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I’ll take that as a compliment, thank you for watching!

Then they wouldn’t be “mighty in number”!

@@bensyverseni see lol

Thank you for watching!

Hahaha

Thanks for watching!

Thank you!

I don’t understand the question

Thanks for watching!

I understand why you feel that way, but at the same time one thing that I find fascinating about this story is that if the codex hadn't been made into a prayer book it likely wouldn't have survived at all. The monks preserved and protected it. Also, it was Christian scribes who made the 10th century codices in the first place.

I hope to learn more about Indian mathematics and eventually make some videos on the topic. However, my process is quite slow so this could take me a while

@@bensyversen I am glad to hear that. Thank you so much from the depth of my heart.🙏♥️

Thank you, that is very kind!

Thank you!

Thank you for watching! Yes I’ve left a lot out and probably described some events in a way that would be too casual for a rigorous telling of history in order to give an overview of this quite long timeline of the palimpsest.

Thank you for watching!

It's not Bill Gates (and I don't think it's Jeff Bezos either, which Wikipedia reports as a "rumor"). In "The Archimedes Codex," it actually specifies that at the time of the auction the buyer was described as "not Bill Gates." Here is how William Noel describes his first meeting with the owner, in 1998: "I couldn’t get a measure of the man. All I knew was that he was retiring, rich-richer than Croesus-and that he liked food. I knew he liked books too, but I wasn’t learning anything more." So, for starters, Bezos and Gates are probably too young. And Bezos was definitely not retiring in 1998. I was also told by somebody who knew Jim Simons personally that it was not him either. But yes, credit is absolutely due to the owner as well for funding the restoration and preservation of the book that likely wouldn't have been possible had it been in the hands of an institution...the project would very likely have been bogged down in bureaucratic red tape. Noel elaborates on this a bit in his TED Talk: th-cam.com/video/VqtEppZmjfw/w-d-xo.html

🤣🤣🤣

Yes during one of the times it was sacked…I would have to double check this but I believe that there were other sackings of Constantinople as well

You’re welcome. I’m glad you enjoyed It and found it valuable!

Thank you very much!

Thank you!

Yes, it's true. In William Noel's TED Talk (th-cam.com/video/VqtEppZmjfw/w-d-xo.html) and in his book he makes the point that had the palimpsest been in the possession of an institution or government, the imaging project might not have been nearly as successful because it could have gotten bogged down in red tape, grant paperwork, etc etc. It certainly is a case of the private owner doing the right thing, and possibly the case that private ownership was indeed the best outcome for the sake of this project. However, I will add on the other hand that the Palimpsest is unfortunately no longer on public display, and the website that holds the images and data (archimedespalimpsest.net) is still accessible but not well maintained. In his book, Noel describes the buyer of the palimpsest as somebody who had "made his fortune and retired" by 1998, so it's also presumably possible that the anonymous buyer is not still alive. I don't have any evidence for that either way, but it's worth noting that the buyer was supposedly already retired 26 years ago.

You mean Bill Gates. Yes, the Mr Microsoft himself, Bill Gates was the buyer. Not only did Bill Gates purchase the palimpsest, but he sponsored all the cost of the preservation, research and putting its contents on the internet for free, so that future generations could enjoy it without hiding it behind paywalls and subscriber-based systems.

It's not Bill Gates (and I don't think it's Jeff Bezos either, which Wikipedia reports as a "rumor"). In "The Archimedes Codex," it actually specifies that at the time of the auction the buyer was specifically described as "not Bill Gates." (though I suppose you could disbelieve that statement from the representatives of the buyer, but I think it would have been strange if the buyer had been Bill Gates and his representatives went out of their way to specifically say "oh, it's not Bill Gates! No way!") :) Here is how William Noel describes his first meeting with the owner, in 1998: "I couldn’t get a measure of the man. All I knew was that he was retiring, rich-richer than Croesus-and that he liked food. I knew he liked books too, but I wasn’t learning anything more." So, for starters, Bezos and Gates are probably too young. Bezos definitely hadn't retired in 1998. I was also told by somebody who knew Jim Simons personally that it was not him either. But yes, credit is absolutely due to the owner as well for funding the restoration and preservation of the book that likely wouldn't have been possible had it been in the hands of an institution...the project would very likely have been bogged down in bureaucratic red tape. Noel elaborates on this a bit in his TED Talk: th-cam.com/video/VqtEppZmjfw/w-d-xo.html

