It's nonsensical to talk about an "optimal" distribution of wealth.
Also, technology allows for more total production (hence more total wealth), which would be great, but social policies in the western world inhibit the general population from scaling the number of children they have to track labor demand.
I should have referred to a 'Pareto distrubtion' rather than 'Pareto optimality' (which is more properly used to describe production possibility frontiers), but the underlying concept here is that it's quite natural for ~20% of the population to control ~80% of the wealth, on the basis that similar proportions recur throughout nature. I think this is 'optimal' insofar as growth is maximized by such a distribution, but of course you only get such distributions in theoretically perfect markets.
I don't think rigor necessitates the use of equations. Ronald Coase's nobel-winning contributions to the field of economics are almost wholly conceptual and devoid of math; at the opposite extreme, over-reliance on Li's Gaussian Copula proved unwise for Wall Street (http://www.wired.com/techbiz/it/magazine/17-03/wp_quant?curr...).