Browsing Category


interesting facts about ramanujan

Interesting facts about Ramanujan

Srinivasa Ramanujan ©WikiMedia
Srinivasa Ramanujan was an Indian great Mathematician who lived during the British Rule in India. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems considered to be unsolvable. Ramanujan initially developed his own mathematical research in isolation: “He tried to interest the leading professional mathematicians in his work, but failed for the most part. What he had to show them was too novel, too unfamiliar, and additionally presented in unusual ways; they could not be bothered”.

Early life

Ramanujan (literally, “younger brother of Rama”, a Hindu deity was born on 22 December 1887 into a Tamil Brahmin Iyengar family in Erode, Madras Presidency (now Tamil Nadu), at the residence of his maternal grandparents. His father, K. Srinivasa Iyengar, originally from Thanjavur district, worked as a clerk in a sari shop. His mother, Komalatammal, was a housewife and also sang at a local temple. They lived in a small traditional home on Sarangapani Sannidhi Street in the town of Kumbakonam. The family home is now a museum. When Ramanujan was a year and a half old, his mother gave birth to a son, Sadagopan, who died less than three months later. In December 1889, Ramanujan contracted smallpox, though he recovered, unlike 4,000 others who would die in a bad year in the Thanjavur district around this time. He moved with his mother to her parents’ house in Kanchipuram, near Madras (now Chennai). His mother gave birth to two more children, in 1891 and 1894, both failing to reach their first birthdays.

On 1 October 1892, Ramanujan was enrolled at the local school. After his maternal grandfather lost his job as a court official in Kanchipuram, Ramanujan and his mother moved back to Kumbakonam and he was enrolled in the Kangayan Primary School. When his paternal grandfather died, he was sent back to his maternal grandparents, then living in Madras. He did not like school in Madras, and tried to avoid attending. His family enlisted a local constable to make sure the boy attended school. Within six months, Ramanujan was back in Kumbakonam.

Since Ramanujan’s father was at work most of the day, his mother took care of the boy as a child. He had a close relationship with her. From her, he learned about tradition and puranas. He learned to sing religious songs, to attend pujas at the temple, and to maintain particular eating habits—all of which are part of Brahmin culture. At the Kangayan Primary School, Ramanujan performed well. Just before turning 10, in November 1897, he passed his primary examinations in English, Tamil, geography and arithmetic with the best scores in the district. That year, Ramanujan entered Town Higher Secondary School, where he encountered formal mathematics for the first time.

By age 11, he had exhausted the mathematical knowledge of two college students who were lodgers at his home. He was later lent a book by S. L. Loney on advanced trigonometry. He mastered this by the age of 13 while discovering sophisticated theorems on his own. By 14, he was receiving merit certificates and academic awards that continued throughout his school career, and he assisted the school in the logistics of assigning its 1200 students (each with differing needs) to its approximately 35 teachers. He completed mathematical exams in half the allotted time, and showed a familiarity with geometry and infinite series. Ramanujan was shown how to solve cubic equations in 1902; he developed his own method to solve the quartic. The following year, Ramanujan tried to solve the quintic, not knowing that it could not be solved by radicals.

In 1903, when he was 16, Ramanujan obtained from a friend a library copy of A Synopsis of Elementary Results in Pure and Applied Mathematics, G. S. Carr’s collection of 5,000 theorems. Ramanujan reportedly studied the contents of the book in detail. The book is generally acknowledged as a key element in awakening his genius. The next year, Ramanujan independently developed and investigated the Bernoulli numbers and calculated the Euler–Mascheroni constant up to 15 decimal places. His peers at the time commented that they “rarely understood him” and “stood in respectful awe” of him.

When he graduated from Town Higher Secondary School in 1904, Ramanujan was awarded the K. Ranganatha Rao prize for mathematics by the school’s headmaster, Krishnaswami Iyer. Iyer introduced Ramanujan as an outstanding student who deserved scores higher than the maximum. He received a scholarship to study at Government Arts College, Kumbakonam, but was so intent on mathematics that he could not focus on any other subjects and failed most of them, losing his scholarship in the process. In August 1905, Ramanujan ran away from home, heading towards Visakhapatnam, and stayed in Rajahmundry for about a month. He later enrolled at Pachaiyappa’s College in Madras. There he passed in mathematics, choosing only to attempt questions that appealed to him and leaving the rest unanswered, but performed poorly in other subjects, such as English, physiology and Sanskrit. Ramanujan failed his Fellow of Arts exam in December 1906 and again a year later. Without a FA degree, he left college and continued to pursue independent research in mathematics, living in extreme poverty and often on the brink of starvation.

