I don't think the invention of calculus was hard. Yes of course it takes a "great person", but there always are some of those around at any one time.
What made calculus possible and the reason why it wasn't invented earlier was that it just wasn't needed. All inventions are part of a context. In support of my assertion: When it was needed it was promptly developed twice on the same continent and at the same time.
Which has implications for learning calculus: I guess it's especially hard to learn this, or anything, if you don't see a need for it (in your life).
I - now pretty old - found out that while I had always been good at school I had forgotten almost everything even slightly advanced in biology, chemistry, and other fields. When I had to learn it I learned only that particular knowledge and only for the exam since that was the only use I had for it. Recently, a few years ago, I suddenly became interested in medical topics - only to understand how the body works, the pathologies don't interest me. Anyway, I had to learn a lot of chemistry, org. chemistry, biochemistry (citric acid cycle is fun, but understanding how mitochondria create energy using that cycle is even more so), and it took me very little time, and this time I won't forget any of it. That's because it now is embedded into a big subject that I actually care about. If I had just to learn the citric acid cycle and only to pass some exam I would learn it - and afterwards promptly forget. Now it's part of a larger "story" that interests me and I actually think about it occasionally while walking around town because it matters to me, and I explain to my inner self whole physiological processes just because I find it so interesting.
Same with calculus, if you are an engineer and care about e.g. building a chemical plant to produce XYZ you will care about calculus so much you will learn it in no time. Simply because it helps you. You don't care about the calculus - you care about what it can do for you.
Did you ever wonder what language the wizards in the fantasies movies speak to invoke magic? It must be math. It is the language of miracles. You can move mountains, you can put stuff into orbit, you can hit the moon circling around a planet hundreds or even thousands of millions of miles away. Or you can simulate ecosystems on earth. Or pretty much any somewhat advanced simulation of anything, like the weather, or airflow, etc.
So the best way to learn calculus is to not care about calculus - but to care very much about a subject where calculus is the magic language to get stuff done.
By the way, the wizard/fantasy analogy can be taken further. The "magical items" that they have are actually pretty much exactly how we use technology: Somebody else made it and the person using it has no idea how. Basically, the knowledge of many, in our time often millions of people working together in both space and time, is poured into "magical items". That can be electronics, but even a piece of concrete or steel is a high-tech "magical" product these days. So next time you watch a fantasy movie remember it is actually real, they only got the language and the symbolism wrong. We do live in a world of exactly such magic, but the language is math and we don't wave wands around, wear different clothing than in the movies, and use labs, computers, robots and industrial processes. And boring team meetings to coordinate everybody :)
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And a few words about the religion of Europe at the time - from an atheist. I recommend reading up on European history. It seems to me from the things I did read, although I'm definitely nobody who would be allowed to post in /r/AskHistorians, that Europeans owe a lot to Christianity. It seems to me it was what kept Europe at least somewhat together, a unifying force spanning all peoples and kingdoms. Also, the tension between worldly and religious leaders seemed to have been advantageous because it didn't allow one party to get all the power. Since it was a somewhat "orthogonal" force and not directly competing like other kings it could exist in parallel. Also, from what I read it does seem to be true that the monks were chiefly responsible from getting knowledge saved for when it was again needed centuries later, from old Greece and Rome. As for the example of Galileo, I remember that it was in /r/AskHistorians, the actual story is far more complicated and the simple story "church evil, Galileo good" not even close to true. [Here is one thread](https://www.reddit.com/r/AskHistorians/comments/42bbfx/what_...), it was not the only one.
The only thing I would like to add to the end is to point out another thing that set organized religion positively apart: No inheritance. Today we perceive the "no family" rule for priests as backwards, but it served an IMHO good purpose. Even today we have the problem of wealth and power being concentrated in families. That aspect of the Catholic Roman church was incredibly advanced IMHO.
>> I don't think the invention of calculus was hard.
If you look at it with ~2k years of hindsight and mathematical knowledge, sure, it wasn't hard. Neither was it "hard" to think of using zero or infinity, or even the unit.
