Detail of Shriniwasa an indian Methemeticians
s...@bitscape.co.in
Shrinivas Ramanujan in his short life-span, proved to be a mathematical
genius comparable to the likes of Karl Jacobi and Leonhaed Euler.
Despite lack of formal higher education and battling against heavy odds
like poverty and ill health, his mathematical genius flowed unhindered.
His contribution in the fields of elliptic functions, infinite series
and the analytical theory of numbers is immeasurable. Even after his
death at the young age of 32, his notes continued to be a subject of
research and a source of further mathematical theorems, formulae and
solutions.
Born in India, which was then under British rule, he received
encouragement and recognition not only from discerning Indians but also
from his contemporary British mathematicians. Against the dictum of his
religion, he traveled overseas to Britain where he collaborated with
Prof. Hardy at the Trinity College. Between 1914-1918, which coincided
with World War I, Ramanujan stayed and worked at the Trinity College.
Though his health was deteriorating, his mental faculties and
mathematical genius flourished. It took an impressive list of eminent
mathematicians to propose his name for election as a Fellow at The
Royal Society of London. This unique honor was conferred on him on May
2, 1918. Read on to have an insight into the life and mind of one of
the most prolific and yet elusive Indian personality who left behind a
mathematical legacy, for others to reveal.
To know more about the shri nivasa www.worldofbiography.com
bookburn
proceeding on his own without much formal education or family support and
attaining worldwide recognition; and that this is relevant to the Shakespeare
authorship question concerning the very modest beginnings of William
Shakespeare, AKA Stratman.
It remains for anti-Strats to dispute that mathematics aptitude is comparable
to language arts aptitude. bookburn
bookburn
"bookburn" <book...@yahoo.com> wrote in message
news:125123g...@corp.supernews.com...
Coincidentally, there is an "A.K. Ramanujan, a legendary translator, poet and
former professor in the Committee on Social Thought, who also won a MacArthur
fellowship, recently published in The Oxford India Ramanujan. He taught
Shakespeare and other poets at The University of Chicago. bb
Art Neuendorffer
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________ £ = ALT 0163
----------------------------------------------------------
http://mathworld.wolfram.com/163.html
163 (= 1 + 8 + 28 + 56 + 70) is VERy important in number theory
[1] 1 1 1 1 1 1 ...
2 [3] 4 5 6 7 8 ...
4 7 [11] 16 22 29 37 ....
8 15 26 [42] 64 93 130 ....
16 31 57 99 [163] 256 386 ...
32 63 120 219 382 [638] ....
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The "Ramanujan Constant": exp(pi*sqrt(£))
------------------------------------------------------------
http://mathworld.wolfram.com/RamanujanConstant.html
http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMa...
calConstants/chap79.html
<<The irrational constant exp(pi*sqrt(163))=
262537412640768743.9999999999992500... which is VERy close to an
integer. Numbers such as the Ramanujan constant can be found using
the theory of modular functions. In fact, the nine Heegner numbers
(which include 163) share a deep number theoretic property related
to some amazing properties of the j-function that leads to this sort
of near-identity. Although Ramanujan (1913-14) gave few rather
spectacular examples of almost integers (such), he did not actually
mention particular near-identity give above. In fact, the first to
observe this property of 163 was Hermite (1859).
The name "Ramanujan's constant" seems to derive from an April Fool's
joke played by Martin Gardner (Apr. 1975) on the readers of Scientific
American. In his column, Gardner claimed that was exactly an integer,
and that Ramanujan had conjectured this in his 1914 paper.
Gardner admitted his hoax a few months later (Gardner, July 1975).>>
----------------------------------------------------------------
Godfrey Harold Hardy
http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Hardy.html
----------------------------------------------------------------------
http://www-groups.dcs.st-and.ac.uk/~history/PictDisplay/Hardy.html
<<G.H. Hardy was known for his eccentricities. He could not endure
having his photograph taken and only five snapshots are known to
exist. He also hated mirrors and his first action on entering any
hotel room was to cover any mirror with a towel. He always played an
amusing game of trying to fool God (which is also rather strange since
he claimed all his life not be believe in God). For example, during a
trip to Denmark he sent back a postcard claiming that he had proved
the Riemann hypothesis. He reasoned that God would not allow the boat
to sink on the return journey and give him the same fame that Fermat
had achieved with his "last theorem". Another example of his trying to
fool God was when he went to cricket matches he would take what he
called his "anti-God battery". This consisted of thick sweaters, an
umbrella, mathematical papers to referee, student examination scripts
etc. His theory was that God would think that he expected rain to come
so that he could then get on with his work. Since Hardy thought that
God would then have the sun shine all day to spite him, he would be
able to enjoy the cricket in perfect sunshine.
