The math behind MPT might be hand waved as followed: goal seek a maximum portfolio return by combining assets with minimal correlation under a fixed risk scenario. In the end, you will have portfolio that will give you the maximum theoretical return for your selected amount of risk.
In practice, outside of running a hedge fund, or a mutual fund with explicit investment guidelines (e.g. we invest in emerging market energy companies), a responsible asset manager has no choice but to follow MPT. In other words, if you are not a specialized fund, there is no mathematical justification for deviating from an MPT constructed portfolio. By definition, any deviation from a MPT balanced portfolio means you have either a) taken on more risk than necessary or b) reduced your potential return or c) do not believe in the underlying assumptions of MPT.
So what is the amateur person worth $25M to do today? As with all things, you should seek professional advice. There are many nuances of tax efficiency, estate efficiency, asset protection, personal needs, etc. that a professional advisor should guide you through.
Apparently the folks at WealthFront and FutureAdvisor are selling MPT driven portfolios to employees of SF bay area tech firms.
edit: As a couple of users point out below, there is controversy over the effectiveness of MPT including: whether the models effectively capture the distribution of risk vs return and whether the values desired by the models can be calculated with proper accuracy. PMPT (post-modern portfolio theory) builds upon MPT. Lastly there are critics such as Nassim Taleb (of Black Swan fame) who find some of the core assumptions flawed.