Coo-Coo For Calculus

Joel Walbert

Oct 29, 2023

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Source: Principia Scientific

This Is the Calculus They Won’t Teach You

Written by A Well-Rested Dog

There is an inspiring story hidden behind the formulas and word problems of single-variable calculus–a story that should be told in every introductory calculus course, but usually isn’t. Regardless of if you’ve taken a few calculus courses before or are just beginning your study of calculus, this video aims to give a taste of the insights that can be gained from learning about the history and philosophy behind the key ideas of this field of math.

Infinity is a common concept in math but to the ordinary person infinity is a horrifying concept so how did it come to be used in this way. The first thing broken down is what calculus actually is as well as introducing the history of math as we know it. Math started in Ancient Greece with geometry since the way we depict mathematical equations now wasn’t used them. The video also breaks down integration and integrals used in calculus.

Archimedes created the idea that a rectangle could be the same size as a circle and produced the proof to this hypothesis after the statement was made. Math is commonly about finding “moral” solutions to problem or solutions that should be right and the coming up with a formal proof to justify it. Archimedes wrote about this very way of thinking in The Method and this method is still recognized today.

Description

"Infinity is mind numbingly weird. How is it even legal to use it in calculus?"
"After sitting through two years of AP Calculus, I still feel like I don’t know anything about it."
"What do you mean that historically, integrals came before derivatives? Seriously, what’s the deal with calculus?"
There is an inspiring story hidden behind the formulas and word problems of single-variable calculus–a story that should be told in every introductory calculus course, but usually isn’t. Regardless of if you’ve taken a few calculus courses before or are just beginning your study of calculus, this video aims to give a taste of the insights that can be gained from learning about the history and philosophy behind the key ideas of this field of math… brought to you by a dog and some rough animations!
This video was part of #SoME2, a math video making contest created by @3blue1brown in the summer of 2022.

CORRECTIONS LIST (periodically being updated):

3 : 47 I start a description of Archimedes' circle proof here, but I want to note that the one I present is a modified version of it; it does contain a few "hand-wavy" mistakes near the end and may still be difficult to follow; that's on me. My goal with showing this proof wasn't to give a proper explanation of it, but to give a taste of what I thought is the spirit of rigorous reasoning. If you would like to see something that is closer to Archimedes' argument, there's a link in the further reading you can check out--or you could also just google "Archimedes circle proof".
8 : 45 I made a typo... Viete lived from 1540-1603, not 1540-1693
14 : 35 This is embarrassing. Kepler's 2nd law is true because angular momentum is constant, not because velocity is constant. Whoops!
A lot of comments have brought up Indian contributions to calculus that I left out, particularly the Kerala School and Madhava of Sangamagrama, where the first instances of derivation came about. A few reasons for why I missed this in my research could be because attributing the beginnings of calculus with Indian mathematicians seems like a relatively new historical narrative, and many sources in English likely have a bit of Eurocentric bias. Regardless, this goes to show how the narrative I shared does have its flaws, and similarly to the misleading impression of calculus I criticized modern introductory courses of spreading, this narrative is not the whole picture. If you have any sources you'd like me to add to the further reading, please let me know!
I may have suggested that Euler discovered the number e, but he did not--some attribute it to Napier, and many others before Euler used it. On that note, I probably misleadingly attributed a lot of other ideas I brought up to one or a few people, when they are much more nuanced; so take the briefly brought up associations in this video with a grain of salt. This video is intended to share a broad narrative instead of establish definitive history of calculus. Hopefully this can just act as an intro to the subject!

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Source: Principia Scientific

First mention by EU mathematician that calculus was discovered/derived in India

Published on May 19, 2023

Written by Dr M Nisa Khan

The following video by Mathologer was first released 4 days ago, narrated by Burkard

This is the first publication I am aware of from the West/mainstream that mentions that Indians knew ‘pi’ as infinite series, knew how to approximate pi with many digits after the decimal, and calculus was known to the Indians before Newton and Leibniz.

While I am somewhat encouraged by this, I have several concerns with this video publication.

Perhaps, for me, the biggest concern is that although the West or the larger colonized world now admits that a great deal of mathematics including calculus was found in ancient India, they now claim that the West decoded it better and brought to the world using better notations.

A related article on this is by Fermat’s Library in LinkedIn posted a few days ago about the notation of derivatives in calculus introduced first by Leibniz:

(See the LinkedIn link below. You can also see my comments there.)

linkedin.com

Calculus’ importance is definitely not in the notation. It is in the core concept!

I have noted form the way calculus is taught and used in the West and colonized world, one may postulate why analytic calculus is neither well understood by many who teach it at the university level; nor is it used for solving any practical physics problems including in quantum mechanics.

So could it be true that calculus was actually stolen from India and reclaimed elsewhere? After all, the colonizers of India burnt many books and libraries from around 700 A.D. through many subsequent centuries.

At the very least, it now seems all but clear that calculus in Europe became largely dysfunctional and the claim that it was discovered by Newton and Leibniz is now being corrected.

There likely is some involvement of theft regarding calculus – although I cannot prove it; but I think that others doing research on this can and in time we might see such proof.

I think a book like the Surya Siddhanta from Bharat may have been taken to the Middle-East during 600-800 A.D. which was then taken into the possession of certain Europeans a few hundred years later.

Such a book contains a great deal of remarkable mathematics, calculus, astronomy, laws of mass and energy and much more.

I have some reasons to postulate that Leonardo Da Vinci may have known about such work originating in India and had in his possession such a book as I watched a documentary on Da Vinci in the New York Public Television channel recently.

I shall entertain the idea of elaborating on my postulate at a later time.

I continue to support what Professor Raju says and I myself see this as a grave issue: that being that through the possession of calculus and arithmetic by the West, they still failed to understand arithmetic for a very long time and they, including most in the colonized world today, still fail to understand calculus.

My assertions are further elaborated in my previous article in PSI on Newton.

As early as 2400 years ago, Greek philosophers were coming up with paradoxes that seemingly had no solution.
Early mathematicians came up with problems that seemed impossible to solve.
It wasn’t until the 17th century that the techniques were finally developed to solve these problems and unlock new fields of science and mathematics.