In 1957, Hugh Everett proposed that the probabilistic nature of quantum mechanics could be framed as a knowledge structure. Instead of a quantum being in superposed states, each possible state could be viewed as a separate 'world' of existence; in each world the state of the quantum was definite. Most importantly, he showed that equations based on this structure could be mathematically identical to the wave formulation of Erwin Schrödinger and to the particle formulation of Werner Heisenberg.
Then, in 1973, Hans Dehmelt and his students succeeded in trapping a single electron for over a year, showing that single particles are as real as golf balls. He continued this work by trapping a single ion of barium in an electrodynamic trap and showing that the single quantum defining the orbit of the single outer electron was also real and clear. I continued this work at Canada's National Research Council, and also observed that this single quantum was real and precise, in strontium as well as barium. Clearly, the 'fuzziness' of quantum mechanics was not in the individual quanta as had been assumed for so long.
Everett's formulation provides the clue: the uncertainty of quantum mechanics lies in the observer's perception, not in the individual quantum. (Remember that an observer in quantum mechanics can be as small as a single observable; assemblages as complex as humans are not required.) Schrödinger's Cat is in one state, it's us outside the cat's closed box that are in two states. It even provides the framework for many different views of the same quantum object, as I describe in The Many Memories of Quantum Mechanics.
So, the most productive view of quantum mathematics is that each quantum is in one state, it's the observers who are in multiple states. The math is correct, it's just that the standard interpretation of it has been backward.
other notes on physics