>> When it was needed it was promptly developed twice on the same continent and at the same time.
Most probably the right way to see this is completely the opposite: calculus was needed countless times before and it was only developed twice.
Comment included below:
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I don't think the invention of calculus was hard. Yes of course it takes a "great person", but there always are some of those around at any one time.
What made calculus possible and the reason why it wasn't invented earlier was that it just wasn't needed. All inventions are part of a context. In support of my assertion: When it was needed it was promptly developed twice on the same continent and at the same time.
Which has implications for learning calculus: I guess it's especially hard to learn this, or anything, if you don't see a need for it (in your life).
I - now pretty old - found out that while I had always been good at school I had forgotten almost everything even slightly advanced in biology, chemistry, and other fields. When I had to learn it I learned only that particular knowledge and only for the exam since that was the only use I had for it. Recently, a few years ago, I suddenly became interested in medical topics - only to understand how the body works, the pathologies don't interest me. Anyway, I had to learn a lot of chemistry, org. chemistry, biochemistry (citric acid cycle is fun, but understanding how mitochondria create energy using that cycle is even more so), and it took me very little time, and this time I won't forget any of it. That's because it now is embedded into a big subject that I actually care about. If I had just to learn the citric acid cycle and only to pass some exam I would learn it - and afterwards promptly forget. Now it's part of a larger "story" that interests me and I actually think about it occasionally while walking around town because it matters to me, and I explain to my inner self whole physiological processes just because I find it so interesting.
Same with calculus, if you are an engineer and care about e.g. building a chemical plant to produce XYZ you will care about calculus so much you will learn it in no time. Simply because it helps you. You don't care about the calculus - you care about what it can do for you.
Did you ever wonder what language the wizards in the fantasies movies speak to invoke magic? It must be math. It is the language of miracles. You can move mountains, you can put stuff into orbit, you can hit the moon circling around a planet hundreds or even thousands of millions of miles away. Or you can simulate ecosystems on earth. Or pretty much any somewhat advanced simulation of anything, like the weather, or airflow, etc.
So the best way to learn calculus is to not care about calculus - but to care very much about a subject where calculus is the magic language to get stuff done.
By the way, the wizard/fantasy analogy can be taken further. The "magical items" that they have are actually pretty much exactly how we use technology: Somebody else made it and the person using it has no idea how. Basically, the knowledge of many, in our time often millions of people working together in both space and time, is poured into "magical items". That can be electronics, but even a piece of concrete or steel is a high-tech "magical" product these days. So next time you watch a fantasy movie remember it is actually real, they only got the language and the symbolism wrong. We do live in a world of exactly such magic, but the language is math and we don't wave wands around, wear different clothing than in the movies, and use labs, computers, robots and industrial processes. And boring team meetings to coordinate everybody :)
-
And a few words about the religion of Europe at the time - from an atheist. I recommend reading up on European history. It seems to me from the things I did read, although I'm definitely nobody who would be allowed to post in /r/AskHistorians, that Europeans owe a lot to Christianity. It seems to me it was what kept Europe at least somewhat together, a unifying force spanning all peoples and kingdoms. Also, the tension between worldly and religious leaders seemed to have been advantageous because it didn't allow one party to get all the power. Since it was a somewhat "orthogonal" force and not directly competing like other kings it could exist in parallel. Also, from what I read it does seem to be true that the monks were chiefly responsible from getting knowledge saved for when it was again needed centuries later, from old Greece and Rome. As for the example of Galileo, I remember that it was in /r/AskHistorians, the actual story is far more complicated and the simple story "church evil, Galileo good" not even close to true. [Here is one thread](https://www.reddit.com/r/AskHistorians/comments/42bbfx/what_...), it was not the only one.
(End of included comment.)
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The only thing I would like to add to the end is to point out another thing that set organized religion positively apart: No inheritance. Today we perceive the "no family" rule for priests as backwards, but it served an IMHO good purpose. Even today we have the problem of wealth and power being concentrated in families. That aspect of the Catholic Roman church was incredibly advanced IMHO.