The problem here is that what computers are good at is brute-forced logic and computations, whereas the human mind works heuristically. To overcome the human mind with brute-force logic and computations, you have to follow each possible branch of action--and there must be a preset conclusion, at which point you evaluate each eventuality, rank the paths, and follow the best one.
There are much better ways of doing it. One example,
Artificial Neural Networks, essentially model the neurons found in the brain; they would work exactly the same as a human brain if programmed correctly. The difficulty is in getting the structure correct.
There are, of course, some more current modes of AI where the program is shown "good" and "bad" examples, and its job is to learn what makes the good examples good and the bad examples bad. The problem is that many situations are too complex for the AI to properly evaluate within a "reasonable" amount of time, whereas the human mind generally does a much better job at playing such combinatorial games as chess and go.
Learning algorithms do not depend on combinatorial methods all that frequently. The only place combinatorial methods are the sole method of an AI are in video games, where emergent learning algorithms like ANNs are to much of a pain to use. In a video game, combinatorial methods are used because the number of tasks they must do is relatively small, and the tasks themselves are simple. Learning algorithms are bad for this since the emergent behavior is extremely difficult to predict and adding a single new task to the game AI means an entirely new training set must be made up and run through. In an attempt to make a strong AI though, the problem size and responses required would be massive. Learning algorithms like ANNs are much more efficient than combinatorial approached for these universe-sized problem sets.
In general, though, to unlock AI that surpasses the human mind you're going to need much, much better processors than we have right now--and IIRC, it has been proven that our current materials/mode of execution cannot possibly support the needed computing power (even with our rate of increase, there's an asymptote/leveling off that is supposed to happen pretty soon due to physical limitations). On the other hand, there's a good deal of hope in quantum computers and nanotech, but conventional computing will fail us here.
First of all, we have been 10 years away from the end of Moore's Law for several decades. While it is true there are physical limitations in the size of transistors, especially when they reach approximately 10 nanometers, this can potentially be made up for by other coming advances. Quantum computing, 3D chips, spintronics, ect.
* My apologies, by the way, since I can't support most of my statements. Most of it comes from bits of pieces of popularizations and meanderings on the internet, as well as newspaper articles. If you want to know more, you could try out Penrose's The Emperor's New Mind and Hofstader's Godel, Escher, Bach. Other things to search/look into would be the AI winter and refutations of the strong AI hypothesis.
Yes, I've looked into the various AI winters.
http://en.wikipedia.org/wiki/AI_winterThey pass with time and have little to do with the actual AI. Just people's perception of them.