Kayalvizhi wrote:Because it gives the wrong view that Indian culture is northern culture. It may be true if you remove Tamilnadu from it.

As long as Tamil Nadu is forcibly contained within India, we oppose saying Indian culture is Sanskrit.

Celebrate classical language week (Tamil, Telugu, Kannada and Sanskrit). May be Malayalam also because Kerala is asking for classicaL status and I support it.

Kayalvizhi wrote:Because it gives the wrong view that Indian culture is northern culture. It may be true if you remove Tamilnadu from it.

As long as Tamil Nadu is forcibly contained within India, we oppose saying Indian culture is Sanskrit.

Celebrate classical language week (Tamil, Telugu, Kannada and Sanskrit). May be Malayalam also because Kerala is asking for classicaL status and I support it.

Kayalvizhi wrote:Because it gives the wrong view that Indian culture is northern culture. It may be true if you remove Tamilnadu from it.

As long as Tamil Nadu is forcibly contained within India, we oppose saying Indian culture is Sanskrit.

Celebrate classical language week (Tamil, Telugu, Kannada and Sanskrit). May be Malayalam also because Kerala is asking for classicaL status and I support it.

Kayalvizhi wrote:We see it. Respect our feelings. Do not celeb Sansk week in the Tamil country.

Kinnera wrote:
Malayalam already has the classical language status, along with telugu, kannada and tamil.

Kayalvizhi wrote:

Kinnera wrote:
Malayalam already has the classical language status, along with telugu, kannada and tamil.

You are speaking out of your ignorance.

Kinnera wrote:

Kayalvizhi wrote:We see it. Respect our feelings. Do not celeb Sansk week in the Tamil country.

Nobody is forcing you to celebrate it if you don't want to. But if some want to celebrate it in TN, they should be free to do so. You can't tell them not to. It's a free, democratic country, not some restricted, communist country.

Kayalvizhi wrote:

Kinnera wrote:

Kayalvizhi wrote:We see it. Respect our feelings. Do not celeb Sansk week in the Tamil country.

Nobody is forcing you to celebrate it if you don't want to. But if some want to celebrate it in TN, they should be free to do so. You can't tell them not to. It's a free, democratic country, not some restricted, communist country.

As I posted elsewhere, do not celebrate it in schools with our taxes.

Collect funds privately, rent a hall and celebrate it for a week, month or all year long.

Kinnera wrote:

Kayalvizhi wrote:

Kinnera wrote:
Malayalam already has the classical language status, along with telugu, kannada and tamil.

You are speaking out of your ignorance.

In 2004, the Government of India declared that languages that met certain requirements could be accorded the status of a "Classical Language in India".^[29] (These are not classical languages in the usual sense.) Languages thus far declared to be Classical are Tamil (in 2004),^[30] Sanskrit (in 2005),^[31] Telugu (in 2008), Kannada (in 2008),^[32] Malayalam (in 2013)^[33] and Oriya (in 2014).^{[34][35]   from wiki.}

Kinnera wrote:

Kayalvizhi wrote:Because it gives the wrong view that Indian culture is northern culture. It may be true if you remove Tamilnadu from it.

As long as Tamil Nadu is forcibly contained within India, we oppose saying Indian culture is Sanskrit.

Celebrate classical language week (Tamil, Telugu, Kannada and Sanskrit). May be Malayalam also because Kerala is asking for classicaL status and I support it.

It's all in the perception. Others (telugus, kannadigas, malayalis, gujaratis, bengali, etc etc) don't see it as northern culture. They see it as their own culture. There's no 'us vs them' feeling. There's only the 'all our' feeling.

Kayalvizhi wrote:

Kinnera wrote:

Kayalvizhi wrote:We see it. Respect our feelings. Do not celeb Sansk week in the Tamil country.

Nobody is forcing you to celebrate it if you don't want to. But if some want to celebrate it in TN, they should be free to do so. You can't tell them not to. It's a free, democratic country, not some restricted, communist country.

