TL;DR: Article from 2001. Conclusion: "Most of you (again I’m using the plural form of the word) are likely to be around to see the [Cyber] Singularity". Interesting thesis, but the reasoning is flawed in my eyes.
I'd like to note that half the diagrams are "look, this shows an exponential trend with a nice regression line!". Except he often left out data from the linear plot in the exponential one when it didn't fit the regression nicely.
I do think that the topic of transcending human brainpower with artificial intelligence is interesting, but as others have pointed out, 15 year old (!) extrapolations are not exactly the best method for predicting the future today. I mean, you could conclude that, in a few centuries, we'll readily surpass the limits on computations imposed by
Landauer's principle ("there's only so many computations that can be performed before the universe reaches heat death").
Also see this.For comparison, consider the case of a simple biological population (e.g. bacteria). You'll observe exponential growth while nothing limits it, but clearly the earth (and actually the entire solar system) would be nothing but bacteria if one were to extrapolate from that.