Pardon me if the following comes off as pedantic, I do not know your level of expertise and want to continue the discussion from the same point of base knowledge.
To my game playing point, and to start from a simple example, in Tic-Tac-Toe, an AI opponent will always beat humans because they can search through every possible move to end-game and always make the correct move. For games like Chess and Go, the search space is far too large to search to a terminal board position, so we need to use ML and heuristics to evaluate the value of a given board. These evaluation functions and heuristics are designed by utilizing human insight into the game. IBM's retrospective on Deep Blue is a fascinating read, and I suggest anyone check it out if they're interested in AI and game playing[1]. You'll see how they built their evaluation function with the input of chess grandmasters, particularly in implementing opening books and prioritizing center play in the early game. AlphaGo's system is not entirely dissimilar[2]. You'll note that significant advances were made as AlphaGo continued to play and learn from human opponents.
The point is that both these systems (and all game playing AI agents that I know of) search through possible board states and make decisions that are fundamentally reliant on the intuitions of humans. Furthermore, humans make decisions like this as well. We generate all the possible decisions we can make, and rule out invalid choices either implicitly (though sub-conscious bias and knowledge) or explicitly (thinking through a decision). Computers do not have the advantage of implicit evaluation, so we must program that explicit evaluation and use massive amounts of data (for deep learning, anyway) with ML techniques to validate those intuitions.
Both Go and Chess are deterministic games. Given that even these games haven't been solved, the stochasticity of the various domains you described are orders of magnitude more complex and we honestly need several breakthroughs before we come close (I have no sources here, this is just my opinion. I feel that most of the success of AI right now is the standard M.O. of a lot of Academic CS: Things 'work' for certain definitions of 'work'. The breakthroughs are great and impressive, but the constant extrapolation by pundits and the general media is both irresponsible and fallacious).
And yes, it really is a lot about processing power. Neural Networks have been falling in and out of fashion since the 1950s. One big factor of the recent ressurgance in popularity is due to GPU utilization and cloud computing (admittedly, the availability of data via the internet is another large factor, among others). That's why Google, NVidia, Apple, and others are investing so much into ML specific hardware.
And let's not kid ourselves: training any ML model takes a lot of time and a lot of manual adjustment of hyper-parameters. We're talking about possibly hundreds of hours of manual input for a single model (novel ones mostly). That's why every minor breakthrough merits a white paper (sort of joking, sort of not...)!
I think we're making the same argument with your linear algebra example; that machines can't reasonably replace humans. My amended version of that argument is that machines can and should extend and augment human capability. Despite the linear algebra that happens, any form of decision making and cognition is in someway designed by a human. So despite the vectorization of the world (as seen by an AI), they will process through the lens of human cognition; because I don't think we can build systems that don't somehow stem from our own cognitive processes.
As to your specific fears, I seriously doubt we'll be able to make enough progress within 17 years for AI to dominate those fields completely. I agree that AI will probably become a presence in many of those domains, but I do not think we will be "giving up control". Remember, these systems will be operated by individuals. So, I would say that there is some evidence to suggest that within 10-20 years, humans will be using AI to produce higher quality art, jurisprudence, etc. It is also true, that this raises the possibility for humans to abuse this technology, but this is inescapable for almost any human achievement. I think openness and transparency is the best safe-guard against this possibility, and I would encourage everyone to vocally oppose any integration of AI into public systems without extreme transparency.
Beyond that, humans that have and always will be the cause of wealth inequality. Also, you provide no evidence that inequality is greater. In the 21st century, inequality has increased [I don't feel like sourcing this, but Google is reasonably good here], but I would like to see research confirming that we're worse off than the heights of Feudal society, or other equally tyrannical periods of human history. How would you foresee AI contributing to wealth inequality? I only see AI as a contributing factor to increasing wealth inequality if it remains in the hands of few.
I've definitely rambled here, but I blame that on the few drinks I've had. I think my point still stands; humans kill people, AI doesn't kill people (and we're at a point where I think we can ensure that it doesn't).
As a side-question, what exactly is significant about 17 years? Is there some prediction out there that uses this number, or was it an arbitrary number?
1. https://pdfs.semanticscholar.org/ad2c/1efffcd7c3b7106e507396... 2. https://storage.googleapis.com/deepmind-media/alphago/AlphaG...