As I posted elsewhere, do not celebrate it in schools with our taxes.

Collect funds privately, rent a hall and celebrate it for a week, month or all year long.

Marathadi-Saamiyaar wrote:

Kinnera wrote:

Kayalvizhi wrote:Because it gives the wrong view that Indian culture is northern culture. It may be true if you remove Tamilnadu from it.

As long as Tamil Nadu is forcibly contained within India, we oppose saying Indian culture is Sanskrit.

Celebrate classical language week (Tamil, Telugu, Kannada and Sanskrit). May be Malayalam also because Kerala is asking for classicaL status and I support it.

It's all in the perception. Others (telugus, kannadigas, malayalis, gujaratis, bengali, etc etc) don't see it as northern culture. They see it as their own culture. There's no 'us vs them' feeling. There's only the 'all our' feeling.

Kinny I order you to celebrate Tamil week as Telugu came out of Tamil and Andhra came out of Tamil Nadu.

So next week is your Tamil week. Make payasam and pongal and not to mention dosai and idly every day next week.

Kayalvizhi wrote:Because it gives the wrong view that Indian culture is northern culture. It may be true if you remove Tamilnadu from it.

As long as Tamil Nadu is forcibly contained within India, we oppose saying Indian culture is Sanskrit.

Celebrate classical language week (Tamil, Telugu, Kannada and Sanskrit). May be Malayalam also because Kerala is asking for classicaL status and I support it.

Marathadi-Saamiyaar wrote:

Kinnera wrote:

Kayalvizhi wrote:Because it gives the wrong view that Indian culture is northern culture. It may be true if you remove Tamilnadu from it.

As long as Tamil Nadu is forcibly contained within India, we oppose saying Indian culture is Sanskrit.

Celebrate classical language week (Tamil, Telugu, Kannada and Sanskrit). May be Malayalam also because Kerala is asking for classicaL status and I support it.

It's all in the perception. Others (telugus, kannadigas, malayalis, gujaratis, bengali, etc etc) don't see it as northern culture. They see it as their own culture. There's no 'us vs them' feeling. There's only the 'all our' feeling.

Kinny I order you to celebrate Tamil week as Telugu came out of Tamil and Andhra came out of Tamil Nadu.

So next week is your Tamil week. Make payasam and pongal and not to mention dosai and idly every day next week.

Kayalvizhi wrote:Because it gives the wrong view that Indian culture is northern culture. It may be true if you remove Tamilnadu from it.

As long as Tamil Nadu is forcibly contained within India, we oppose saying Indian culture is Sanskrit.

Celebrate classical language week (Tamil, Telugu, Kannada and Sanskrit). May be Malayalam also because Kerala is asking for classicaL status and I support it.

MaxEntropy_Man wrote:

Kayalvizhi wrote:Because it gives the wrong view that Indian culture is northern culture. It may be true if you remove Tamilnadu from it.

As long as Tamil Nadu is forcibly contained within India, we oppose saying Indian culture is Sanskrit.

Celebrate classical language week (Tamil, Telugu, Kannada and Sanskrit). May be Malayalam also because Kerala is asking for classicaL status and I support it.

one of the greatest medieval math treatises in india the yuktibhasa was written in malayalam.

Kayalvizhi wrote:Because it gives the wrong view that Indian culture is northern culture. It may be true if you remove Tamilnadu from it.

As long as Tamil Nadu is forcibly contained within India, we oppose saying Indian culture is Sanskrit.

Celebrate classical language week (Tamil, Telugu, Kannada and Sanskrit). May be Malayalam also because Kerala is asking for classicaL status and I support it.

MaxEntropy_Man wrote:this is posted for the benefit of those interested in knowing more about the contributions of the kerala school of medieval mathematicians.

http://www.pas.rochester.edu/~rajeev/papers/canisiustalks.pdf

sanskrit and malayalam were both used by the kerala mathematicians and astronomers.  sanskrit and the dravidian languages have always coexisted and mutually benefited. we don't need some johnny-come-lately hindians to urge us to look into sanskrit.

in particular, no hindi was used by the kerala mathematicians.

