DEAD HEROES OF MATHEMATICS: SRINIVASA RAMANUJAN

[Korpsy Knievel]

Srinivasa Ramanujan (22 December 1887 – 26 April 1920) was an Indian mathematician and autodidact who, with almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions. Living in India with no access to the larger mathematical community, which was centered in Europe at the time, Ramanujan developed his own mathematical research in isolation. As a result, he sometimes rediscovered known theorems in addition to producing new work. Ramanujan was said to be a natural genius by the English mathematician G.H. Hardy, in the same league as mathematicians such as Euler and Gauss. - wikipedia

Mathematician's Century-Old Secrets Unlocked
By Live Science Staff | LiveScience.com – Thu, Dec 27, 2012

While on his death bed, the brilliant Indian mathematician Srinivasa Ramanujan cryptically wrote down functions he said came to him in dreams, with a hunch about how they behaved. Now 100 years later, researchers say they've proved he was right.

"We've solved the problems from his last mysterious letters. For people who work in this area of math, the problem has been open for 90 years," Emory University mathematician Ken Ono said.

Ramanujan, a self-taught mathematician born in a rural village in South India, spent so much time thinking about math that he flunked out of college in India twice, Ono said.

But he sent mathematicians letters describing his work, and one of the most preeminent ones, English mathematician G. H. Hardy, recognized the Indian boy's genius and invited him to Cambridge University in England to study. While there, Ramanujan published more than 30 papers and was inducted into the Royal Society.

"For a brief window of time, five years, he lit the world of math on fire," Ono told LiveScience.

But the cold weather eventually weakened Ramanujan's health, and when he was dying, he went home to India.

It was on his deathbed in 1920 that he described mysterious functions that mimicked theta functions, or modular forms, in a letter to Hardy. Like trigonometric functions such as sine and cosine, theta functions have a repeating pattern, but the pattern is much more complex and subtle than a simple sine curve. Theta functions are also "super-symmetric," meaning that if a specific type of mathematical function called a Moebius transformation is applied to the functions, they turn into themselves. Because they are so symmetric these theta functions are useful in many types of mathematics and physics, including string theory.

Ramanujan believed that 17 new functions he discovered were "mock modular forms" that looked like theta functions when written out as an infinte sum (their coefficients get large in the same way), but weren't super-symmetric. Ramanujan, a devout Hindu, thought these patterns were revealed to him by the goddess Namagiri.

Ramanujan died before he could prove his hunch. But more than 90 years later, Ono and his team proved that these functions indeed mimicked modular forms, but don't share their defining characteristics, such as super-symmetry.

The expansion of mock modular forms helps physicists compute the entropy, or level of disorder, of black holes.

In developing mock modular forms, Ramanujan was decades ahead of his time, Ono said; mathematicians only figured out which branch of math these equations belonged to in 2002.

"Ramanujan's legacy, it turns out, is much more important than anything anyone would have guessed when Ramanujan died," Ono said.

The findings were presented last month at the Ramanujan 125 conference at the University of Florida, ahead of the 125th anniversary of the mathematician's birth on Dec. 22.

[rat1]

He strived to translate hindu deities & astrological patterns into math.

[Korpsy Knievel]

Well goddamn, give us a link.

[rat1]

He was raised in a Brahmin family, which is the priestly class in indian society. Being in a Brahmin family, he was instructed from a young age to attain the highest spiritual knowledge. Not everyone in india gets to study the vedas. Brahmins study the vedas. Vedic astrology is a vendega - one of six technical subjects contained in the vedas; this is what the Brahmins are studying. They also study all the hindu deities and the myths about them, how they interact / relate to one another.
http://en.wikipedia.org/wiki/Brahmin
http://en.wikipedia.org/wiki/Srinivasa_Ramanujan
As you learn hindu, you realize the deities are metaphysical principles. As you learn astrology, you realize how mathematical it is. It's not something I can describe to you, you'd just have to study it. But there are so many hindu deities it's insane.
It's not like his mind is gona separate his upbringing in studying hinduism / the vedas / astrology, which are very mathematical disciplines, from his studies of mathematics. He remains a devout hindu through his whole life, and apparently he was pretty adamant about his beliefs.

