Well, it turns out that there isn't a handy-dandy reference for the numbers for various religions in the past. Mark Kirkorian over at The Corner linked to my earlier post where I expressed skepticism about the contention by the Vatican demographer that a larger number of Muslims than Roman Catholics is new. Other people have contacted me as well. In any case, my hunch is that in fact Muslims were more numerous than Roman Catholics in the period between 950 and 1750, though the window could be shorter. My reasoning below the fold....
1) By about 1000 most of the core Islamic lands had become majority Muslim. That is, Iran and what would become the Arab speaking world had fewer Christians, Jews and Zoroastrians than Muslims for the first time since the original Islamic conquest. It seems likely that Christianity was already extinct in the Maghreb by 1000 judging by the observations of Christian pilgrims, though Islam was likely only near parity in the Levant and Egypt (even today 10-20% of Arabs by ancestry from this region are Christian, the differential emigration rates has resulted in a far more Muslim Levant in 2008 than in 1900). South Asia (which is today 1/3 Muslim) was barely Islamicized, and in Indonesia only Aceh was Muslim. So the number of Muslims was far smaller...but what about Catholics?
2) Catholics in 1000 would be those who were both Chalcedonian and followed the Western Rite (the East-West Schism hadn't happened, but there was already a pretty obvious difference between Latin and non-Latin Chalcedonian Christianity). Spain was likely majority Catholic, but there was probably parity. The British Isles, Italy (except Sicily), France and Germany were Roman Catholic, but Poland, Hungary and Bohemia were only recently converted through the baptism of their ruling houses. Scandinavia was mostly pagan, though Christianization of the elites was already starting. The Baltic region was going to be pagan for centuries, while much of the Balkans and what became Russia were Eastern Rite.
In other words, though there were far fewer Muslims, there were also far fewer Roman Catholics. Here are some population numbers for the year 1000 from Power & Plenty:
Western Europe = 25 million
Eastern Europe = 15 million
Islamic World = 28 million
Central Asia = 9 million
South Asia = 79 million
Southeast Asia = 9 million
East Asia = 67 million
If I assume that Europe as a whole is 75% Christian (Catholic + Eastern),1 while the Islamic World is 2/3 Muslim and Central Asia is 1/2 Muslim, then for there to be more Catholics than Muslims, 88% of Christians in Europe would have to be Catholic. I don't think that's plausible, it was around 1000 that Byzantium as a mature civilization peaked in expanse. Around 1000 there were likely more Christians than Muslims because the ancient Christian communities of the Near East were extant at a much higher proportion than today. Finally, the Islamic demographic expansion into South and Southeast Asia had only begun, so we can't add too much to the balance from outside of the original Islamic empires.
I assume that in the period between 1000 and 1500 Islam attained a relatively large lead over Roman Catholicism. My rationale is simple: the areas that Catholicism conquered during this period, the Baltic, the Nordic region and a few regions of Eastern Europe were numerically trivial compared to the expansion of Islam into South and Southeast Asia. Additionally, the Christian communities of the Near East were further eroded at the expense of Islam, and Central Asia was fully Islamicized. It seems likely that even in 1492 around 25% of Spain's population was Muslim, so that reconquest was of only limited effect, while the Turks were expanding into the Balkans and likely balancing out the expansion in the number of Christians in Iberia.
It is after 1500 that Roman Catholicism "broke out" of its European ghetto. But at the same time that Catholic missionaries were leaving for the New World and Asia about 1/2 of Catholic Europe became Protestant. 2/3 of the German speaking lands, most of the British Isles and Scandinavia left the fold. In much of Austria, Poland and Hungary there was an initial erosion which it took two centuries of Counter Reformation work to undo. Meanwhile, in the New World the nominally baptized indigenous populations were dying; so the compensation for the loss of Europe would take centuries as a mixed-populations expanded across the American frontiers.
I will admit that I think that at some periods it may well be that Catholicism was the more numerous faith than Islam, right before the Black Death for example. Medieval Western European agriculture could usually obtain a high yield because of improved techniques in comparison to antiquity (mouldboard plow, 3-field rotation, etc.), but I suspect Muslim expansion into very densely populated regions of Asia easily outstripped this (Catholic Christians put more technological inputs into land, while Muslims simply increased the amount of land). 10% of South Asians at any time is far more numerous than all of Scandinavia or the Baltic; expansion within Europe is always outclassed by expansion within Asia because the latter has always had a larger population.
I might crunch some more numbers later, as you might guess I'm not super confident about these sorts of back extrapolations, though I'd be willing to bet that the Vatican is very wrong for much of the past one thousand years. I think that the four hundred years between 1300 and 1700 were probably the best for Islam numerically vis-a-vis Roman Catholicism, the loss of the much of Europe, Muslim expansion into South Asia and the latency of the New World demographic bounce back being the primary factors. After 1700 the Muslim world had basically attained its current expanse, while Europe and the New World went into demographic overdrive. In the 21st century the "X factor" in the Islam vs. Christianity numbers game is Africa, since 1950 Christians have been much better at converting the remaining pagans than Muslims, and all these new convert poulations have very high rates of natural increase.
Corrections and input appreciated; assuming you actually know something and aren't offering your "opinion." (Please don't assume that I'm guessing about facts like the switch of Iran to becoming majority Muslim in the 10th century, I'm drawing these from the literature. I might be wrong, but then so are the scholars who study these sorts of topics).
1 - I'll elaborate on this point a bit. Of European regions the British Isles, the Low Countries, Germany, France and Italy were solidy Roman Catholic. These are populous regions. But that leaves out Scandinavia, Hungary, Bohemia and much of interior Central & Eastern Europe as well as the whole Baltic region. These would later be fully Catholicized, but they were either officially or operationally pagan. Right before the year 1000 multiple Christian monarchies emerged in many of these pagan lands, but they had done little at this point to totally eradicate the old beliefs. And what later become Sweden, Finland and across the whole Baltic region even nominal Christianization of the ruling elite had not occurred.
Stupid Factoid. Catholicism and Islam are not like categories. There are still more Christians than Muslims, and more Catholics than Sunni Muslims.
and more Catholics than Sunni Muslims.
it's a close number. i did a back of-the-evenlope, and depends on the proportion of shia to sunni (which varies from 10 to 15% vs. 90 to 85%).
The spread of Christianity in Scandinavia is quite complex. It is possible that it started already in 9th century, and the first missionaries were Irish(!), via Viking connections. It took some time until Rome got its act together in Germania, and later in Scandinavia. Also the Eastern Christianity was present by 10th century. But we're talking only about a few thousand people, irrelevant in the big picture.
I agree with Ikram about different categories. At least you should be comparing Catholics with Sunnis. But unlike Catholics who have a centralised organization, the decentralised Sunni can be further split to subfactions.
My reaction was: BFD. More Muslims just means more Muslims to fight other Muslims.
Anyway, if Islamic women follow Iranian and Turkish women's example, this issue will resolve itself soon enough.
Picky but it's debatable to what extent the British isles outside England could be described as Roman Catholic in 1000. Couple of hundred years later certainly.
There's an awful lot of "spin" in contemporary documents and even more in later commentaries, but even so it does seem plausible that in Wales, for example, the Church was not brought into the Roman mainstream until the appointment of Norman sponsored bishops in the late 11th and early 12th centuries, and in Ireland until after Laudabiliter.