MaxEntropy_Man wrote:much modern interest in medieval indian mathematics comes from the malayalam text yuktibhasa which summarized and explained the main results of infinite series.

Rashmun wrote:

MaxEntropy_Man wrote:much modern interest in medieval indian mathematics comes from the malayalam text yuktibhasa which summarized and explained the main results of infinite series.

that is true. but the Yukitbhasa is a commentary on a primary text. the Yuktibhasa is unusually detailed; perhaps it was designed to help along some mathematician(s) who was a dullard. but because it is so detailed it is very useful to help us understand the knowledge of the Kerala mathematicians.

MaxEntropy_Man wrote:

Rashmun wrote:

MaxEntropy_Man wrote:much modern interest in medieval indian mathematics comes from the malayalam text yuktibhasa which summarized and explained the main results of infinite series.

that is true. but the Yukitbhasa is a commentary on a primary text. the Yuktibhasa is unusually detailed; perhaps it was designed to help along some mathematician(s) who was a dullard. but because it is so detailed it is very useful to help us understand the knowledge of the Kerala mathematicians.

the words dullard and mathematician seldom go together.

Rashmun wrote:

MaxEntropy_Man wrote:

Rashmun wrote:

MaxEntropy_Man wrote:much modern interest in medieval indian mathematics comes from the malayalam text yuktibhasa which summarized and explained the main results of infinite series.

that is true. but the Yukitbhasa is a commentary on a primary text. the Yuktibhasa is unusually detailed; perhaps it was designed to help along some mathematician(s) who was a dullard. but because it is so detailed it is very useful to help us understand the knowledge of the Kerala mathematicians.

the words dullard and mathematician seldom go together.

All right, let us use the words weak student or mediocre student of mathematics.

MaxEntropy_Man wrote:

Rashmun wrote:

MaxEntropy_Man wrote:

Rashmun wrote:

MaxEntropy_Man wrote:much modern interest in medieval indian mathematics comes from the malayalam text yuktibhasa which summarized and explained the main results of infinite series.

that is true. but the Yukitbhasa is a commentary on a primary text. the Yuktibhasa is unusually detailed; perhaps it was designed to help along some mathematician(s) who was a dullard. but because it is so detailed it is very useful to help us understand the knowledge of the Kerala mathematicians.

the words dullard and mathematician seldom go together.

All right, let us use the words weak student or mediocre student of mathematics.

i doubt that. we (you and i) don't know that the yuktibhasa is a mere repetition of earlier results with explanatory notes. mathematicians often derive new results based on older results. that doesn't mean the authorship of the newer results lies with the older author. you state things with such decisiveness without having explored it yourself. i think the whole world of medieval kerala mathematics is very rich and people have only now begun to grasp the full extent of their achievements. i wouldn't state anything with such finality including whether any new results were contained within the yuktibhasa. let's wait for the mathematicians who are also linguistically proficient in sanskrit and malayalam to give a fuller account. your anxiousness to make pronouncements only solidifies my view that you are as usual agenda driven. take a chill pill, go for a walk and reconsider.

MaxEntropy_Man wrote:rashmun:

(a) i have a hearsay of a piece of conversation you long ago had with someone who is supposedly an authority on kerala mathematics.

(b) when it comes to controversial subjects it is my wont to consult many many sources rather than take the word of one person even if that one person has won a nobel prize. so we fundamentally have a different approach to such things and unlikely to agree on much. let's just leave it at that.

i am not a big fan of vaLLuvar, but i heed him when he says: "kaNNAl kaNbathum poi, kAthal kEtpathum poi, thIra visAripathE mei". what you see is false, what you hear is false, what you learn yourself through deep inquiry is the truth.

MaxEntropy_Man wrote:rashmun:

(a) i have a hearsay of a piece of conversation you long ago had with someone who is supposedly an authority on kerala mathematics.

