He actually constructs a solid foundation for nulity which probably most of the people yelling at him via comments to the news storycouldn't read 3 words of.
here. So Gohkan (my math genious Turkish roomie) says that the proof is pretty good but not really controvertable because he actually adjusts the axioms of algebra and calls the whole thing not algebra but 'transreal algebra.' Therefore contradictions with algebra are expected and the transreal 'field' is not expected to actually fit the definitions of a field. It sounds like a pretty sturdy system and really useful for computing but still requires development of a lot of things - how do you take derivitives what happens to limits if you don't have discontinuities etc? fun stuff but my brain is mush now ;-)