A scrutiny of the contributions of key mathematicians and scientists
shows that there has been much controversy (throughout the development of
mathematics and science) concerning the use of mathematics and the nature of
mathematics too. In this work, we try to show that arithmetical operations of approximation lead to
the existence of a numerical uncertainty, which is quantic, path dependent and
also dependent on the number system used, with mathematical and physical implications.
When we explore the algebraic equations for the fine structure constant, the
conditions exposed in this work generate paradoxical physical conditions, where
the solution to the paradox may be in the fact that the fine-structure constant
is calculated through different ways in order to obtain the same value, but
there is no relationship between the fundamental physical processes which
underlie the calculations, since we are merely dealing with algebraic
relations, despite the expressions having the same physical dimensions.
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