I was doing a little research on a related subject when I came across a simple fact; up until the Crusades Europeans only used Roman numerals. Think about how difficult that would be. Roman Numerals are simple enough with a sun dial, the numbers never get too big to be obnoxious. However, think about adding up the number of warriors that you and your vassals have – xv + xxiii + ilxii and so forth. I have seen the Tribal Hidage dating from the Arthurian period and it amounts to a list of kingdoms and taxes due. The list is only a few dozen but in that format it would be difficult to tally.
Now imagine working with basic multiplication and division. Very difficult, right? It is much too easy to get lost when dealing with up to eight symbols that might be used to represent a single digit. I personally can’t imagine doing any mathematics that I could not do in my head if all I could use were the symbols i,v,x,l, and c.
Now imagine basic algebra; 2x + 7 = 13/2x = 6/x=3
with “a” as a symbol for an unknown number it becomes iia + vii = xiii/iia = vi/a=iii
How about 3x^2 + 15x + 18=0/3(x +3)(x+2)=0/x=-2 and -3
You could get to iiia^ii +xva + xviii, but you could go no further in the equation. Before the introduction of the zero with the Arabic system the Europeans had a placeholder for no number, but no real conception of zero. Negative numbers aren’t even possible without it, either.
Because of the absence of both the zero and negative numbers Trigonometry, Calculus, and advanced mathematics in general are impossible. Even if someone had managed to do equations without either they would have been extremely complicated procedures. To have invented any of the higher mathematics would have been entirely inconceivable.
So, a brief history. In 1095 the Byzantine Pope contacted the Roman Pope and requested assistance. Ostensibly it was to recover the Holy Land from the unbelievers, but Jerusalem had been in Muslim hands for some time by then. The reality was that the Muslims were encroaching on Byzantine lands and the remnant of Ancient Rome was unable to stop them. The call was meant to get reinforcements so that the Byzantine Empire could limp on for awhile longer.
It worked. Despite progressively less effective crusades (and the occasional tragedies such as the Children’s Crusade), the Muslim people were put back on their heels enough that it wouldn’t be till almost 60 years after the last crusade, in 1396, that the city of Constantinople would fall.
Western Europe was not directly effected by that, however. With the invasion of the Mongols in the thirteenth century and the resulting conflicts between the two superpowers, there is no way to be certain that Germany or Italy would have dealt with an invading force of Muslims.
Unexpected though it was, Western Europe’s greatest positive from the crusades was the exposure to new ideas. Many of them were actually old ideas that had been preserved in areas from India to Egypt that were by controlled by the Muslims. Some were new. Arabic Numerals were perhaps the most important of all these in the development of science much as the exposure to Greek philosophy would be important to the development of Renaissance thinking.