It's an interesting topic that I'm looking over for a class. Both sides of this discussion have their points.
First, let's suppose we're going to take the position that the human mind is more than a machine. We would argue that a human can fall in love and a machine can not. Although, I'm not sure if I really should make that an advantage on the mind side of the argument, considering heartbreak and all... Anyhow, a mind can look at a small computer program and figure out if that computer program will crash or not. However, no program can be written to decide this, not even for small programs. If one could write such a program, no commercial program would crash, as you can bet that all software developers would have a copy of this program.
Some of the great mathematicians of the past century have weighed in that mind is more than a machine. Kurt Godel wrote out some fancy theorems back in the 1930's where he said that humans can sometimes solve an undecidable problem. Actually, I pointed that out in the above paragraph with the example of the halting problem. Sir Roger Penrose (his name already sounds like a genius' name) stated that brain uses quantum gravity. Well, computers are not quite up to the quantum gravity level.
In 1950, Alan Turing who is another great math geek of the century wrote a paper, "Computing Machinery and Intelligence." Despite the misleading title of his paper, he, too, felt that the mind was over the machine. Douglas R. Hofstadter pointed out the mind's abliity for self-reference, something which machine's lack. Although, I'm not so sure I know what's going on in my own mind sometimes, how about you?
On the flip side, there is the emerging field of artificial intelligence. Can a machine become "more" than a human? Some say that the mind is, essentially a machine. If you are someone that believes that, then you should have no problem accepting this concept. A machine can most certainly do math better than most humans. I know when I encounter the four letter word (see http://michalbasavraham.blogspot.com/2009/11/four-letter-word-which-haunts-my.html)
I'm quick to whip out my calculator. Yes, that little trusty machine that can break out the "M" lightning fast, what would I do without it?
Another example of machines being more than the mind may surprise you. It seems that in May of 1997, a chess guru was beaten by Deep Blue. Deep Blue is, of course, a supercomputer. When one considers this, who knows what shall come next for the advancement of machines? Some say that quantum computers are not that far off. Any Trekkie will immediately exclaim that Dr. Noonien Soong has proved this when he created Data. Unfortunately, Dr. Soong and Data are ficticious characters in a fictitious future world of "Star Trek: The Next Generation."
I conclude, that the question of mind vs. machine cannot be determined. Perhaps, each group has it's strengths or weaknesses. After all, aren't there humans that can do that which another cannot, yet that same other human has talents which the first doesn't have. For example, in high school, I was friends with this guy who was awesome at Math, Science and Computers. Yes, when it came to the "Catcher In The Rye," he was sooooooooo lost. Guess who got to tutor him? I love the bragging rights of that. I tutored a guy who graduated in the top ten of our class-wha ha ha!
As I write this post, I can't help but think of what one of my drill sergeants in the Army used to say, "It's mind over matter. I don't mind that you don't matter."