My personal favorite example is clip pens. It's such a simple tool. There is no electricity, steam power or even gears in it. But I think very few people can come up with how it works internally.
Without that level of accuracy you can’t make a ballpoint pen and without it there is no real advantage of making the click mechanism.
And making these balls is very challenging even today. These are often still used as an example for manufacturing deficiencies in places like China as whilst they tend to make the bulk of the ballpoint pens they still have to buy the balls form German and Swiss manufacturers.
They fixed this problem by 2017: https://www.washingtonpost.com/news/worldviews/wp/2017/01/18...
The article only says that it took some research facility 5 years.
It's fascinating the lack of imagination people have for a certain level of innovation. They can see the benefit of small incremental changes pretty well but large disruptive changes fall off a cliff very quickly into a chasm of sceptism - "I'm sure there is something wrong with this idea but I can't think of the problems so I will make up some reasons why it won't work". I feel like this sceptical reaction itself must have an evolutionary basis as it seems highly instinctive.
You can look at the current technological changes in play to day and think about them through this lens and it's quite interesting (AI, obviously, then AR/VR/metaverse etc).
I wouldn't be surprised if someone kid were to intuit a bunch of major conclusions from calculus by just looking at algebra and graphs of plots.
If you start with pre-newtonian mathematics, arriving at calculus would indeed be quite some feat. But then, a lot of Newton and his contemporaries were reasoning about mathematics that's fairly reminiscent of Euclid (and very alien to modern readers).
Unless you're Gottfried Wilhelm Leibniz.
Or Darwin and Wallace.
Which suggests these ideas might be a product of their zeitgeist with a number of contempories bording on being the first to publish.
In both cases, neither stole ideas from the other. However, at least my understanding, is that Newton and Leibniz did the work at the same time, but because Newton already had a reputation, Newton took all the credit. In the case of Darwin vs Wallace instead, Darwin had years and years of research, notes, and writings done but unpublished, but he rushed to publish when he heard that Wallace had similar ideas. So in a sense, Darwin didn't walk away with more credit than he deserved, as he was there first anyway. Newton vs Leibniz doesn't look as clear cut.
(By the way, in before Edison vs Tesla, that's yet another entirely different situation of plain exploiting and stealing of Tesla by Edison)
Fun unrelated Darwin fact: he's the person who figured out the geology of how and why coral reefs and atolls form where they do.
Not to cast any shade on either of those two brilliant people, but it does suggest Calculus was "ready" for 17th-century mathematicians (or, you know, the other way around).
Book-printing presses have been one of the most influential inventions ever for precisely that reason.
I would imagine the next biggest influential invention is AGI.
Not starvation wages, certainly, but neither was it vast riches.
You wouldn't have known in Newton's time if alchemical transmutation into gold worked. Certainly, you knew then that some substances could be transformed into other substances, and it was such research that developed into modern high-school chemistry.
So why not earlier? Because the others didn't have Fermat to learn from.
In as much as things build upon other things, you were not likely to get Calculus before, say, Algebra. But once all the pieces are in place the field is wide open for the smart people of the time to plunder it.
Or at least bent to purpose, in this case the narrow zeitgeist of the 17th Century European numerate intellectuals .. those were the days of very slow limited copy exchanges of the latest thoughts by mail and by word of mouth via salons.
Somewhat like Mastodon with the bandwidth of a hikers backpack full of parchment.
Calculus was discovered by several mathematicians in India - unfortunately little survives of several works.
https://iks.iitgn.ac.in/wp-content/uploads/2016/02/Developme....
Militant societies successfully preserved their knowledge and kickstarted their industrial revolution. (Relatively) Non militant societies did not and their knowledge was made extinct. But if you had ten thousand copies of works floating around - it could have survived.
My experience in college, trying to figure out how math ideas from the Indian subcontinent and from around Mediterranean fit together was that the only claims for ancient Hindu rigorous math were from Indian sources and they were pretty hand-wavy about rigor.
It reminded me of (a geographically, temporally translated) Tom Lehrer's "Lobachevsky."
Jainism in particular should be given a massive shout-out for being the largest and oldest organized genuine religion of non violence. These are the people who are unhappy about washing dishes as killing the bacteria left of the plate is "kitchen violence".
"His expansion of the kingdom, especially his annexation of the kingdom of Anga to the east, is considered to have laid the foundations for the later expansion of the Mauryan Empire." (https://en.wikipedia.org/wiki/Bimbisara)
"He forcefully took over the kingdom of Magadha from his father and imprisoned him. He fought a war against the Vajjika League, led by the Licchavis, and conquered the republic of Vaishali." (https://en.wikipedia.org/wiki/Ajatashatru)
Another problem is people assume prevailing discovery narratives are truthful. It's harder to do that in the sciences because of the breadcrumbs left behind.
>it is extremely hard to be Newton and think about it first and prove it.
Newton wasn't first, Calculus was known in India almost 1000 years earlier and it wouldn't be surprising if Newton was a student of work gathered from parts of the world that were illegal to credit with such discoveries at the time.
A lot of people contributed theorems over the centuries that would now be considered part of calculus. Developing a mathematical framework like calculus is more of a gradual and continuous building of knowledge than a single event. There's a reason Leibniz and Newton happened to independently create calculus at the same time.
Non-christian origins could not be recognized by western institutions until very recently. Generally the first European christian to relay existing information from the non-christian world was credited with invention or discovery.
In many cases, people still credited with discovery didn't fully understand the source material and failed at relaying it accurately.
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I think provable academics for academics sake is far more recent than Newton.
can confirm, I have been trying to do/understand something but since I ain't seen it, I cannot just tell you what it is.
less stubborn people (and people with other's depending on them) would have given up already.