1. If we want to "solve" chess "problem" we should calculate only important moves. I predict if we would make a close to perfect artificial neural network then we could "solve" it. But if that happens I am going to be really upset.
2. I can agree only partly. There are some openings in which you are forced to trade off minor pieces for instance Petrov's Defence.
3. 100 % correct - if you are at least a mediocre player you know that pieces on the board somehow reflect your personality.
4. Chess has great history. I highly recommend you to read Garry Kasparov's "My Great Predecessors".
As man of the humanitarian profession (mathematician) I can say that chess is an art. I like chess because it's the only thing I can't calculate.
1. Complexity- 10^120 combinations is more than the number of atoms in the known universe.
2. Exchanges- I think it's cool for example when Magnus and Fabiano were playing and they agree on exchanges that simplify down the position. Two players in competition with one another yet at that moment in time they are mutually cooperating with one-another. It is hard to think of an analogy for this in other sports or games- chess is a confrontation of two minds yet much of the course of the game is an agreement, or negotiation between the players. One could of course play belligerently and refuse any exchanges as well
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3. Layers - one can play on different elements - you can play for a space advantage, a material advantage, a positional advantage, a tactical advantage, playing for initiative or controlling tempo, etc... there are all these different ways of analyzing the game and in one situation a material advantage might win, yet in another sacrificing material for a positional advantage might win. Is the element or layer you are trying to play for a reflection of your personality?
4. History I always get a kick when I am playing a game with someone and the game explorer tells me I just played some variation of an opening like queens pawn zuckertort chigorin variation for example. As a noob I have very limited knowledge of openings and various lines, so when I make the same opening choices as some notable historic player it always gives my brain a little tickle. Like an explorer unearthing a dusty tome of some ancient wisdom. Typically afterwards I will go see if there are any lectures on youtube on that variation.
What do you like about chess? What keeps you coming back for more?