:My reference was http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=335649. This is not my area of speciality, but the paper claims that the result therein proves Bernstein's conjecture up through real dimension 8; in other words, the Bernstein conjecture is proved as a consequence of the more general results in this paper. The paper also mentions that there were previous results of Almgren that established the Bernstein conjecture in real dimension 5 (presumably in lower dimensions as well, but I don't know for sure about this point). Hope that helps.  -