Now he's saying "these patterns were revealed to me by the goddess Namagiri". Most people do not understand this statement, and dismiss it as an eccentric personal belief. He's conveying a metaphysical principle when he says that. Metaphysical principles remain the same in mathematical form or in religious deity forms. It's not much of a leap to think he wouldnt explore all the dieties and their mathematical natures. I don't see why he would just stick to namagiri for inspiration, the whole religion is metaphysics.

Among his contributions he was known for work on infinite series. His math here fragments and then interrelates different folds of infinite. I glanced over some of his proofs on the infinite series and one of the first things he proves is that infinite is constantly in a state of fluctuation between expansion and contraction. Well, that's exactly what Hindus believe the supreme Hindu God Vishnu does. Vishnu is said to be constantly alterating between the creative aspect Brahma and the destructive aspect Shiva to preserve the universe.

Now try to think metaphorically. God is the beginning and the end; considered the one unspeakable, unbounded, unknowable.... infinite. See, infinite is the mathematical representation of God.. or Vishnu, if you're hindu.

His proofs on the infinite series are dividing and interrelating different aspects of infinite. The numerous Hindu deities are all fragments of God. If you've ever seen a tree of hindu deities, vishnu the supreme "God" is at the top and divisions of God trail downward, each deity with different qualities and being a different 'piece' of God; a different piece of infinite. These pieces all relate to eachother in various ways, described in myths and in their qualities.

[Korpsy Knievel]

One could dispute various notions contained here but on the whole your post is very interesting and well put together.

[Absurd]

And this is exactly the reason fruit diet is welcomed if any of yous want to be the next Ramanujan.

[Kalinoche buenanoche]

shizzle was telepathically channeled by the aliens to the indian boi.

[rat1]

Is this so farfetched to you?

[Kalinoche buenanoche]

Is this so farfetched to YOU?

[Absurd]

Jennifer and crazed, don't stop posting.

[rat1]

Is this so farfetched to YOU?

Why would you publicly mock me for believing in aliens if you don't think this discussion is farfetched?

[Absurd]

Don't quote her, it is sign of doom...

[rat1]

It's a war of illusions.

[Absurd]

Yes, reptilians are coming.

Anyway, before this wonderful thread created by korpsey turns into a trolling fest even though it was its aim from the start, coming from an troll of Internet forums, IRC and tiny chat I'm going to say, yes, Rmamamama was a great mathematician who dabbled in empirical mathematics, something korpsey and Gamma quadra ought to be fond of...

[rat1]

Absurd, what do you even want out of this discussion? Why are you participating in it?

I've never bought into reptilians. The reptilian shit looks more like propaganda to me than anything. I could be wrong though, who really knows..

[Absurd]

I've never bought into reptilians. The reptilian shit looks more like propaganda to me than anything. I could be wrong though, who really knows..

Yes, yes, I've got a big cunt on my vagina and elephants ride the monkeys.

[rat1]

You have no identity. It's like you're lost in a dream world.

[Absurd]

You have no identity. It's like you're lost in a dream world.

Hahaha, of course, I hate the to use the Jungian/"korpseian" definition of projection, I don't want to be accused of being "intellectually dishonest" by Scapegrace and branded ILE, but you're projecting as fuck, crazie rat.

Let me emphasise this more, a mathematician is posted by korpsey and "likes" and "constrictives" flow, great. After that a guy called crazed rat shows up and start talking about astrology, okay.

I don't have anything against it per se, but what is are trying to say?

[rat1]

It's like you're constantly shifting your identity. It is unclear what you want in discussions. You don't have a solid definition of yourself. You focus on the illusions in every conversation, and you respond with these mysterious statements which cannot be clearly identified. Yeah I am highly aware and manipulative of projections. Everyone has projections, some more than others; but your entire social personality is projections. Which I don't have a problem with, it can be entertaining as long as you aren't being a dickhead like you are now. But then it becomes annoying.

[Absurd]

It's like you're constantly shifting your identity. It is unclear what you want in discussions. You don't have a solid definition of yourself. You focus on the illusions in every conversation, and you respond with these mysterious statements which cannot be clearly identified. Yeah I am highly aware and manipulative of projections. Everyone has projections, some more than others; but your entire social personality is projections. Which I don't have a problem with, it can be entertaining as long as you aren't being a dickhead like you are now. But then it becomes annoying.

