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The 'problem' with Indian math was the general aversion (or ignorance) of the importance of the method of proof. The more well known works of Greek mathematics

by shas3 13y ago

The 'problem' with Indian math was the general aversion (or ignorance) of the importance of the method of proof. The more well known works of Greek mathematics were great in emphasizing the importance of the concept of mathematical proof. Yet, Greek mathematics, with the exception of Archimedes and Diophantus had an aversion for arithmetic (especially the concept of infinity and infinitesimals) and algebra and an over-reliance on geometry[1]. Engaging in a bit of counter-factuals, if either of the following had happened: (1) Indians picking up on the method of proof, (2) Greeks adopting more arithmetic and algebra, history of mathematics may have looked significantly different than today. However, the OP link has a ton of apologist/revisionist history with insufficient archaeological evidence mixed in with a little bit of the good stuff. Example: references to vastu shastra, which is astrological woo. [1] Eric Temple Bell, 'The Development of Mathematics,' Dover, 1992.

pflats 13y ago
Based on my reading, I couldn't agree more with your post. Hence my note about Bhaskara II's work being "rough"; I was trying to write for a lay audience. I too find myself wondering what the world would be like if there were more crossover between the early mathematical cultures. A few pages of Fibonacci's Liber Abaci pretty much transformed European math. I saw a couple criticisms of the page's overall tone; I wanted to direct people to the stuff I knew was pretty good. I don't know enough about things like the vastu shastra, but I've studied my math history pretty extensively and am more than happy to comment on that.
- novalis78 13y ago
  Regarding the "what-if" section: Could have been quite interesting if the early ancient Indian Universities around 1000 AD in Nalanda, Vikramasila etc. had actually persisted (that is without obliterating Islam and the Muslim conquest) and instead connected with the Europeans (or Byzanz for that matter) directly. Indian logic seems to have been quite developed at an early stage as well, Dignaga is an interesting character.
abecedarius 13y ago
Were there any ancients besides the Greeks who did appreciate proof? It seems like Europe didn't quite measure up on that score again until the 1800s, either.
monsterix 13y ago
> vastu shastra, which is astrological woo. I'd give you that in its current marketed form it is astrological bullshit, but originally Vastu Shastra was a formal form of science [1] grounded on engineering principles and urban design. All persevering to obtain a 'calm' for the dweller. One can still infer from the high precision N-S-E-W positioning of fairly huge ancient Hindu temples, historical remains of homes and dwellings, monasteries and other artefacts. Even the 1000+ step staircases in some of the forts and fortresses [2][3], transoceanic bridges [4] suggest the quality of math that was in play. The choice and placement of stone, wood and metal w.r.t Sun, tropical climate and other ergonomic needs is simply mind blowing. Math has to be at the root of it. Obviously not many records exist to substantiate the level of skill and academia prevalent at the time. I wish someone undertook a journey to research and substantiate just about "everything" that we have from Egypt to Indonesia (Hindu kingdoms spanned that far, yes!). At the risk of being shooed away by existing pride. [1] http://en.wikipedia.org/wiki/Vastu_shastra http://en.wikipedia.org/wiki/Vastu_shastra Even the wikipedia here, for example, says ... "while Vastu had long been essentially restricted to temple architecture..." which is completely wrong, and they defeat it in the third paragraph where they define "the Sanskrit word vastu means a dwelling or house with a corresponding plot of land" which is what Vaastu Shastra was all about, not temples alone. [2] http://en.wikipedia.org/wiki/File:ChandBaori.jpg http://en.wikipedia.org/wiki/File:ChandBaori.jpg [3] http://en.wikipedia.org/wiki/Chand_Baori http://en.wikipedia.org/wiki/Chand_Baori [4] http://en.wikipedia.org/wiki/Adam%27s_Bridge http://en.wikipedia.org/wiki/Adam%27s_Bridge
- wrongc0ntinent 13y ago
  >Math has to be at the root of it. Numerology is just as likely of a root.
  - monsterix 13y ago
    All right, scepticism taken. Look at these images: http://3.bp.blogspot.com/-qzhiolzuxsw/UK0HEPH7x4I/AAAAAAAAH8g/nJJp53oeilI/s1600/ChandBaori19.jpg http://3.bp.blogspot.com/-qzhiolzuxsw/UK0HEPH7x4I/AAAAAAAAH8... http://1.bp.blogspot.com/-a7UIHnAfmH0/UK0Ga-RmigI/AAAAAAAAH5I/Q7hjypv5Z9g/s1600/ChandBaori1.jpg http://1.bp.blogspot.com/-a7UIHnAfmH0/UK0Ga-RmigI/AAAAAAAAH5... http://bldgblog.blogspot.com/2012/11/chand-baori.html http://bldgblog.blogspot.com/2012/11/chand-baori.html http://bldgblog.blogspot.com/2012/11/chand-baori.html http://bldgblog.blogspot.com/2012/11/chand-baori.html This is just an example. What do you think has higher probability of being used to build this? 1. Math and calculations or 2. Numerology?
sn41 13y ago
This criticism of aversion to proofs is in general valid. However, be aware that Indians also made some significant steps towards calculus, and the first book explaining this had "arguments" and worked out examples. (This is not second hand knowledge, I know the language and have a copy of one volume of the book.) http://en.wikipedia.org/wiki/Yuktibh%C4%81%E1%B9%A3%C4%81 http://en.wikipedia.org/wiki/Yuktibh%C4%81%E1%B9%A3%C4%81 http://en.wikipedia.org/wiki/Kerala_school_of_astronomy_and_mathematics http://en.wikipedia.org/wiki/Kerala_school_of_astronomy_and_...

