9 ms·

If you take a look at the math subsection (https://sites.google.com/site/ancientbharat/math https://sites.google.com/site/ancientbharat/math) be aware that Brah

by pflats 13y ago

If you take a look at the math subsection (https://sites.google.com/site/ancientbharat/math https://sites.google.com/site/ancientbharat/math) be aware that Brahmagupta was a beast of a mathematician. His sucessors, the two Bhaskaras, were ridiculously good as well. Their names aren't nearly as big as any of the European mathematicians you know, but they were powerhouses of math during Europe's dark ages. Brahmagupta was pretty much the first recorded dude to use 0 in math, so he's got that going for him, and the only issue people take with his work is that he was weak around the indeterminate forms (e.g. claiming 0/0 = 0)[1]. His work on Pell's equation is pretty awesome too, but then we're veering into more esoteric mathematics, so I digress. Bhaskara II invented a rough and early verison of differential calculus to calculate instaneous rates of change in the mid 1100s. Newton finished his Method of Fluxions in 1671. (Newton's work was independent of Bhaskara II's and is said to be far more rigourous with greather breadth and depth of usage and applications; I haven't read enough of either to be an honest source, but the claim seems reasonable.) [1]For an ancient, though, this is understandable. We know that 0⨯0 = 0, that b|a iff a = b⨯k, and that a = bq + r, so it's reasonable to assume that since 0 = 0⨯0 + 0 and 0|0, that 0/0 = 0. (Phew!) When you pretty much codify 0 in math, I'll cut you a break on that one.

unmole 13y ago
Don't forget Aryabhata. His work in trigonometry and calendars was perhaps a wee bit more important Bramhagupta's acomplishments in practical terms.
- pflats 13y ago
  I had done exactly that. Oops! (I knew a major trigonometer came before Bramhagupta, but I forgot his name.)
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

by pflats 13y ago

unmole 13y ago

Don't forget Aryabhata. His work in trigonometry and calendars was perhaps a wee bit more important Bramhagupta's acomplishments in practical terms.

pflats 13y ago
I had done exactly that. Oops! (I knew a major trigonometer came before Bramhagupta, but I forgot his name.)

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