(b) when it comes to controversial subjects it is my wont to consult many many sources rather than take the word of one person even if that one person has won a nobel prize. so we fundamentally have a different approach to such things and unlikely to agree on much. let's just leave it at that.

i am not a big fan of vaLLuvar, but i heed him when he says: "kaNNAl kaNbathum poi, kAthal kEtpathum poi, thIra visAripathE mei". what you see is false, what you hear is false, what you learn yourself through deep inquiry is the truth.

Rashmun wrote:

MaxEntropy_Man wrote:rashmun:

(a) i have a hearsay of a piece of conversation you long ago had with someone who is supposedly an authority on kerala mathematics.

(b) when it comes to controversial subjects it is my wont to consult many many sources rather than take the word of one person even if that one person has won a nobel prize. so we fundamentally have a different approach to such things and unlikely to agree on much. let's just leave it at that.

i am not a big fan of vaLLuvar, but i heed him when he says: "kaNNAl kaNbathum poi, kAthal kEtpathum poi, thIra visAripathE mei". what you see is false, what you hear is false, what you learn yourself through deep inquiry is the truth.

I am willing to change my views on this issue if I come across a primary text of the Kerala school of mathematicians ( which is not a commentary on a primary text) that is not in Sanskrit.

The work was unique for its time, since it contained proofs and derivations of the theorems that it presented; something that was not usually done by any Indian mathematicians of that era.[7] Some of its important developments in analysis include: the infinite series expansion of a function, the power series, the Taylor series, the trigonometric series for sine, cosine, tangent and arctangent, the second and third order Taylor series approximations of sine and cosine, the power series of π, π/4, θ, the radius, diameter and circumference, and tests of convergence.

Kayalvizhi wrote:To anyone who has real knowledge about this,


I was told that all that Sanskrit texts contain are shortcuts to multiplication, division and calculating areas and volumes. Is there more to it? If so, what? Can you give authentic references in english?

MaxEntropy_Man wrote:

Rashmun wrote:

MaxEntropy_Man wrote:rashmun:

(a) i have a hearsay of a piece of conversation you long ago had with someone who is supposedly an authority on kerala mathematics.

(b) when it comes to controversial subjects it is my wont to consult many many sources rather than take the word of one person even if that one person has won a nobel prize. so we fundamentally have a different approach to such things and unlikely to agree on much. let's just leave it at that.

i am not a big fan of vaLLuvar, but i heed him when he says: "kaNNAl kaNbathum poi, kAthal kEtpathum poi, thIra visAripathE mei". what you see is false, what you hear is false, what you learn yourself through deep inquiry is the truth.

I am willing to change my views on this issue if I come across a primary text of the Kerala school of mathematicians ( which is not a commentary on a primary text) that is not in Sanskrit.

that statement itself is predicated on your assumption (as yet unproven) that the yuktibhasa contains no new results, although it does contain older results. wikipedia only says that it is "based" on the tantra samgraha. not that it is a mere translation.

further on the wiki text says:

The work was unique for its time, since it contained proofs and derivations of the theorems that it presented; something that was not usually done by any Indian mathematicians of that era.[7] Some of its important developments in analysis include: the infinite series expansion of a function, the power series, the Taylor series, the trigonometric series for sine, cosine, tangent and arctangent, the second and third order Taylor series approximations of sine and cosine, the power series of π, π/4, θ, the radius, diameter and circumference, and tests of convergence.

the idea of rigorous proof in mathematics is something that is thought of as a western (greek) thing generally. it is creditable that the yuktibhasa paid attention to proofs and derivations (which you thoughtlessly said was for the dullards!) in an era when indian mathematicians were not known for it.  perhaps you don't realize that stating a theorem or a result and proving it are two different things. sometimes mathematicians get divided credit -- one for stating a result or a theorem and another for proving it.  for example the poincare' conjecture. poincare' came up with the notion, but perelman is the one who is given credit for coming up with the proof. this is why i am not ready to buy the idea that the yuktibhasa is a mere translation of the tantra samgraha. if that was the case, since there are many sanskrit trained scholars (no shortage of it i am sure), mathematicians would refer to it alone rather than the yuktibhasa as the main source text.  they don't. they refer to the yuktibhasa.  hence my conclusion that it contains proofs in addition to newer expository material. we have to tread carefully.

