A close read of the article suggests it is not Goldstein that says we have only enough uranium for 25 years of world energy. That seems to be the reporter’s statement as it is not in quotations. Indeed, so-called known reserves would only last a short time supplying the world’s energy in our current reactor systems without reprocessing. The anti-nuclear organizations have translated that qualified statement into the “factoid” the reporter repeats. It is promoted extensively and repeated till it is taken as fact.
Goldstein has a related article on the web.
http://www.its.caltech.edu/~dg/Essay2.pdf He does not claim uranium is soon to run out in this article.
I looked at nuclear fuel supplies for my own satisfaction back about 1990. The resultant article was published in Engineering Digest and is posted on my website. It goes a bit further into looking at fuel supply but does not cover all the bases. It looks like there are supplies for a long time, if we really need to scrape for it.