It's not as simple as that, and I wish people would stop citing things like this. Yes, brain atrophy is a normal part of aging, and left unchecked this can impair mental function even at as young an age as 27. However, mental stimulation can slow and reverse the effects of this atrophy.

As an extreme example, check out this article: http://www.nature.com/nature/journal/v447/n7141/full/nature0... (ignore the title, the 'chromatin remodelling' is not the important part here)