We will try to conceptualize a basic introduction to probability theory and quantum mechanics. There are a wide variety of open questions regarding the useful methods to find parameters that can be of importance in experimental quantum mechanics - or quantum information theory. In mathematics this question arises in the Shannon conjecture (the Shannon Entropy problem), this was proved in 2004 by four mathematicians Artstein, Ball, Barthe, and Naor. This version is a purely analysis problem, and is very much related to important characteristics of Fisher informa- tion, Entropy, and the Normal/Gaussian distribution. We will try to look at how they proved the entropy conjecture, and why it is of importance for physics motivated theories.