Every one does that, just look at this site. ILI once, LII after, SEI once ESI after, ILe once LSe after, etc. And I don't know what the heck you're talking about, and no, not everyone "has projections". healthy people don't at all. I don't see a reason healthy people would actually project their miserable shit when it is not even miserable at other people, you just failed at basic psychology. Healthy people don't care nor give a fuck. It's the unhealthy ones that try to judge in some way or another, some way that doesn't meet their standard.

As for looking as a "dickhead", well, you see what you want to see, I must be other quadra. Anyhow, again what are you trying to say, I know I am "projecting", thanks korpsey, I mean, crazed rat, but what else am I doing wrong?

Seriously, I stripped myself of TIM, changed my avatar, as the cool kids do, not that those who don't change their avatars are static types...

Anyhow, crazed, I'm alright, hit me best you can, and as for the RAMANUJAN, whose name isn't even spelled the proper way, I learned most things by doing them myself, I'm a genius, it seems.

[rat1]

Projection is anticipating a future situation by examining the present. The present is a superficial layer of perception, like a screen. Psychological projection bias is reading into what you want to see. Psychological projection bias is different than projection. I said you are projecting an identity, and that your identity is like a smokescreen... intangible. I didn't say you were using psychological projection bias.
There is nothing wrong with projection; it is part of consciousness, totally natural and unavoidable. Everyone is projecting constantly, healthy people and unhealthy people.

[Absurd]

hahahaha, you really talk this in real life? God have mercy on you...

[Radio]

stop ruining this thread.

[Absurd]

stop ruining this thread.

[Creepy-pikachu]

Absurd likes to lick baby ice cream cones filled with watermelon-laced soft serve.

[Creepy-pikachu]

stop ruining this thread.

Your avatar is y0 shadow.

[Absurd]

Your avatar is y0 shadow.

Said the STj one, apparently.

[Creepy-pikachu]

So kind of you to reply to me on short notice. Tea is at 1:00 PM PST.

[Absurd]

So kind of you to reply to me on short notice. Tea is at 1:00 PM PST.

Well, your NF shit is at 2:00.

I don't drink coffee you cunt, the only thing I drank starting 2:00 was beer, wine and vodka.

It is culture, you wob'g, you don't appreciate, fuck off.

[Korpsy Knievel]

Srinivasa Ramanujan

It is one of the most romantic stories in the history of mathematics: in 1913, the English mathematician G. H. Hardy received a strange letter from an unknown clerk in Madras, India. The ten-page letter contained about 120 statements of theorems on infinite series, improper integrals, continued fractions, and number theory (Here is a .dvi file with a sample of these results). Every prominent mathematician gets letters from cranks, and at first glance Hardy no doubt put this letter in that class. But something about the formulas made him take a second look, and show it to his collaborator J. E. Littlewood. After a few hours, they concluded that the results "must be true because, if they were not true, no one would have had the imagination to invent them".

Thus was Srinivasa Ramanujan (1887-1920) introduced to the mathematical world. Born in South India, Ramanujan was a promising student, winning academic prizes in high school. But at age 16 his life took a decisive turn after he obtained a book titled A Synopsis of Elementary Results in Pure and Applied Mathematics. The book was simply a compilation of thousands of mathematical results, most set down with little or no indication of proof. It was in no sense a mathematical classic; rather, it was written as an aid to coaching English mathematics students facing the notoriously difficult Tripos examination, which involved a great deal of wholesale memorization. But in Ramanujan it inspired a burst of feverish mathematical activity, as he worked through the book's results and beyond. Unfortunately, his total immersion in mathematics was disastrous for Ramanujan's academic career: ignoring all his other subjects, he repeatedly failed his college exams.

As a college dropout from a poor family, Ramanujan's position was precarious. He lived off the charity of friends, filling notebooks with mathematical discoveries and seeking patrons to support his work. Finally he met with modest success when the Indian mathematician Ramachandra Rao provided him with first a modest subsidy, and later a clerkship at the Madras Port Trust. During this period Ramanujan had his first paper published, a 17-page work on Bernoulli numbers that appeared in 1911 in the Journal of the Indian Mathematical Society. Still no one was quite sure if Ramanujan was a real genius or a crank. With the encouragement of friends, he wrote to mathematicians in Cambridge seeking validation of his work. Twice he wrote with no response; on the third try, he found Hardy.