by shas3 13y ago

pflats 13y ago

Based on my reading, I couldn't agree more with your post. Hence my note about Bhaskara II's work being "rough"; I was trying to write for a lay audience. I too find myself wondering what the world would be like if there were more crossover between the early mathematical cultures. A few pages of Fibonacci's Liber Abaci pretty much transformed European math. I saw a couple criticisms of the page's overall tone; I wanted to direct people to the stuff I knew was pretty good. I don't know enough about things like the vastu shastra, but I've studied my math history pretty extensively and am more than happy to comment on that.

novalis78 13y ago
Regarding the "what-if" section: Could have been quite interesting if the early ancient Indian Universities around 1000 AD in Nalanda, Vikramasila etc. had actually persisted (that is without obliterating Islam and the Muslim conquest) and instead connected with the Europeans (or Byzanz for that matter) directly. Indian logic seems to have been quite developed at an early stage as well, Dignaga is an interesting character.

abecedarius 13y ago

Were there any ancients besides the Greeks who did appreciate proof? It seems like Europe didn't quite measure up on that score again until the 1800s, either.

monsterix 13y ago

> vastu shastra, which is astrological woo. I'd give you that in its current marketed form it is astrological bullshit, but originally Vastu Shastra was a formal form of science [1] grounded on engineering principles and urban design. All persevering to obtain a 'calm' for the dweller. One can still infer from the high precision N-S-E-W positioning of fairly huge ancient Hindu temples, historical remains of homes and dwellings, monasteries and other artefacts. Even the 1000+ step staircases in some of the forts and fortresses [2][3], transoceanic bridges [4] suggest the quality of math that was in play. The choice and placement of stone, wood and metal w.r.t Sun, tropical climate and other ergonomic needs is simply mind blowing. Math has to be at the root of it. Obviously not many records exist to substantiate the level of skill and academia prevalent at the time. I wish someone undertook a journey to research and substantiate just about "everything" that we have from Egypt to Indonesia (Hindu kingdoms spanned that far, yes!). At the risk of being shooed away by existing pride. [1] http://en.wikipedia.org/wiki/Vastu_shastra http://en.wikipedia.org/wiki/Vastu_shastra Even the wikipedia here, for example, says ... "while Vastu had long been essentially restricted to temple architecture..." which is completely wrong, and they defeat it in the third paragraph where they define "the Sanskrit word vastu means a dwelling or house with a corresponding plot of land" which is what Vaastu Shastra was all about, not temples alone. [2] http://en.wikipedia.org/wiki/File:ChandBaori.jpg http://en.wikipedia.org/wiki/File:ChandBaori.jpg [3] http://en.wikipedia.org/wiki/Chand_Baori http://en.wikipedia.org/wiki/Chand_Baori [4] http://en.wikipedia.org/wiki/Adam%27s_Bridge http://en.wikipedia.org/wiki/Adam%27s_Bridge

wrongc0ntinent 13y ago
>Math has to be at the root of it. Numerology is just as likely of a root.
- monsterix 13y ago
  All right, scepticism taken. Look at these images: http://3.bp.blogspot.com/-qzhiolzuxsw/UK0HEPH7x4I/AAAAAAAAH8g/nJJp53oeilI/s1600/ChandBaori19.jpg http://3.bp.blogspot.com/-qzhiolzuxsw/UK0HEPH7x4I/AAAAAAAAH8... http://1.bp.blogspot.com/-a7UIHnAfmH0/UK0Ga-RmigI/AAAAAAAAH5I/Q7hjypv5Z9g/s1600/ChandBaori1.jpg http://1.bp.blogspot.com/-a7UIHnAfmH0/UK0Ga-RmigI/AAAAAAAAH5... http://bldgblog.blogspot.com/2012/11/chand-baori.html http://bldgblog.blogspot.com/2012/11/chand-baori.html http://bldgblog.blogspot.com/2012/11/chand-baori.html http://bldgblog.blogspot.com/2012/11/chand-baori.html This is just an example. What do you think has higher probability of being used to build this? 1. Math and calculations or 2. Numerology?

sn41 13y ago

This criticism of aversion to proofs is in general valid. However, be aware that Indians also made some significant steps towards calculus, and the first book explaining this had "arguments" and worked out examples. (This is not second hand knowledge, I know the language and have a copy of one volume of the book.) http://en.wikipedia.org/wiki/Yuktibh%C4%81%E1%B9%A3%C4%81 http://en.wikipedia.org/wiki/Yuktibh%C4%81%E1%B9%A3%C4%81 http://en.wikipedia.org/wiki/Kerala_school_of_astronomy_and_mathematics http://en.wikipedia.org/wiki/Kerala_school_of_astronomy_and_...