Too much abstraction? I would rather suspect lacking awareness of logical restrictions in combination with lacking checks of correctness, in particular by means of application without contradictions and other complaints.
Let me look back at the man who stands for introducing rigor into mathemats: Dirichlet. Jacobi wrote to Humboldt: "It is only Dirichlet, not Gauss, Cauchy or Jacobi who knowa what a completely rigorous mathematical proof is."
Was it really reasonable when Dirichlet "gave the well known example of the function f(x) that is 0 for rational and 1 for irrational x" (Ferreiros, p. 150)?
Mathematicians are trained to naively confirm this. I consider my question a decisive one. Likewise we may ask whether, as Cantor argued, one may infer from the fact that the amount of irrational numbers is neither smaller nor equal to that of the already infinite rational ones that it exceeds it and is larger than infinity. Didn't he ignore the so called 4th logical possibility: Such comparison does not have a reasonable basis. Galilei's Salviati came to this correct conclusion. With reference to the actual infinite, Steiner considered the reasonable Euclidean conception of line, plane, bundle of lines, etc. as aggregates of infinitely "many" points. I consider him still correct because the actual infinite is a useful while self-contradictory fiction. I would only prefer to replace "many" by much of because the amount of potential points strictly speaking evades counting even in the tiniest piece of the line.
In all, we find many mathematicians involved in obvious mistakes that are still not jet consequently admitted. It is obvious that Gauss meant phasors when he wrote points in complex plane. Rotation of points is obvious nonsense. Mathematics should not simply return to Euclid's notion of number. I recommend interpreting a number as the end-tip of a measure (arrow), no longer as a point that can neither be attributed to the left nor to the right.
Such benign corrections to the foundations of mathematics will merely cause some simplification. They are nonetheless required as to pave the way for acceptance of a mathematics in R for the sake of more realism in physics.
Do not get me wrong. I am fully aware of useful complex quantities. Let's clearly separate between correct and wrong. I maintain: The apparent symmetry of wave-function is an avoidable artifact.
Eckard