Hardy wrote enthusiastically back to Ramanujan, and Hardy's stamp of approval improved Ramanujan's status almost immediately. Ramanujan was named a research scholar at the University of Madras, receiving double his clerk's salary and required only to submit quarterly reports on his work. But Hardy was determined that Ramanujan be brought to England. Ramanujan's mother resisted at first--high-caste Indians shunned travel to foreign lands--but finally gave in, ostensibly after a vision. In March 1914, Ramanujan boarded a steamer for England.

Ramanujan's arrival at Cambridge was the beginning of a very successful five-year collaboration with Hardy. In some ways the two made an odd pair: Hardy was a great exponent of rigor in analysis, while Ramanujan's results were (as Hardy put it) "arrived at by a process of mingled argument, intuition, and induction, of which he was entirely unable to give any coherent account". Hardy did his best to fill in the gaps in Ramanujan's education without discouraging him. He was amazed by Ramanujan's uncanny formal intuition in manipulating infinite series, continued fractions, and the like: "I have never met his equal, and can compare him only with Euler or Jacobi."

One remarkable result of the Hardy-Ramanujan collaboration was a formula for the number p(n) of partitions of a number n. A partition of a positive integer n is just an expression for n as a sum of positive integers, regardless of order. Thus p(4) = 5 because 4 can be written as 1+1+1+1, 1+1+2, 2+2, 1+3, or 4. The problem of finding p(n) was studied by Euler, who found a formula for the generating function of p(n) (that is, for the infinite series whose nth term is p(n)xn). While this allows one to calculate p(n) recursively, it doesn't lead to an explicit formula. Hardy and Ramanujan came up with such a formula (though they only proved it works asymptotically; Rademacher proved it gives the exact value of p(n)).

Ramanujan's years in England were mathematically productive, and he gained the recognition he hoped for. Cambridge granted him a Bachelor of Science degree "by research" in 1916, and he was elected a Fellow of the Royal Society (the first Indian to be so honored) in 1918. But the alien climate and culture took a toll on his health. Ramanujan had always lived in a tropical climate and had his mother (later his wife) to cook for him: now he faced the English winter, and he had to do all his own cooking to adhere to his caste's strict dietary rules. Wartime shortages only made things worse. In 1917 he was hospitalized, his doctors fearing for his life. By late 1918 his health had improved; he returned to India in 1919. But his health failed again, and he died the next year.

Besides his published work, Ramanujan left behind several notebooks, which have been the object of much study. The English mathematician G. N. Watson wrote a long series of papers about them. More recently the American mathematician Bruce C. Berndt has written a multi-volume study of the notebooks. In 1997 The Ramanujan Journal was launched to publish work "in areas of mathematics influenced by Ramanujan".

- link

[Korpsy Knievel]

ஸ்ரீனிவாஸ ஐயங்கார் ராமானுஜன்

• Srinivasa Ramanujan was the strangest man in all of mathematics, probably in the entire history of science. He has been compared to a bursting supernova, illuminating the darkest, most profound corners of mathematics, before being tragically struck down by tuberculosis at the age of 33, like Riemann before him.

Michio Kaku, in Hyperspace: a scientific odyssey through parallel universes, time warps, and the tenth dimension (1995), p.172

• One day he was explaining a relation to me; then he suddenly turned round and said, "Sir, an equation has no meaning for me unless it expresses a thought of GOD.".

Shiyali Ramamrita Ranganathan: Ramanujan, the Man and the Mathematician. Asia Publishing House Bombay 1967. p. 88

• Paul Erdos has passed on to us Hardy's personal ratings of mathematicians. Suppose that we rate mathematicians on the basis of pure talent on a scale from 0 to 100, Hardy gave himself a score of 25, Littlewood 30, Hilbert 80 and Ramanujan 100.

Bruce C. Berndt in Ramanujan's Notebooks : Part I (1994), "Introduction", p. 14

• He could remember the idiosyncrasies of numbers in an almost uncanny way. It was Littlewood who said that every positive integer was one of Ramanujan's personal friends. I remember once going to see him 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."

G. H. Hardy, in Ramanujan : Twelve Lectures on Subjects Suggested by His Life and Work (1940)

• Every positive integer is one of Ramanujan's personal friends.

