The meat of Markowitz 1952

In the end, what Markowitz 1952 does is twofold:

First, it introduces the problem of minimisation of variance subject to constraints in the application context of portfolios of return-bearing entities.  Once introduced, the case of a small number of entities is solved geometrically.   By 1959, the preferred solution to this was the simplex method.  By 1972 Black noted that all you need is two points on the efficient frontier to be able to extrapolate all points.  By 2019 you have a plethora of R (and other) libraries which can do this for you.

Second, a connection is established with the then current economic theory of rational utility.  Here he sketches the briefest of arguments for whether his maxim (expected mean maximisation with expected variance minimisation) is a decent model of investment behaviour.  He claims that his rule is more like investment behaviour than speculative behaviour.  However he makes a typo (one of several I spotted).  He claims that, for his maxim  $\frac {\partial U}{\partial E} > 0$ but also that $\frac {\partial U}{\partial E} < 0$ whereas that second one should read $\frac {\partial U}{\partial V} < 0$.  His claim that his approximation to the wealth utility function, having no third moment, distinguishes it from the propensity to gamble.  It was t be over a decade later before a proper mathematical analysis of how the E-V shaped up as a possible candidate investor utility function, and, if so, what an equilibrium world would look like if every investor operated under the same utility function.