The following quotation from A mathematicians apology gives
a clear idea of Hardy's thoughts on mathematics:-
The mathematician's pattern's, like those of the painter's or the
poet's, must be beautiful, the ideas, like the colours or the words,
must fit together in a harmonious way. There is no permanent place
in the world for ugly mathematics.>>
----------------------------------------------------------------------
<<G.H. Hardy visited Ramanujan in the hospital, travelling in a taxi
. numbered 1729. When he arrived, Hardy commented to Ramanujan that
1729 was not a VERy interesting number. Ramanujan immediately replied,
. "No, it is an interesting number. It is the smallest number which
. can be written in two different ways as the sum of two cubes." :
.
__ 1729 = [10*10*10+9*9*9] = [1*1*1+12*12*12]>>
.
__ [1+7+2+9] = [10+9] = 19
.
______ 1729 = 19*91
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Matthew 2:18 In *RAMA* was there a voice heard, lamentation,
. and weeping, and great mourning, Rachel weeping for her
children, and would not be comforted, because they are not.
-----------------------------------------------------------
________ *RAMAnUJAN*
_______ *RAMA 'n JUAN*
_______ *RAma hANUMAN*
*RAMA* : Avatar of Vishnu; any of three incarnations:
*RAMAchandra or parashuRAMA or balaRAMA*
*RAMA* performed many wonderful exploits, such as killing
giants, demons, and monsters. He won Sita to wife because
he was able to bend the bow of Siva. (Brewer's Dictionary)
-----------------------------------------------
(From Wikipedia, the free Encyclopedia)
<<Rama was a real or mythical king in ancient India, whose life and
heroic deeds are related by the Sanskrit epic Ramayana. Astronomical
data in the Ramayana has been interpreted to suggest that his reign
would have been at approximately 2015 BC, however the Ramayana was
written many centuries after this date, probably two thousand years
later. It cannot be taken as an accurate guide to the life of the
historical Rama, except by devout Hindus.
In Hinduism, Rama is regarded as the seventh avatar of the god Vishnu
and worshipped together with his companion Hanuman, the monkey-god who
assists him in the epic narrative of the Ramayana.
He is the Prince of Ayodhya and is banished to a forest by his
stepmother. While in exile, his wife, Sita, is kidnapped by Ravana,
King of the Rakshas on Lanka (cur: Sri Lanka). Rama, along with
Hanuman, rescued her, killed Ravana and becomes King of Ayodhya.
Rama also killed Vali, the monkey-King of Kishkindhya. He is protected
during his adventures by Agastya, and also rescued Ahalya after she
was turned to stone by her husband for having an affair with Indra.
----------------------------------------------------------------
Kings of Thailand of the Chakri dynasty have the royal title *RAMA*
In Arthur C. Clarke's Rendezvous with *RAMA* ,
*RAMA* is a giant, cylinder-shaped alien built
spacecraft containing a self-sustaining biosphere.
----------------------------------------------------------------
*RAMA* : Isaiah (10:29) refers to it, and also Jeremiah, who was
once a prisoner there among the other captives of Jerusalem when
it was taken by Nebuchadnezzar (Jer. 39:8-12; 40:1).
Rachel, whose tomb lies close to Bethlehem, is represented as
weeping in Ramah (Jer. 31:15) for her slaughtered children.
This prophecy is illustrated and fulfilled in the re-awakening
of Rachel's grief at the slaughter of the infants in Bethlehem
(Matt. 2:18). It is identified with the modern village of er-Ram,
between Gibeon & Beeroth, about 5 miles due north of Jerusalem.
----------------------------------------------------------------
Godfrey Harold Hardy
http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Hardy.html
------------------------------------------------------------------
<<G H Hardy's father, Isaac Hardy, was bursar and an art master at
Cranleigh school. His mother Sophia had been a teacher at Lincoln
Teacher's Training School. Both parents were highly intelligent with
some mathematical skills but, coming from poor families, had not been
able to have a university education. Hardy (he was always known as
Hardy except to one or two close friends who called him Harold)
attended Cranleigh school up to the age of twelve with great success
His parents knew he was prodigiously clever, and so did he. He came
top of his class in all subjects. But, as a result of coming top of
his class, he had to go in front of the school to receive prizes:
and that he could not bear.
