Did Charlemagne exist? Were the Middle Ages nothing but a vast chronological hoax? Conspiracy fantasies about this have been thriving since the early 1990s, when a German self-promoter, Heribert Illig, began to publish on the subject. He had previously published books attempting to argue a new chronology of ancient Egypt, in the style of Immanuel Velikovsky. He switched to the Middle Ages with a 1992 book alleging Charlemagne is a hoax. See a list of his books here.
At about the same time, there has been a parallel spate of mathematicians ariring their suspicions about the ‘neatness’ of history (round numbers for durations of phenomena; the apparent cyclic nature of parallel events, etc.). Because of such ‘neatness’ of suspiciously round-numbered or symmetrical timelines, they allege, such histories must be the product of invention. I know less about this particular argument at first hand, but it seems that Gary Kasparov has published a sort of synthesis of these two types of argument—to judge from discussions which periodically arise on Usenet groups soc.genealogy.medieval and soc.history.medieval.
Based on a perusal of a couple of Illig’s books, and some of the stuff that floats around the Internet, it seems that such medieval chronological hoax theories boil down to something like this (in the mind of Heribert Illig or someone who buys his junk):
1. I don’t know a lot about the early Middle Ages; it seemed like not much happened then.
2. The Romans were very sophisticated; their empire was big, with lots of money, lots of people, and lots of technology. How could it fall? Did it really fall? (Variant: did it really exist?)
3. Europe allegedly ‘became’ sophisticated again after the year 1000, in the ‘Romanesque period’, when people built buildings that emulated Roman prototypes (hence the term ‘Romanesque’). Now, the era in between was alleged to have been one of depopulation, political instability, poverty, and the loss of various technological and aesthetic know-how. How can that be true? Maybe there was really no time between the Roman and the Romanesque periods, and we’re looking at the false insertion of centuries which didn’t actually exist?
4. Since there appears to be a big time period that I don’t know much about, maybe it has been a hoax perpetuated by a conspiracy of long-dead monks for evil purposes (Christianity, Latinization, world domination, etc.—fill in your pet bugbear here).
5. [etc.: the variations are predictable].
Well, the only basis for these ideas is a reductionist ignorance of the vast tapestry of historical and cultural material from Europe and her neighbors from the late Antique period to the year 1000. More and more rich and varied primary sources are available in modern translations each year, not to mention facsimiles of original documents (Codices latini antiquiores, etc.) and exhaustive studies of surviving buildings, etc. Any attempts to allege fraud or cover-up among a cabal of church leaders, or to use naive mathematical modeling for military or population history, look pretty silly to any one with a passing acquaintance with sources from the era.