Double entry accounting is a lot more work than is single entry method. It only makes sense when you have a lot of money compared to the cost of keeping track of it (ie you're rich - accountants are cheap it seems).
You do it to catch errors and to accurately track the various streams of money in your business, not only for yourself, but because others want to know your finances and you need to have the information available in a format they understand. The agreed language is double entry accounting.
People had been tracking money (to pay bills, collect taxes) for thousands of years, but it wasn't till the 1400's that the Italians invented double entry accounting. This made banking reliable, enhanced trade and commerce and very quickly Italy became the banking capital and wealthiest country in Europe. It was the 1400's equivalent of the invention of the internet and the dotcom boom. They had buckets of money to spend. They spent it on paintings of Adam talking to God done on black velvet. Well they would have but velvet hadn't been invented yet. They made do with what they had, which was plaster ceilings. They spent money on painters, sculptors and people like Leonardo da Vinci.
In grade school this period is called the Renaissance, a flowering of art and intellect, that appeared in Italy for no obvious reason and then spread to the rest of Europe.
Quite why all these geniuses suddenly appear without any warning is not explained by your history teachers (who spend their life pondering deep questions like this), but Jared Diamond (Guns, Germs and Steel, Pub: Norton 1997) is happy to tell you. He says that geniuses like Michealangelo and Einstein are rather commonplace. Most of them are oppressed and are living in abject poverty, and are busy surviving if they even do that. Give them a good feed, treat them well, put them in the company of peers and pretty soon they'll be coming up with all sorts of things you hadn't dreamed of.
The Renaissance then was a result of the invention of double entry accounting, not (as we've been told) a flowering of intellect and art that happened for no reason at all.
About 200yrs after the invention of double entry accounting, the scientific revolution occured. People realised that you could ask questions of nature (by doing an experiment) and you got answers. Not only that, you got the same answers every time. It was much easier than asking questions of people, who never give the same answer twice. The simple questions were asked first ("do heavier objects fall faster?" - no-one had ever asked nature about this before). This lead to more complicated and more interesting questions. Marshall Brain who talked to us in Apr 2001 can now tell us how beer works. With lots of data rolling in, a mathematical revolution soon followed, one part being calculus.
I found double entry accounting more difficult to learn than calculus. The fact that calculus was invented 200yrs after double entry accounting would indicate that calculus is conceptually more difficult than double entry accounting, but I'll offer the following evidence to support the opposite postulate.
Any 10yr old who tries, even in principle, to calculate the distance travelled by a car by tracking the varying position of a car speedometer needle, is working on deriving integration and numberical methods from first principles.
Double Entry accounting
The names of the inventor(s) of double entry accounting have been kept secret. You can't prove anything about double entry accounting - no-one has proved or derived the self consistent orthogonal set, even 600yrs later.
All we know is that it just works. It may as well be magic.
You have to be a lot smarter to invent something for which there is no need, that no-one can understand and for which there is no proof that it's right (other than it works) and for which no modifications have been possible, than to invent something whose need is obvious and which you can check by proof for correctness as you go.
Not only this, the total salaries paid to people who understand accounting is much higher than that paid to the people who understand calculus.