg wished they would go away.