Talk:Madhava of Sangamagrama

Citation Needed

Please provide a citation for Madhava being "considered the father of mathematical analysis" . . . I know of no printed sources that make a reasonable claim of this . . . the father of analysis as we know them today are more likely to be consider Karl Weierstraß, as he was interested in the basis of the Calculus . . . before his time, there were no clear definitions regarding the fundamentals of calculus, and thus theorems could not be properly proven. Madhava in contrast, like many before him, merely introduced the idea of infinity to certain classes of functions, like many after him would do before analysis was put on a firm footing. Arundhati bakshi 18:45, 24 March 2006 (UTC)

See Mathematical analysis and it's talk page for more detail (and a printed source for the claim). Also see [1] highlighting all pioneers in analysis - it considers Madhava the founder of mathematical analysis in contrast with Weierstrass as father of modern analysis. Weierstrass' page also says the same. --Pranathi 00:29, 6 April 2006 (UTC)

Put on Kerala School

Hi, I put these questions on the Kerala school.

Could we get some cleanup on the maths stuff?

• Infinite series expansions of functions.

Ok. How? By Taylor series? Fourier series?

• The power series.

Power series of what?

• The Taylor series.

Taylor series of what? There are 4 or 5 trigonmetric functions listed below.

• Trigonometric series.

...

• Rational approximations of infinite series.

...

• Taylor series of the sine and cosine functions (Madhava-Newton power series).

Ok. Wouldn't that fall above?

• Taylor series of the tangent function.

Likewise

• Taylor series of the arctangent function (Madhava-Gregory series).

Likewise?

• Second-order Taylor series approximations of the sine and cosine functions.

What's the 2nd order Taylor series? If the "1st order" is just sin(x) ~ x, then the second order would be sin(x) ~ x + x^3/3!.

• Third-order Taylor series approximation of the sine function.

So that would be sin(x) ~ x + x^3/3! + x^5/5! ?

• Power series of π (usually attributed to Leibniz).

Which one? π = 4/1 - 4/3 + 4/5 - ...

• Power series of π/4 (Euler's series).

Which one? Does this mean Leibniz above?

• Power series of the radius.

What radius?

• Power series of the diameter.

What diameter?

• Power series of the circumference.

What circumference?

• Power series of angle θ (equivalent to the Gregory series).

??? What does this mean?

• Infinite continued fractions.

Ok. As solutions to quadratics? Cubics?

• The solution of transcendental equations by iteration.

As solutions to ...

• Approximation of transcendental numbers by continued fractions.

Which transcendental number?

• Tests of convergence of infinite series.

Ok...

• Correctly computed the value of π to 11 decimal places, the most accurate value of π after almost a thousand years.

Ok...

• Sine tables to 12 decimal places of accuracy and cosine tables to 9 decimal places of accuracy, which would remain the most accurate upto the 17th century.

Ok...

• A procedure to determine the positions of the Moon every 36 minutes.

Ok...

• Methods to estimate the motions of the planets.

Ok

• Integration.

Including the fundamental theorem of calculus? Which rules? Integration of polynomials?

• Term by term integration.

Ok

• Laying the foundations for the development of calculus, which was then further developed by his successors at the Kerala School.

...

Thanks! --M a s 01:57, 12 May 2006 (UTC)

Obvious Thing

Okay in the article, the expansion for pi/4 is a direct result of the Madhava-Gregory series(theta=pi, n=1), but the article points to some expansion of the arctangent as the source. Is this a mistake?

Disputed

None of the questions under Put on Kerala School have been answered.

To give an example, the article claims that Madhava invented the fundamental ideas of:

1. Infinite series expansions of functions.
2. Power series.
3. Taylor series.
4. Maclaurin series.
5. Trigonometric series

First question, were these expansions really infinite as claimed? Further, for some functions he gave what looks like the first terms of a Taylor or Maclaurin series of that function. That is a nice accomplishment. But the fundamental idea of a Maclaurin or Taylor series consists of giving the rule how to develop a function into a series. No evidence that he knew this is given. -- Zz 17:56, 29 March 2007 (UTC)

Tag removed

Just added a number of facts, such as the location of Sangramagrama, the uncertainty regarding which of the results are specifically attributable to Madhava (including a sketch of some of the arguments), ensuring that the reader is aware of the degree of doubt on this matter.

Removed many of the indirect references (e.g. several instances of the Mactutor pages) with journal articles. Merged the "bibliography" section into references (though some people may disagree, I feel this is cleaner - you get a sense of what the text does; if we need to repeat the citations in a bibliography, it should have annotations).

Also added a citation for integration along with the original malayalam text.

As for the disputed facts, I think among the examples given, with citations to various texts, we have many examples of these three :

1. Infinite series expansions of functions (mostly trig functions)
2. Power series : all are power series expansions
3. Trigonometric series : many involve the trig functions in the expansion

The following two however appear to be unlikely:

1. Taylor series.
2. Maclaurin series.

Since these express functions as powers of the derivative for a general function, it is unclear that the understanding of higher-order derivatives was sufficiently understood. While derivatives are being computed, it is not clear whether power series of derivatives were used. Unless other facts come to light, I am removing reference to these two. mukerjee (talk) 17:42, 6 September 2007 (UTC)

Transmission to Europe

I have no expertise in this matter, but the section This is due to wrong understanding of the authors concerned. It was almost impossible for the Jesuits in the sixteenth century, who are experts with the eminence of Mādhavan or his disciples, to study Sanskrit and Malayalam and to transmit them to European Mathematicians, instead of they themselves claiming the credit for the discovery. is very unclear. Who is misunderstanding whom? What is impossible? Were the Jesuits able to understand Mādhavan but unable to transmit them? Were they experts in Sanskrit and Malayam or not? Can anyone offer something to clarify it? Moreover, it reads to me like original research. Perhaps it would be clearer to say acknowledge priority in discovery of the relevant work to Mādhavan etc. but to state that there was no actual evidence that this knowledge was transmitted to the West; therefore the question of tranmission to Europe is simply unresolvable without more evidence. Rob Burbidge (talk) 09:51, 18 May 2011 (UTC)

I asked pretty much the same questions when reading those sentences. They make almost no sense. There are quite a few grammar issues (and shaky claims) in the current article. The part you pointed out is just the worst of it. 24.220.188.43 (talk) 14:53, 2 September 2011 (UTC)

Usage of "we"

I added a tone tag, because the article uses the plural third person ("we") very frequently, e.g. "We find Madhava's work on the value of π cited in..." This is not in keeping with the style guidelines. I'd fix it myself, but I'm supposed to be working instead of reading about approximations of Pi, let alone repairing a Wikipedia article! :D --13.12.254.95 (talk) 16:04, 15 March 2012 (UTC)