Hardy did not appear to have the passion for mathematics that many
mathematicians experience when young. Hardy himself writes:
"I do not remember having felt, as a boy, any passion for mathematics,
and such notions as I may have had of the career of a mathematician
were far from noble. I thought of mathematics in terms of examinations
and scholarships: I wanted to beat other boys, and this seemed to be
the way in which I could do so most decisively."
Indeed he did win a scholarship to Winchester College in 1889,
entering the College the following year. Winchester was the best
school in England for mathematical training yet, despite admitting
later in life that he had been well-educated there, Hardy disliked
everything about the school other than the academic training he received.
While at Winchester Hardy won an open scholarship to Trinity College,
Cambridge, which he entered in 1896. At Cambridge Hardy was assigned
to the most famous coach R R Webb. He quickly realised that the point
of the training was simply to achieve the best possible marks in the
examinations by learning all the tricks of the trade. He was shocked
to discover that Webb was not interested in the subject of
mathematics, only in the tricks of examinations.
Briefly Hardy thought he might change topics and study history
instead. However, he managed to change his coach to A E H Love.
Hardy expresses his gratitude to Love:
"My eyes were first opened by Professor Love, who first taught me a
few terms and gave me my first serious conception of analysis. But the
great debt which I owe to him was his advice to read Jordan's "Cours
d'analyse"; and I shall never forget the astonishment with which I
read that remarkable work, the first inspiration for so many
mathematicians of my generation, and learnt for the first time as I
read it what mathematics really meant."
Hardy was placed as fourth wrangler in the Mathematical Tripos of
1898, a result which continued to annoy him for, despite feeling that
the system was very silly, he still felt that he should have come out
on top. Hardy was elected a fellow of Trinity in 1900 then, in 1901,
he was awarded a Smith's prize jointly with J H Jeans 'with
unspecified relative merit'.
The next period of Hardy's career was up to 1911 when he:-
"... wrote many papers on the convergence of series and integrals and
allied topics. Although this work established his reputation as an
analyst, his greatest service to mathematics in this early period was
A course of pure mathematics (1908). This work was the first rigorous
English exposition of number, function, limit, and so on, adapted to
the undergraduate, and thus it transformed university teaching."
This was a period of which Hardy wrote himself:-
"I wrote a great deal... but very little of any importance; there are
not more than four of five papers which I can still remember with some
satisfaction."
A major change in Hardy's work came about in 1911 when he began his
collaboration with J E Littlewood which was to last 35 years. Then in
early 1913 he received Ramanujan's first letter from India which was
to start his second major collaboration. By the time World War I
started in 1914, Ramanujan was in Cambridge and this eased
for Hardy what was to be a very difficult period.
Littlewood left Cambridge for war service in the Royal Artillery.
Hardy volunteered for war service but was rejected on medical grounds.
However Hardy's views on the war left him at odds with most of his
colleagues at Cambridge. He had great respect for Germany:
... he had a strong feeling for Germany. Germany had, after all, been
the great educating force of the nineteenth century. To Eastern
Europe, to Russia, to the United States, it was the German
universities which had taught the meaning of research. ... in most
respects the German culture, including its social welfare, appeared to
him higher than his own. ... Hardy, like Russell ... did not believe
that the war should have been fought. Further, with his ingrained
distrust of English politicians, he thought the balance of wrong was
on the English side.
Deeply unhappy at Cambridge, Hardy took the opportunity to leave in
1919 when he was appointed as Savilian professor of geometry at
Oxford. These were in many ways the years when he was happiest and
also the years when he produced his best mathematics in the
collaboration with Littlewood. This collaboration was achieved during
a period when Littlewood was in Cambridge and Hardy was in Oxford,
making joint research a quite difficult logistical exercise:-
"I was at my best at a little past forty, when I was a professor at
Oxford."
Despite his background and the positions he held, Hardy preferred the
poor and disadvantaged to those he called the 'large bottomed' who
included:
"... the confident, booming, imperialist bourgeois English. The
designation included most bishops, headmasters, judges, and all
politicians, with the single exception of Lloyd George."
