[roboys]

The dark ages also saw a huge disparity in education between the East and the West.

Until the 15th century less than 5 people in Europe could do long division. For comparison, Aryabhatta discovered calculus in 5th century India and Madhava made large contributions in the 13th century (Newton/Leibniz were wrongly credited for similar work many years later).

[leereeves]

The way I heard it, Aryabhatta and those who followed discovered some of the ideas behind calculus and a few useful results, but not calculus itself, neither the basic ideas like derivatives and integrals nor the vast conclusions that followed from those.

[Retric]

> Until the 15th century less than 5 people in Europe could do long division.

That’s wildly inaccurate. Arithmetic was very much a subject at several schools with the addition, subtraction, multiplication, and division all being taught. https://en.m.wikipedia.org/wiki/Quadrivium

Long division being difficult in Roman numerals is one of the reasons for the switch.

[roboys]

>That’s wildly inaccurate. Arithmetic was very much a subject at several schools...

I'm talking specifically about "long division" in Europe... and have heard this factoid from multiple mathematicians including Nasim Taleb. So I expect there is a basis for the claim...

[tripzilch]

Well, especially Taleb's claims are worth it to source check. Especially if they are these really juicy stories (like only 5 people in Europe knowing long division).

He has bit of a habit exaggerating and elaborating on stories for the sake of making tasty reading. There was a story in Black Swan about two hospitals and a simple statistical riddle that he claimed professional statisticians would get wrong. It wasn't even a trick question, most people would get it right. I found this hard to believe but I was still sort of surprised when the source spoke of a much harder statistics question that was surveyed at a psychologists convention, not statisticians. That was the first (and the last) source I checked on him. I'd have checked a few more but I don't have the book any more.

But now I guess I can add this one to the list of examples.

[Retric]

Let’s be clear, if you mean the modern notation, that was was ‘invented’ after the dark ages. So under that definition it’s ~0 people world wide in the dark ages. Excluding independent discovery.

However, if we are talking about the number of people being able to accurately do 1234 / 56 = 22 r 2. That was regularly taught in the Middle Ages with plenty of examples of such calculations being available.