How Many Dimensions are There?

Dimensionality has been a much discussed subject since Minkowski formalized special relativity by extending 3D space to 4D space-time. However, there has never been any consensus on the number of dimensions that nature requires and there has been no explanation of why dimensions are needed at all. It is proposed here that dimensions originate in the theory of numbers, that extending the number of dimensions beyond the 3 required by Euclidean space necessarily requires a fundamental change in the meaning of the concept, and that, although various algebraic techniques allow such extension of dimensionality, the structures required always ensure that the number of dimensions and their fundamental characteristics remain ambiguous, leaving the final question unanswerable.