James Anderson is perpetrating an elaborate hoax, claiming to have finally "solved" the issue of division by zero in the real numbers. The BBC is apparently unaware that this is a joke.
As so many others who have tried to "solve" division by zero have found out in the past, issue here, of course, is not that one can't divide by zero; you can modify the axioms of the real line and define division by zero in any way you want. The issue is that changing these axioms makes the real line no longer satisfy the axioms of a ring, and so much of algebra and topology can no longer apply. Of course one is free to invent their own ring theory and topology, but why bother? A century of research into abstract algebra will no longer hold, and it is not clear what good such a number system is.
All in all, James does a great job of parodying how out of touch with reality computer science professors really are. The paper is written in Microsoft Word, not LaTeX -- check out the unreadable notation and poor formatting, its hilarious.