Do you believe that a computer can out-do, out-wit, out-smart man's brain?
The current standard in establishing actual artificial intelligence for computers is called the Turing Test, and was introduced by Alan Turing in 1950 as a way of measuring if a computer could think. At this point (2012) there is no computer that passes the Turing Test, although many computers are attempting to simulate the passing of limited portions of the Turing Test.
A computer is a device that performs many operations very quickly (billions of times per second!), and yet it does not think or interpret any of the data that it manipulates. With the invention of faster computers, it seems as though they are out-thinking humans. For example, computers regularly beat humans at playing chess, and yet, they have no actual knowledge or understanding of the game. There is no feeling or thought involved, just billions of calculations.
Despite all of the advances with computer science in the last 70 years, these devices have no ability to reason or think or out-do humans, and that does not look like a possibility any time soon.
On the other hand, you may say that eventually computers can do so many things better than humans. This is true, but in the same way, a car goes faster than people, and yet we do not feel threatened by cars!
This sounds like a questions coming out of the film, "The Matrix." There is much in way of writing on this issue about intelligence and whether or not artificial intelligence can match or surpass that of the human mind. I think that humans can remain distinctly ahead of a computer's level of intelligence. Seeing that computers remain as an application of a human's mind, I think that we hold the advantage of them and must be mindful of that. With this in mind, I do believe that a computer can outwit or outsmart a human in particular settings. Computerized chess games are a fine example of this, in that the computer can calculate potential outcomes of a move in a faster rate of speed and with more accuracy than many humans. This is only one instance where a computer can process information faster and with greater accuracy than a human being. Spreadsheets, calculations, as well as other endeavors where the processing of information is an end product is something where a computer can be more effective than a human.
It depends on the subject. While a computer might be able to calculate difficult formulas faster and more accurately than a human could, that same computer cannot write a thoughtful analysis of another written work which includes personal opinion and a discussion of nuances (as least not yet). The key to answering this question in general is to ask who creates a computer in the first place? Would a computer even exist without the human brain required to design and program it?