...and yes, you're right that it's great that the buyer put the contents online for free. Though having just spent multiple months with the information, I wish that its online presence was maintained a bit better. It's no longer available on Google Books like it was originally, and the site holding the images used to have a little applet that made finding specific pages and even compositing the different image colors on top of each other easy and intuitive (Dr Noel had a demonstration of this on his TH-cam page). None of that is available anymore and it takes a fair amount of work to understand how to properly navigate and access everything on archimedespalimpsest.net!

Yes, it is very sad. It was a vehicle accident. Here is a touching and thoughtful remembrance and celebration of William Noel: boltonhillmd.org/bulletin/mourning-and-celebrating-will-noel/

Sources in the description

Yes - Archimedes is the first to mathematically prove the relationship.

@@bensyversen No way, 100% wrong, he is not the first... Archimedes, Plato, Aristotle and most of all those philosophers and mathematicians of now-days Greece and middle-east studied from priests in Alexandria/Egypt (read Aristotle , he does even acknowledge that those ancient Egyptians were too black by the way). There is no way whatsoever ''one could build a pyramid with a such level of precision without mastering mathematically the notion of levers and geometry in general''. Unless you mean the first in Europe to elaborate on that notion; the only way Archimedes would be the first in the world is via the immoral whitewashing of the power of knowledge (period).

You're certainly right that prior civilizations (such as Egyptians and probably Babylonians) would have had certain knowledge of levers and an empirical understanding of their use. To clarify, the claim about Archimedes is that he is credited as the first to write an "axiomatic proof" of the relationship...he's the first to employ what we might describe as "mathematical physics." I think that there is a larger discussion here about what counts as "inventing" a concept though. Does this mean proving it mathematically? If so, it would systematically tend to exclude certain cultures that did not prioritize this type of formal axiomatic proof. For example, I understand from my limited knowledge of Indian mathematics that it's not based on the same type of axiomatic system as western mathematics -- correct results would be seen as sufficient. This is a topic that I hope to research further and eventually explore in a future video. Another question that I have (which I don't know the answer to; perhaps you have more knowledge than me in this area), is how these figures such as Archimedes and Eratosthenes (who was born in what is now Libya and lived in Alexandria) map onto our modern understanding of race. I know that Ancient Greek civilization is claimed as "European" (read: white), but I don't know if some of that is because of how we have imposed cultural and racial narratives onto these civilizations after the fact. It's an area where I could stand to learn more and would certainly welcome any book recommendations on the subject.

Just common sense, an inventor (one who devises some new process, appliance, machine, or article) must have both physical and mathematical proof of his invention for further elaboration and mass-production... that's why there are more than one pyramid. That said, we do agree that there is no a kind of nowadays form of axiomatic genuine proof or writings on the notion of levers from early ancient time ( could be simply because writing was still evolving, could also be the loss of the documents unwillingly or willingly same as the book that you're talking about in your video... it was my first time to hear about it by the way...thanks). Now, I wonder how sure are you the book is a genuine book wrote by Archimedes or just a fake copy (it only can be an original one if it is a kind of more than 2000 years aged papyrus... just saying)? The trick is ''there had been several attempts to falsify the history on the scientific progress of ancient non-western civilizations''; for instance (the burning of the Alexandria library). Now the question is ''why did it happen''? ... And any viable imaginable reason tends to agree with what you've just very well articulated about racial narratives. I wish I could recommend an ancient document that talks about your raised question, but I don't have any unfortunately and neither I can pretend to be an expert in the field, I'm just a curious scientist... but if if you enjoy ancient stuff, try the EBERS papyrus.