Rashmun wrote:

MaxEntropy_Man wrote:

Rashmun wrote:

MaxEntropy_Man wrote:rashmun:

(a) i have a hearsay of a piece of conversation you long ago had with someone who is supposedly an authority on kerala mathematics.

(b) when it comes to controversial subjects it is my wont to consult many many sources rather than take the word of one person even if that one person has won a nobel prize. so we fundamentally have a different approach to such things and unlikely to agree on much. let's just leave it at that.

i am not a big fan of vaLLuvar, but i heed him when he says: "kaNNAl kaNbathum poi, kAthal kEtpathum poi, thIra visAripathE mei". what you see is false, what you hear is false, what you learn yourself through deep inquiry is the truth.

I am willing to change my views on this issue if I come across a primary text of the Kerala school of mathematicians ( which is not a commentary on a primary text) that is not in Sanskrit.

that statement itself is predicated on your assumption (as yet unproven) that the yuktibhasa contains no new results, although it does contain older results. wikipedia only says that it is "based" on the tantra samgraha. not that it is a mere translation.

further on the wiki text says:

The work was unique for its time, since it contained proofs and derivations of the theorems that it presented; something that was not usually done by any Indian mathematicians of that era.[7] Some of its important developments in analysis include: the infinite series expansion of a function, the power series, the Taylor series, the trigonometric series for sine, cosine, tangent and arctangent, the second and third order Taylor series approximations of sine and cosine, the power series of π, π/4, θ, the radius, diameter and circumference, and tests of convergence.

the idea of rigorous proof in mathematics is something that is thought of as a western (greek) thing generally. it is creditable that the yuktibhasa paid attention to proofs and derivations (which you thoughtlessly said was for the dullards!) in an era when indian mathematicians were not known for it.  perhaps you don't realize that stating a theorem or a result and proving it are two different things. sometimes mathematicians get divided credit -- one for stating a result or a theorem and another for proving it.  for example the poincare' conjecture. poincare' came up with the notion, but perelman is the one who is given credit for coming up with the proof. this is why i am not ready to buy the idea that the yuktibhasa is a mere translation of the tantra samgraha. if that was the case, since there are many sanskrit trained scholars (no shortage of it i am sure), mathematicians would refer to it alone rather than the yuktibhasa as the main source text.  they don't. they refer to the yuktibhasa.  hence my conclusion that it contains proofs in addition to newer expository material. we have to tread carefully.

Yuktibhasa is a commentary on a specific text: Tantrasangraha by Nilakantha. See here:

http://books.google.com/books?id=DAPLaxw-53IC&pg=PA606&lpg=PA606&dq=yuktibhasa+is+a+commentary+on&source=bl&ots=kl2JrxX4ny&sig=dfD754iL5Dz-t4RU9qBW2xSR-7U&hl=en&sa=X&ei=ADDRU82QB9GJogTv-4CABg&ved=0CCEQ6AEwAQ#v=onepage&q=yuktibhasa%20is%20a%20commentary%20on&f=false

Tantrasangraha is in Sanskrit and Nilakantha was either the founding father of the Kerala school of mathematics and or one of the founding fathers.

Kayalvizhi wrote:Max,
I was told that all that Sanskrit texts contain are shortcuts to multiplication, division and calculating areas and volumes. Is there more to it? If so, what? Can you give authentic references in english?

MaxEntropy_Man wrote:

Rashmun wrote:

MaxEntropy_Man wrote:

Rashmun wrote:

MaxEntropy_Man wrote:rashmun:

(a) i have a hearsay of a piece of conversation you long ago had with someone who is supposedly an authority on kerala mathematics.

