"Goodstein, a physicist, vice provost of the California Institute of Technology and an advocate of nuclear power"
I'm not sure what the "current known reserves" are. I would expect the known reserves to increase when mining companies look for more uranium. "The earth's energy needs" -- does he mean all the energy needs? The article seems a bit loose.
Generally we extract less than 1% of the energy that could be released from uranium. I wouldn't be surprised if future generations built accelerator-driven reactors and used spallation to fission the other 99%.