John Littlewood, on hearing of the taxicab incident.

• Euler and Ramanujan are mathematicians of the greatest importance in the history of constants (and of course in the history of Mathematics...

E. W. Middlemast

• In his book Scientific Edge, noted physicist Jayant Narlikar stated that "Srinivasa Ramanujan, discovered by the Cambridge mathematician G.H. Hardy, whose great mathematical findings were beginning to be appreciated from 1915 to 1919. His achievements were to be fully understood much later, well after his untimely death in 1920. For example, his work on the highly composite numbers (numbers with a large number of factors) started a whole new line of investigations in the theory of such numbers." Narlikar also goes on to say that his work was one of the top ten achievements of 20th century Indian science and "could be considered in the Nobel Prize class."[86] The work of other 20th century Indian scientists which Narlikar considered to be of Nobel Prize class were those of Chandrasekhara Venkata Raman, Megh Nad Saha and Satyendra Nath Bose.

- wikipedia

[Korpsy Knievel]

a guy called crazed rat shows up and start talking about astrology, okay.

Given that Ramanujan was a modern Indian of a strongly religious orientation and that he was a profoundly intuitive phenomenon of relational logic, it is entirely appropriate and useful for commentary here to concern itself with gunas, tattvas, and other concepts of Indian metaphysics.

stop ruining this thread.

That is unpossible since it was begun without preconceived notions.

At this stage I'm leaning toward Ne-LII.

And this is exactly the reason fruit diet is welcomed if any of yous want to be the next Ramanujan.

Ya aamam maansamadanti paurusheyam cha ye kravih Garbhaan khaadanti keshavaastaanito naashayaamasi

Those who eat flesh uncooked, and those who eat the bleeding flesh of men, Feeders on babes unborn, long-haired, far from this place we banish these.

- Atharva Veda 8.6.23

[Korpsy Knievel]

Srinivasa Ramanujan credits his mathematical findings to goddess Namagiri. According to Ramanujan, she appeared in his visions, proposing him mathematical formulae, which Ramanujan would then had to verify. One such event was described by him as follows:

"While asleep, I had an unusual experience. There was a red screen formed by flowing blood, as it were. I was observing it. Suddenly a hand began to write on the screen. I became all attention. That hand wrote a number of elliptic integrals. They stuck to my mind. As soon as I woke up, I commited them to writing."

Namagiri is a Hindu goddess worshipped especially in the Namakkal district of Tamil Nadu state in Southern India. The name "Namagiri" translated from Sanskrit into Tamil sounds like "Namakkal". Her devotees worship her as a consort of Narasimha, an avatar (incarnation) of the deity Vishnu. Namagiri was the mathematician Srinivasa Ramanujan's family deity.

http://srinamagiri.org/
http://namakkalnarasimhaswamyanjaneyartemple.org/

Personality and spiritual life

Ramanujan has been described as a person with a somewhat shy and quiet disposition, a dignified man with pleasant manners. He lived a rather Spartan life while at Cambridge. Ramanujan's first Indian biographers describe him as rigorously orthodox. Ramanujan credited his acumen to his family Goddess, Namagiri of Namakkal. He looked to her for inspiration in his work, and claimed to dream of blood drops that symbolised her male consort, Narasimha, after which he would receive visions of scrolls of complex mathematical content unfolding before his eyes. He often said, "An equation for me has no meaning, unless it represents a thought of God."

Hardy cites Ramanujan as remarking that all religions seemed equally true to him.[85] Hardy further argued that Ramanujan's religiousness had been romanticised by Westerners and overstated—in reference to his belief, not practice—by Indian biographers. At the same time, he remarked on Ramanujan's strict observance of vegetarianism.

[Korpsy Knievel]

[Korpsy Knievel]

MATH FORMULA GIVES NEW GLIMPSE INTO THE MAGICAL MIND OF RAMANUJAN

[Korpsy Knievel]

It appears I may have been devaluing the Tamil element.

[Korpsy Knievel]

ராமானுஜன் 125

[The Reality Denialist]

LII?
rpi.png
To be honest his formulas looks like some sort of witchcraft.
Quite a number head.
Some people say that mental calculation and fascination towards numbers is not that important in maths. I begin to think otherwise.