Mathematical reason for MCPP in audio recognition?
The Mel is an empirical model that describes the change in human pitch perception at different frequencies: until 1 kHz we perceive pitch changes in a linear way, after that, we perceive it in a logarithmic way, just as you said.

The pitch function relating real and perceived pitch differences is approximated based on the measurements made by Stevens in this work; an equation commonly used to approximate it is: 

$$f_{mel}=2595\:\log_{10}\:10\:\left(1+\frac{f}{700}\right)$$

As I understand there is no mathematical reason for using it, is just choosing a model of how human beings perceive sound and applying it to some interactive human-machine application in order to enhance it's performance