(b) when it comes to controversial subjects it is my wont to consult many many sources rather than take the word of one person even if that one person has won a nobel prize. so we fundamentally have a different approach to such things and unlikely to agree on much. let's just leave it at that.

i am not a big fan of vaLLuvar, but i heed him when he says: "kaNNAl kaNbathum poi, kAthal kEtpathum poi, thIra visAripathE mei". what you see is false, what you hear is false, what you learn yourself through deep inquiry is the truth.

I am willing to change my views on this issue if I come across a primary text of the Kerala school of mathematicians ( which is not a commentary on a primary text) that is not in Sanskrit.

that statement itself is predicated on your assumption (as yet unproven) that the yuktibhasa contains no new results, although it does contain older results. wikipedia only says that it is "based" on the tantra samgraha. not that it is a mere translation.

further on the wiki text says:

The work was unique for its time, since it contained proofs and derivations of the theorems that it presented; something that was not usually done by any Indian mathematicians of that era.[7] Some of its important developments in analysis include: the infinite series expansion of a function, the power series, the Taylor series, the trigonometric series for sine, cosine, tangent and arctangent, the second and third order Taylor series approximations of sine and cosine, the power series of π, π/4, θ, the radius, diameter and circumference, and tests of convergence.

the idea of rigorous proof in mathematics is something that is thought of as a western (greek) thing generally. it is creditable that the yuktibhasa paid attention to proofs and derivations (which you thoughtlessly said was for the dullards!) in an era when indian mathematicians were not known for it.  perhaps you don't realize that stating a theorem or a result and proving it are two different things. sometimes mathematicians get divided credit -- one for stating a result or a theorem and another for proving it.  for example the poincare' conjecture. poincare' came up with the notion, but perelman is the one who is given credit for coming up with the proof. this is why i am not ready to buy the idea that the yuktibhasa is a mere translation of the tantra samgraha. if that was the case, since there are many sanskrit trained scholars (no shortage of it i am sure), mathematicians would refer to it alone rather than the yuktibhasa as the main source text.  they don't. they refer to the yuktibhasa.  hence my conclusion that it contains proofs in addition to newer expository material. we have to tread carefully.

Yuktibhasa is a commentary on a specific text: Tantrasangraha by Nilakantha. See here:

http://books.google.com/books?id=DAPLaxw-53IC&pg=PA606&lpg=PA606&dq=yuktibhasa+is+a+commentary+on&source=bl&ots=kl2JrxX4ny&sig=dfD754iL5Dz-t4RU9qBW2xSR-7U&hl=en&sa=X&ei=ADDRU82QB9GJogTv-4CABg&ved=0CCEQ6AEwAQ#v=onepage&q=yuktibhasa%20is%20a%20commentary%20on&f=false

Tantrasangraha is in Sanskrit and Nilakantha was either the founding father of the Kerala school of mathematics and or one of the founding fathers.

but not (merely) a translation, a point you seem to be deliberately obfuscating. sometimes a commentary is more useful than the original text. further, i am not sure if nilakantha's texts contains proofs and derivations. if the yuktibhasa contains proofs and derivations not contained in the original text, that should be considered a new contribution.

from your own reference (thanks by the way; seems like a volume i would like to read and enjoy), at the bottom of page 615, is a nice statement and proof of what is today known as euler's series for pi.  it states that the result is "given" in tantra samgraha (TS), but that the derivation that is described by the author of your textbook is "a method outlined" in yuktibhasa (YB).  if it was all contained in the TS there would be no need for the YB.  there is a reason modern mathematicians refer to the YB, (dullards the whole lot of them).

Rashmun wrote:The author of the TS knew about the derivations and proofs given in YB but only gave his results.

southindian wrote:

Kayalvizhi wrote:Max,
I was told that all that Sanskrit texts contain are shortcuts to multiplication, division and calculating areas and volumes. Is there more to it? If so, what? Can you give authentic references in english?

Really?