He had chosen not to live in the best rooms while at Cambridge, and
Hilbert was so concerned that Hardy was not being properly treated
that he wrote to the Master of the College pointing out that the best
mathematician in England should have the best rooms. However, Hardy
did not think that way. He held a trade union office for two years
(1924-26) as President of the Association of Scientific Workers. At a
time when it seemed difficult to do so, Hardy liked equally both the
United States and Russia. He spent the academic year 1928-29 at
Princeton in an exchange with Veblen, who spent the year in Oxford.
Despite having been unhappy at Cambridge, Hardy returned to the
Sadleirian chair there in 1931 when Hobson retired. Snow in says that
Hardy returned to Cambridge for two reasons, firstly that he still
considered Cambridge the centre of English mathematics and the
Sadleirian chair the foremost mathematics chair in England, and
secondly, that he could keep his rooms in College at Cambridge while
this was not possible at Oxford. To the unmarried Hardy, this held an
attraction as he began to look toward old age.
Hardy's interests covered many topics of pure mathematics -
Diophantine analysis, summation of divergent series, Fourier series,
the Riemann zeta function, and the distribution of primes. His long
collaboration with Littlewood produced mathematics of the highest
quality. It was a collaboration in which Hardy acknowledged
Littlewood's greater technical mathematical skills, but at the same
time Hardy brought great talents of mathematical insight and a great
ability to write their work up in papers with great clarity.
Even more remarkable was Hardy's collaboration with Ramanujan. Hardy
instantly spotted Ramanujan's genius from a manuscript sent to him by
Ramanujan from India in 1913. Two other top class mathematicians had
previously failed to spot the genius. Hardy brought Ramanujan to
Cambridge and they wrote five remarkable papers together.
It was not only with Littlewood and Ramanujan that Hardy collaborated.
He was a natural collaborator who also wrote joint papers with
Titchmarsh, Ingham, Edmund Landau, Pólya, E M Wright, W W Rogosinski
and Marcel Riesz.
Hardy was a pure mathematician who hoped his mathematics could never
be applied. However in 1908, near the beginning of his career, he gave
a law describing how the proportions of dominant and recessive genetic
traits would be propagated in a large population. Hardy considered it
unimportant but it has proved of major importance in blood group
distribution.
There was only one passion in Hardy's life other than mathematics and
that was cricket. In fact for most of his life his day, at least
during the cricket season, would consist of breakfast during which he
read The Times studying the cricket scores with great interest. After
breakfast he would work on his own mathematical researches from 9
o'clock till 1 o'clock. Then, after a light lunch, he would walk down
to the university cricket ground to watch a game. In the late
afternoon he would walk slowly back to his rooms in College. There he
took dinner, which he followed with a glass of wine. When cricket was
not in season, it was the Australian cricket scores he would read in
The Times and he would play real tennis in the afternoons.
As World War I had been painful for Hardy, World War II was equally
so. He had remained remarkably youthful in both mind and body until
1939 when, at the age of 62, he had a heart attack. His remarkable
mental powers began to leave him and sports which he had loved to
participate in up till then became impossible. He was filled with
anger that Europe had again entered the lunacy of war. However,
Hardy had one further gift to leave to the world, namely A
mathematicians apology which has inspired many towards mathematics.
Hardy's book A mathematicians apology was written in 1940. It is one
of the most vivid descriptions of how a mathematician thinks and the
pleasure of mathematics. But the book is more, as Snow writes in:
A mathematicians apology is, if read with the textual attention it
deserves, a book of haunting sadness. Yes, it is witty and sharp with
intellectual high spirits: yes, the crystalline clarity and candour
are still there: yes, it is the testament of a creative artist. But it
is also, in an understated stoical fashion, a passionate lament for
creative powers that used to be and that will never come again. I know
nothing like it in the language: partly because most people with the
literary gift to express such a lament don't come to feel it: it is
very rare for a writer to realise, with the finality of truth, that he
is absolutely finished.
By the time the war ended in 1945 Hardy health was failing fast. He
longed to be creative again, for that was all that really mattered to
him in life, but he knew that his creativity was gone and that he
became very depressed. By 1946 he could only get around by taking taxi
rides, a few steps would make him short of breath. In early summer
of 1947 he tried to take his own life by taking a large dose of
barbiturates. He took so many, however, that he was sick
and survived. Snow writes:
In the Evelyn nursing home, Hardy was lying in bed. As a touch of
farce, he had a black eye. Vomiting from the drugs, he had hit his
head on the lavatory basin. He was self-mocking.