@@hakiza-technologyltd.8198 Hi, I'd recommend taking a look at starting around 9:38, and more at 20:37 of my video for more info on the creation of this palimpsest. Indeed it is not an original papyrus scroll but a copy. The book "The Archimedes Codex" includes a lot more detail about how scholars who study documents like this ascertain its authenticity and trace the evidence about what parts are original and what parts are modified. It's a fascinating process -- almost akin to how scientists analyze evidence to reconstruct zoological classifications and family trees of species. As far as the question of axiomatic argument: I don't think that it necessarily follows that a culture that was able to use a particular mathematical fact for practical purposes (for example Babylonians using knowledge of the Pythagorean theorem and 3-4-5 triangles to construct precise right angles) also has to have possessed an axiomatic system for "proving" those theorems in the abstract. Indeed something that is unique about mathematics as a discipline is that doesn't directly try to describe reality, but instead it begins with idealized forms that can only exist in ones' imagination. A "circle" isn't the round shape that you draw in the sand -- that's just a REPRESENTATION of a circle, which has imperfections and flaws. A truly perfect circle can only exist in the imagination, outside of the realm of practical application. The thing that is truly remarkable is the degree to which these imaginary, almost philosophical shapes, are useful in describing and making predictions about the real world.

Hi thank you for writing in. I very much started my research process for this video with a more or less similar perspective to the one that you describe here -- the idea that knowledge of The Method certainly must have had SOME impact had it been known. I originally had quite a bit more material for the video about this question but I cut it for time. Here are a few points though that you might find interesting: - In his book "Calculus Reordered," David M Bressoud makes the argument, that Archimedes' extant works would have been more than sufficient to develop "the calculus" had it been possible prior to the 17th century. Here's a bit of what he says about the matter: "As we shall see, Archimedes’ other works were perfectly sufficient to lead the way toward the development of calculus. The delay was not caused by an incomplete understanding of Archimedes’ methods but by the need to develop other mathematical tools. In particular, scholars needed the modern symbolic language of algebra and its application to curves before they could make substantial progress toward calculus as we know it. The development of this language and its application to analytic geometry would not be accomplished until the early seventeenth century. Even then, it took several decades to transform the “method of exhaustion” into algebraic techniques for computing areas and volumes. The work of Eudoxus, Euclid, and Archimedes was essential in the development of calculus, but not all of it was necessary, and it was far from sufficient." - The academic journal Interdisciplinary Science Reviews published an entire issue dedicated to an article by Reviel Netz which claims (to summarize without subtlety) that had it not been for Archimedes, the entirety of the scientific and industrial revolutions would not have been possible. That article was then followed by 13 replies from other scholars on the matter: www.tandfonline.com/toc/yisr20/47/3-4 - Something that I came across in my research is this lecture by mathematician and NYU Professor Sylvain Cappell. math.nyu.edu/Archimedes/AWC/video_cappell.html He says something to the effect (paraphrasing) that "I like to think that, had only Archimedes had a peer or student at his level, then perhaps the entire Dark Ages would have never happened." Given that Cappell is a mathematician and not a historian, I take this as more of an expression of Archimedes' astounding level of mathematical achievement (which, to be sure, I only barely scratch the surface of here), and less as a rigorous historical claim. There's a lot more, including more comments from both Steven Strogatz and Amir Alexander about this question. In fact I'm considering ways that I might release additional excerpts from their interviews, either through Patreon or maybe just an unlisted TH-cam video that I link in my description. If you want to learn more about Archimedes and his influence, I'd say that there is no better source to get a complete picture of him than "A New History of Greek Mathematics" by Reviel Netz. To be sure, Archimedes' mathematical achievements are underappreciated by the public to this day.

His method is very much an early version of integral (but not differential) calculus. However the calculus that we are familiar with today, credited to Newton and Leibniz, couldn’t emerge until after algebra was invented.

I’m not sure that I follow those specific connections, but Archimedes’ method is definitely seen as a precursor to integral calculus (though The Calculus as credited to Newton and Liebniz is far easier to use!). However Archimedes is not seen as having much to say along the lines of differential calculus.

@bensyversen I was taught that simpsons rule was essentially slicing an object into tiny polygons. When I googled it, I got a lot of equations, and no slicing explanation. It's obvious therefore that Not many people teach it that way, so I totally get why you didn't join the dots.

Ah got it. Yeah slicing the shape into polygons is usually known as a Reimann sum

@@bensyversen just don't tell anyone I didn't know that, I'm trying to project an aura of total knowledge 🤪🤪

Don’t worry I won’t tell anyone 😉