Dude,

You are such a joke and a waste.

You still have some years of life left to grow-up... before you die.

Kayalvizhi wrote:Is ther an English translation of any of these Sanskrit math text? Reference?

MaxEntropy_Man wrote:regardless of these language fights, the very idea that ancient indian mathematicians had so many european mathematicians beat by a few millenia on so many aspects of modern mathematics always makes my hair stand on end when i think about it. too bad that the names by which these things are referred to are somewhat set in stone.

MaxEntropy_Man wrote:

Rashmun wrote:The author of the TS knew about the derivations and proofs given in YB but only gave his results.

how can you be so sure of it?  there are many theorems that ramanujan stated without proof that were proved by other mathematicians. that he didn't always know the proof can be inferred from the fact that some of them were proven to be plain wrong. it is not always the case that a mathematician who states a result also knows its proof. a result is one thing. its proof is another. both deserve credit.

MaxEntropy_Man wrote:

Kayalvizhi wrote:Is ther an English translation of any of these Sanskrit math text? Reference?

i don't know of word to word translations, but many authors including some that i posted and some that rashmun referred to have written modern english commentaries on extensive portions of it. there probably isn't a word by word translation because there is probably also some mundane stuff in there in addition to the remarkable.  

Kayalvizhi wrote:

MaxEntropy_Man wrote:

Kayalvizhi wrote:Is ther an English translation of any of these Sanskrit math text? Reference?

i don't know of word to word translations, but many authors including some that i posted and some that rashmun referred to have written modern english commentaries on extensive portions of it. there probably isn't a word by word translation because there is probably also some mundane stuff in there in addition to the remarkable.  

The problem with commentaries is that these Sanskrit lovers make up things (interpret things to suit their agenda). I cannot trust them. I am looking for a plain translation. Then I can make up my mind.

Sometime ago a commentary said some Sanskrit text shows ancient Indians had telegraph. When I found the actual translation, ther wasw nothing like that. Unfortunately I did not save those 2 pages.

There is an old Tamil poem that says cutting the atom into 8 pieces or something. A Tamil scholar interpreted it as Tamils knew how to split atoms. Utter nonsense.

Kayalvizhi wrote:

MaxEntropy_Man wrote:

Kayalvizhi wrote:Is ther an English translation of any of these Sanskrit math text? Reference?

i don't know of word to word translations, but many authors including some that i posted and some that rashmun referred to have written modern english commentaries on extensive portions of it. there probably isn't a word by word translation because there is probably also some mundane stuff in there in addition to the remarkable.  

The problem with commentaries is that these Sanskrit lovers make up things (interpret things to suit their agenda). I cannot trust them. I am looking for a plain translation. Then I can make up my mind.

Sometime ago a commentary said some Sanskrit text shows ancient Indians had telegraph. When I found the actual translation, ther wasw nothing like that. Unfortunately I did not save those 2 pages.

There is an old Tamil poem that says cutting the atom into 8 pieces or something. A Tamil scholar interpreted it as Tamils knew how to split atoms. Utter nonsense.

Rashmun wrote:

MaxEntropy_Man wrote:

Rashmun wrote:

MaxEntropy_Man wrote:

Rashmun wrote:

I am willing to change my views on this issue if I come across a primary text of the Kerala school of mathematicians ( which is not a commentary on a primary text) that is not in Sanskrit.

that statement itself is predicated on your assumption (as yet unproven) that the yuktibhasa contains no new results, although it does contain older results. wikipedia only says that it is "based" on the tantra samgraha. not that it is a mere translation.

further on the wiki text says:

The work was unique for its time, since it contained proofs and derivations of the theorems that it presented; something that was not usually done by any Indian mathematicians of that era.[7] Some of its important developments in analysis include: the infinite series expansion of a function, the power series, the Taylor series, the trigonometric series for sine, cosine, tangent and arctangent, the second and third order Taylor series approximations of sine and cosine, the power series of π, π/4, θ, the radius, diameter and circumference, and tests of convergence.

