What is the best Texas Hold'em Poker Strategy, that has been mathematically well justified? And what's it's mathematical proof?
Your question is far too broad. There are many different variants of NLHE. Cash, multi-table tournaments that are either scheduled or sit'n'go style, heads-up, 6-max, 8-max, 9-max, 10-max, 11-max, live play, online play, etc. etc. etc.
On top of that, NLHE is a game complex enough that it's currently unsolvable. There are too many possibilities and 3-player or more poker can also result in situations where there isn't a game theory optimal solution. As such, most game theory approaches involve approximate games in which player's strategic options, or the setting of the game, are restricted so as to make analysis easier. Principles that can then be applied to real play are then derived from said approximate games.
Poker is a game of uncertainty and risk. The better decisions you make, using the incomplete information at hand, the more money you'll make at poker, regardless of the variant. All poker strategy revolves around that concept.