He had made a mess of it. ...
He talked a little, nearly every time I saw him, about death. He
wanted it. He didn't fear it: what was there to fear in nothingness?
His hard intellectual stoicism had come back. He would not try to kill
himself again. He wasn't good at it. He was prepared to wait. With an
inconsistency which might have pained him - for he ... believed in the
rational to an extent that I thought irrational - he showed an intense
hypochondriac curiosity about his own symptoms.
He is described in as follows:-
He personified the popular idea of the absent-minded professor.
But those who formed the idea that he was merely an absent-minded
professor would receive a shock in conversation, where he displayed
amazing vitality on every subject under the sun. ... He was interested
in the game of chess, but was frankly puzzled by something in its
nature which seemed to come into conflict with his mathematical
principles. >>
------------------------------------------------------------------
Godfrey Harold Hardy
Born: 7 Feb 1877 in Cranleigh, Surrey, England
Died: 1 Dec 1947 in Cambridge, Cambridgeshire, England
[same day as English occultist Aleister Crowley (b.1875) died]
---------------------------------------------------------
December 1
.........................................................
1135 King Henry I of England died at St Denis le Fermont in Normandy,
after being sick for a week following a meal of lamprey fish.
1145 On hearing of the fall of Edessa to the Turks, Pope Eugene III
(pope from 1145 to 1153) sent a papal bull to France?s King Louis VII,
proclaiming the Second Crusade. Led by Louis and Emperor Conrad III
from 1147 - 49, the crusade failed to accomplish its goal. After a
period of relative peace, in which Christians & Muslims coexisted in
the Holy Land, St Bernard of Clairvaux had called for the new crusade.
1167 Northern Italian towns formed the Lombardi League.
1523 Death of Pope Leo X (b. 1475).
1566 Spanish king Philip II named Fernando Alvarez, duke of Alva.
1581 Edmund Campion, the English Jesuit, was hanged for treason
after pamphleteering against Anglicanism in Oxford.
1590 Edmund Spenser's Faerie Queene registered
1640 Portugal regained its independence from Spain
and John IV of Portugal became king.
1663 English poet John Dryden, 32, married Elizabeth Howard,
the daughter of the first Earl of Berkshire.
1804 The first London stage appearance of the child acting prodigy,
William Betty (William Henry West Betty; 1791 - 1874), known as the
Young Roscius, whose acting brilliance caused a sensation in England.
His performances brought in £17,210 in 28 nights, a huge fortune. Like
so many child actors, the public did not like him as an adult and his
career was washed up early. His attempt in 1812 to perform again
bombed, so he retired completely in 1824 and lived off his fortune.
His nickname came from the great comic actor of ancient Rome.
*He died on the 24th of August 1874*
"English actor, known as the young Roscius, was born on the 13th of
September 1791 at Shrewsbury. He first appeared on the stage at
Belfast before he was twelve years old, as Osman in Aaron Hill's Zara,
an English version of Voltaire's Zaire. His success was immediate, and
he shortly afterwards appeared in Dublin, where it is said that in
three hours of study he committed the part of Hamlet to memory.
1834 The slaves of the British Cape Colony were emancipated.
1835 Hans Christian Andersen published first book of fairy tales
1860 The first instalment of Charles Dickens's Great Expectations
was published in All the Year Round.
1887 Sherlock Holmes first appeared in print: A Study In Scarlet.
1903 Edwin S Porter's The Great Train Robbery
1905 A plot to kill Russia's Tsar Nicholas II was discovered in St
Petersburg and twenty army officers and 230 guards were arrested.
1913 Ford Motor Company introduced the first moving assembly line,
1913 USA: The first drive-up gasoline station opened, Pittsburgh.
1918 Iceland became a self-governing kingdom
1919 Lady Astor became first female member of the British Parliament
1922 The first skywriting over the US
? ?Hello USA" ? by Captain Turner of the RAF.
1929 The game of Bingo was invented by Edwin S Lowe. Bingo can be
traced back to a game called Lotto, played in Italy in 1530. The bingo
name comes from a corruption of the name Beano, the name of a form of
bingo played in the United States in the 1920s. Beano was so called
because beans were used to cover the numbers.
1939 In New York, the film Gone with the Wind received its premiere.
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Art Neuendorffer