we've already had a small glimpse into this for at least 15 years now. the best chess player in the world (Casparov) has been beaten by a machine while playing chess. If it can happen in an extremely complex game like chess, it can happen in any niche. and if that happened 15+ years ago, imagine what it can do today with our better technology?
The very best minds on the subject today are almost in 100% agreement the question is not "IF" a computer will be vastly more intelligent than a human, but "when" that will happen.
Many are saying that the singularity will emerge by the year 2045. When this happens, AI will be more intelligent than biological intelligence. And the gap between the two intelligences will only accelerate. Here is an interesting article for you to read:
Singularity: Kurzweil on 2045, When Humans, Machines Merge - TIME
and from wiki:
Technological singularity - Wikipedia, the free encyclopedia
this is with our existing tech (silicon wafer chips utilizing a binary language). All bets are off once we develop a quantum chip/computer. If/when we develop a quantum computer, it's intelligence will grow much faster than the simple squared acceleration chart we are used to seeing. Instead, it will accelerate at it's cubed (squared, then MULTIPLIED by itself again) power, and will go almost vertical on the charts. Shortly after, in comparison, it will have the intelligence of a god, and we the ant. I just hope that it never gets a boot, else it may accidently step on us!!!