By now you've heard about IBM's super reader, Watson, who beat the human Jeopardy! champs.
Simulating artificially how the brain learns will be much more difficult. This article titled How Brains are Built in the January issue of Cerebrum, published by the Dana Foundation, explains why:
But brains, alone among organs, produce thought, learning, recognition. No amount of engineering has yet equaled, let alone surpassed, brains' abilities at these tasks. Despite huge efforts and large budgets, we have no artificial systems that rival humans at recognizing faces, nor understanding natural languages, nor learning from experience.
There are, then, crucial principles that brains encode that have so far eluded the best efforts of scientists and engineers to decode. Much of computational neuroscience is aimed directly at attempting to decipher these principles.