the idea of rigorous proof in mathematics is something that is thought of as a western (greek) thing generally. it is creditable that the yuktibhasa paid attention to proofs and derivations (which you thoughtlessly said was for the dullards!) in an era when indian mathematicians were not known for it.  perhaps you don't realize that stating a theorem or a result and proving it are two different things. sometimes mathematicians get divided credit -- one for stating a result or a theorem and another for proving it.  for example the poincare' conjecture. poincare' came up with the notion, but perelman is the one who is given credit for coming up with the proof. this is why i am not ready to buy the idea that the yuktibhasa is a mere translation of the tantra samgraha. if that was the case, since there are many sanskrit trained scholars (no shortage of it i am sure), mathematicians would refer to it alone rather than the yuktibhasa as the main source text.  they don't. they refer to the yuktibhasa.  hence my conclusion that it contains proofs in addition to newer expository material. we have to tread carefully.

Yuktibhasa is a commentary on a specific text: Tantrasangraha by Nilakantha. See here:

http://books.google.com/books?id=DAPLaxw-53IC&pg=PA606&lpg=PA606&dq=yuktibhasa+is+a+commentary+on&source=bl&ots=kl2JrxX4ny&sig=dfD754iL5Dz-t4RU9qBW2xSR-7U&hl=en&sa=X&ei=ADDRU82QB9GJogTv-4CABg&ved=0CCEQ6AEwAQ#v=onepage&q=yuktibhasa%20is%20a%20commentary%20on&f=false

Tantrasangraha is in Sanskrit and Nilakantha was either the founding father of the Kerala school of mathematics and or one of the founding fathers.

but not (merely) a translation, a point you seem to be deliberately obfuscating. sometimes a commentary is more useful than the original text. further, i am not sure if nilakantha's texts contains proofs and derivations. if the yuktibhasa contains proofs and derivations not contained in the original text, that should be considered a new contribution.

from your own reference (thanks by the way; seems like a volume i would like to read and enjoy), at the bottom of page 615, is a nice statement and proof of what is today known as euler's series for pi.  it states that the result is "given" in tantra samgraha (TS), but that the derivation that is described by the author of your textbook is "a method outlined" in yuktibhasa (YB).  if it was all contained in the TS there would be no need for the YB.  there is a reason modern mathematicians refer to the YB, (dullards the whole lot of them).

Who said it is a translation? A commentary is not a translation. It is an explanatory text elaborating the primary text. The YB is mainly based on the TS and presumably the stuff that is not based on TS is coming from other primary texts. The author of the TS knew about the derivations and proofs given in YB but only gave his results. Am reposting some material since I don't know whether u read it. See in particular the first paragraph.

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Madhava's work on power series for p and for sine and cosine functions is referred to by a number of the later writers, although the original sources remain undiscovered or unstudied. Nilakantha (1445-1555) was mainly an astronomer, but his Aryabhatiya Bhasya and Tantra Samgraha contain work on infinite-series expansions, problems of algebra and spherical geometry. Jyesthadeva (c. 1550) wrote, in a regional language rather than in Sanskrit, Yuktibhasa, one of those rare texts in Indian mathematics or astronomy that gives detailed derivations of many theorems and formulae in use at the time.This work is mainly based on the Tantra Samgraha of Nilakantha.

A joint commentary on Bhaskaracharya's Lilavati by Narayana (c. 1500-75) and Sankara Variar (c. 1500-1560), entitled Kriyakramakari, also contains a discussion of Madhava's work. The Karana Paddhati by Putumana Somayaji (c. 1660-1740) provides a detailed discussion of the various trigonometric series. Finally there is Sankara Varman, the author of Sadratnamala, who lived at the beginning of the nineteenth century and may be said to have been the last of the notable names in Kerala mathematics. His work in five chapters contains, appropriately, a summary of most of the results of the Kerala school, without any proofs though.

http://www.infinityfoundation.com/mandala/t_es/t_es_agraw_kerala.htm