
The legacy of Srinivasa Ramanujan - rehack
http://www.thehindu.com/sci-tech/science/article2746988.ece
======
rehack
"Ramanujan cultivated his love for mathematics singlehandedly and in total
isolation" ...

"At the age of 12, he borrowed from a friend a copy of Loney's book on Plane
Trigonometry, published by Cambridge University Press in 1894"...

"It is not a remarkable book, and Ramanujan's use of it to propel himself to
the centre stage of 20th century mathematics, has made the book remarkable. It
was largely used by students of Carr who were preparing for the entrance
examination in mathematics at Cambridge University. Ramanujan used the book to
master all of 18th and 19th century mathematics. He set about to demonstrate
each of the assertions of the book, using only his slate to do the
calculations. He would jot down the formula to be proved, and then erase it
with his elbow, and then continue to jot down some more formulas. In this way,
he worked through the entire book. People used to speak of his “bruised
elbow.” Sadly, he took Carr's book as a model for mathematical writing and
left behind his famous notebooks containing many formulas but practically no
proofs."

~~~
huhtenberg
_I remember once going to see him [Ramanujan] when he was ill at Putney. I had
ridden in taxi cab number 1729 and remarked that the number seemed to me
rather a dull one, and that I hoped it was not an unfavorable omen. "No," he
replied, "it is a very interesting number; it is the smallest number
expressible as the sum of two cubes in two different ways._

Courtesy of G.H.Hardy

~~~
rehack
Indeed.

<http://en.wikipedia.org/wiki/1729_(number)>

~~~
ricksta
Did he just figured that out on the spot when his ill or knew it from before?

~~~
abhaga
I think Kanigel's book talks about this. It seems he had worked through first
few thousand numbers and knew all of them quite well. Thus instead of a spark
of genius, this seems to be a fruit of years worth of hard work and an
excellent memory.

~~~
Someone
Few thousand? There are only 12 third powers below 1729: 1, 8, 27, 64, 125,
216, 343, 512, 729, 1000, 1331, 1728.

Spotting that 729 + 1000 almost is equal to 1728 is not hard, either.
Everybody who has computed that list will have noticed it. Translating that
observation into a concise, interesting description is not hard, either, but
it does require creativity. That, he had way more than most. I wonder what he
would have said about the pair 3^5 and 7^3 (243 and 343)

~~~
LearnYouALisp
The first few thousand integers, and knew their properties quite well; that
seems to be what is meant.

------
signa11
robert-kanigel's book, "the man who knew infinity" is an excellent chronicle
into his life, and cambridge's culture during 20th century. it was hardy who
created a rising scale of mathematical abilities as follows:

    
    
      g.h.hardy - 25
      littlewood - 30
      hilbert - 80
      ramanujan - 100
    

hardy once described the formulas in ramanujan's first letters as "these must
be true, if they are not, nobody would have the audacity to invent it."

~~~
rehack
You might also like to read this interview of Kanigel on his book and how he
researched on Ramanujan.

<http://www.thehindu.com/opinion/interview/article2747541.ece>

PS: I was half inclined to share this interview (instead of the article, this
is also quite interesting)

~~~
signa11
wow ! it definitely is pretty interesting. thanks for sharing.

------
medius
Whenever I think about Ramanujan, I cannot help but wonder how many Ramanujans
are out there that are just not visible and struggling with poverty.

------
impendia
Ramanujan's second letter to Hardy [1]:

"Dear Sir, I am very much gratified on perusing your letter of the 8th
February 1913. I was expecting a reply from you similar to the one which a
Mathematics Professor at London wrote asking me to study carefully Bromwich's
Infinite Series and not fall into the pitfalls of divergent series. … I told
him that the sum of an infinite number of terms of the series: 1 + 2 + 3 + 4 +
... = −1/12 under my theory. If I tell you this you will at once point out to
me the lunatic asylum as my goal. I dilate on this simply to convince you that
you will not be able to follow my methods of proof if I indicate the lines on
which I proceed in a single letter. ..."

[1] <http://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4>

------
jeswin
Maybe it is just me, but overstating anyone's impact to this extent is
disrespectful to that person.

"....wealth of ideas that have transformed and reshaped 20th century
mathematics"

"His work has had a fundamental role in the development of 20th century
mathematics"

Maybe someone who has delved deeper into math can shine some light here.

~~~
microarchitect
Not a mathematician, but some references I found after goolging a bit:

[1] "The meaning of Ramanujam now and for the future", George E. Andrews.
<http://www.math.psu.edu/andrews/pdf/274.pdf>

[2] "The Ramanujam Journal",
<http://www.springer.com/mathematics/numbers/journal/11139>

Quote from the conclusion of [1]:

 _In his Presidential address to the London Mathematical Society in 1936, G.
N. Watson spoke movingly of his emotional response to Ramanujan's
achievements. I close by quoting his last few paragraphs [54; p. 80]:_

 _"The study of Ramanujan's work and of the problems to which it gives rise
inevitably recalls to mind Lame's remark that, when reading Hermite's papers
on modular functions, \on a la chair de poule." I would express my own
attitude with more prolixity by saying that such a formula as:_

<snipped formula>

 _gives me a thrill which is indistinguishable from the thrill which I feel
when I enter the Sagrestia Nuova of the Capelle Medicee and see before me the
austere beauty of the four statues representing Day, Night, Evening, and Dawn
which Michelangelo has set over the tombs of Guiliano de Medici and Lorenzo de
Medici. Ramanujan's discovery of the mock theta functions makes it obvious
that his skill and ingenuity did not desert him at the oncoming of his
untimely end. As much as any of his earlier work, the mock theta functions are
an achievement sucient to cause his name to be held in lasting remembrance"_

To me, it's interesting that a community where fairly easy to build web-
applications are called transformative and disruptive also has two out of
thirteen comments critical of Ramanujam's impact.

~~~
jeswin
Being critical of the article is not the same as being critical of Ramanujan's
impact. So, there isn't a need to down vote.

I am genuinely interested in knowing what Ramanujan did to "transform and
reshape" 20th century mathematics.

~~~
microarchitect
I was upset by this statement which assumes a priori that the article must be
overstating his impact.

 _Maybe it is just me, but overstating anyone's impact to this extent is
disrespectful to that person._

I don't claim that the article is not overstating Ramanujam's impact, but you
seemed to be arguing that there's no way this could be true, so the article
_must be_ overstating his impact. Given that even you don't claim to have the
background required to objectively evaluate Ramanujam's impact, this seemed to
be a prejudiced comment.

In retrospect, I might have been a bit trigger-happy with the downvote. Sorry
about that.

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rhizome
I believe there are at least several previouslies for this guy.

