He's seriously deluded. He believes that volumes of historical writings, C-14 dating, etc notwithstanding, that about a thousand years of recorded history never happened. Largely on the basis of the fact that the exponential population growth Europe has had since the British Agricultural revolution, if projected backwards in time, would say that there wouldn't have been as many people in Rome as there were.

Even a cursory understanding of, say, the trials our ancestors went through in the 1300s makes it obvious that he's wrong to project back his little exponential curve that far.

See http://www.revisedhistory.org/view-garry-kasparov.htm for details of Kasparov's beliefs. See http://en.wikipedia.org/wiki/British_Agricultural_Revolution and http://en.wikipedia.org/wiki/Medieval_demography for basic historical facts that show some basic flaws in Kasparov's arguments. (About his points on Roman numerals, they are indeed entirely unsuited to calculation. The Romans did all calculations using abacuses, numerals were just their way of writing down the answers for which purpose they are just fine.)