I am, and have been, aware of all this.
Please show me how any of these represent major advances in AI, as opposed to just more processing power and some programming trickery. A clever program still does not represent artificial intelligence.
I am a software engineer by trade, and hardware is something of a hobby of mine. I have been keeping up. And while computing has done some awesome things in the last decade or so, I still have not seen anything that qualifies as a "breakthrough" in AI.
The only way the advances that have been made will lead to AI is if, as I stated, intelligence is more a matter of quantity over quality. And I am not convinced that it is.
The examples you gave, with the possible exception of Robinson's Conjecture, are all special-purpose software or tasks that can reasonably be expected to improve by throwing mere brute force and (human-written) programming behind them. But they will never pass a Turing test or make you a good martini. For the most part the AI question is really more about how a task is being accomplished, than what is being accomplished.
Some of the early computer proofs were seriously questioned because they made use of iterative methods that processed much more data than the verifiers could reasonably be expected to examine any other way. (And iterative methods are what computers have always been good at; they seem to have little in common with AI.) It came close to a situation where it would take one or more other computer programs to verify the validity of the software used, which could literally lead to an endless regression. Not because of any "intelligence" involved, but simply because of the sheer amount of computation.
(I should note that no endless regression should be necessary unless the problem under consideration is NP-complete, in which case there is no way to know in advance.)
In any case, in that context, I would not pretend to make a judgment about how Robinson's Conjecture was proven without knowing more about how it was proven. I know what it is, but I know nothing about the proof.