Why is/are an electron/electrons a sphere/spheres ? Need the mathematical proof...
You won't find a mathematical proof that electrons are spherical because they aren't. What we do know is that the electrical field around a classical electron is, to the limits of the accuracy of the measurements we've made so far, the same as that produced by a spherically symmetrical charge distribution.
If you're thinking in terms of shape and size, you're thinking in purely classical terms, and the best classical description of an electron is that it it is a point particle of size zero. If you've read something that suggests otherwise, either it's wrong or you've misunderstood it.
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