Why can't we see yet computers trying to resolve or prove some of the Milenium Prize Problems or the Smale's list? Can nowadays our computers hop from theory to metatheory in a formalized language in order to discover possibly undecidable propositions? Could Riemann's Hypothesis, for example, always be undecidable for a computer? Could a computer working in first(or some other nth)-order arithmetic recognise the incompleteness of the system finding an undecidable proposition and proving, thus, the Gödel incompleteness theorem? If not, what is that it haven't but Gödel (or other human) yes? How can we equip the computer with this ability? Or we can't?
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