A Comment on "On Some Contradictory Computations in Multi-dimensional Mathematics"

Abstract

In this paper we analyze the status of some `unbelievable results' presented in the paper `On Some Contradictory Computations in Multi-Dimensional Mathematics' [1] published in Nonlinear Analysis, a journal indexed in the Science Citation Index. Among some of the unbelievable results `proved' in the paper we can find statements like that: (i) a linear transformation which is a rotation in R^2 with rotation angle theta different from nphi/2, is inconsistent with arithmetic, (ii) complex number theory is inconsistent. Besides these 'results' of mathematical nature [1],offers also a `proof' that Special Relativity is inconsistent. Now, we are left with only two options (a) the results of [1] are correct and in this case we need a revolution in Mathematics (and also in Physics) or (b) the paper is a potpourri of nonsense. We show that option (b) is the correct one. All `proofs' appearing in [1] are trivially wrong, being based on a poor knowledge of advanced calculus notions. There are many examples (some of them discussed in [2,3,4,5,6]of complete wrong papers using nonsequitur Mathematics in the Physics literature. Taking into account also that a paper like [1] appeared in a Mathematics journal we think that it is time for editors and referees of scientific journals to become more careful in order to avoid the dissemination of nonsense.