It was in 1910, after a meeting between the 23-year-old Ramanujan and the founder of the Indian Mathematical Society, V. Ramaswamy Aiyer, also known as Professor Ramaswami, that Ramanujan started to get recognition within the mathematics circles of Madras, subsequently leading to his inclusion as a researcher at the University of Madras.

Life in England

Ramanujan departed from Madras aboard the S.S. Nevasa on 17 March 1914. When he disembarked in London on 14 April, Neville was waiting for him with a car. Four days later, Neville took him to his house on Chesterton Road in Cambridge. Ramanujan immediately began his work with Littlewood and Hardy. After six weeks, Ramanujan moved out of Neville’s house and took up residence on Whewell’s Court, a five-minute walk from Hardy’s room. Hardy and Littlewood began to look at Ramanujan’s notebooks. Hardy had already received 120 theorems from Ramanujan in the first two letters, but there were many more results and theorems in the notebooks. Hardy saw that some were wrong, others had already been discovered, and the rest were new breakthroughs. Ramanujan left a deep impression on Hardy and Littlewood. Littlewood commented, “I can believe that he’s at least a Jacobi”, while Hardy said he “can compare him only with Euler or Jacobi.”

Ramanujan spent nearly five years in Cambridge collaborating with Hardy and Littlewood, and published part of his findings there. Hardy and Ramanujan had highly contrasting personalities. Their collaboration was a clash of different cultures, beliefs, and working styles. In the previous few decades, the foundations of mathematics had come into question and the need for mathematically rigorous proofs recognized. Hardy was an atheist and an apostle of proof and mathematical rigour, whereas Ramanujan was a deeply religious man who relied very strongly on his intuition and insights. While in England, Hardy tried his best to fill the gaps in Ramanujan’s education and to mentor him in the need for formal proofs to support his results, without hindering his inspiration—a conflict that neither found easy.

Ramanujan was awarded a Bachelor of Science degree by research (this degree was later renamed PhD) in March 1916 for his work on highly composite numbers, the first part of which was published as a paper in the Proceedings of the London Mathematical Society. The paper was more than 50 pages and proved various properties of such numbers. Hardy remarked that it was one of the most unusual papers seen in mathematical research at that time and that Ramanujan showed extraordinary ingenuity in handling it.[citation needed] On 6 December 1917, he was elected to the London Mathematical Society. In 1918 he was elected a Fellow of the Royal Society, the second Indian admitted to the Royal Society, following Ardaseer Cursetjee in 1841. At age 31 Ramanujan was one of the youngest Fellows in the history of the Royal Society. He was elected “for his investigation in Elliptic functions and the Theory of Numbers.” On 13 October 1918, he was the first Indian to be elected a Fellow of Trinity College, Cambridge.

Illness and death of Ramanujan

hroughout his life, Ramanujan was plagued by health problems. His health worsened in England; possibly he was also less resilient due to the difficulty of keeping to the strict dietary requirements of his religion in England and wartime rationing during 1914–1918. He was diagnosed with tuberculosis and a severe vitamin deficiency at the time, and was confined to a sanatorium. In 1919 he returned to Kumbakonam, Madras Presidency, and soon thereafter, in 1920, died at the age of 32. After his death, his brother Tirunarayanan chronicled Ramanujan’s remaining handwritten notes consisting of formulae on singular moduli, hypergeometric series and continued fractions and compiled them.

Ramanujan’s widow, Smt. Janaki Ammal, moved to Bombay; in 1931 she returned to Madras and settled in Triplicane, where she supported herself on a pension from Madras University and income from tailoring. In 1950, she adopted a son, W. Narayanan, who eventually became an officer of the State Bank of India and raised a family. In her later years, she was granted a lifetime pension from Ramanujan’s former employer, the Madras Port Trust, and was also granted pensions from, among others, the Indian National Science Academy and the state governments of Tamil Nadu, Andhra Pradesh and West Bengal. She continued to cherish Ramanujan’s memory, and was active in efforts towards increasing his public recognition; prominent mathematicians, including George Andrews, Bruce C. Berndt and Béla Bollobás made it a point to visit her while in India. She died at her Triplicane residence in 1994.

A 1994 analysis of Ramanujan’s medical records and symptoms by Dr. D. A. B. Young concluded that his medical symptoms—including his past relapses, fevers, and hepatic conditions—were much closer to those resulting from hepatic amoebiasis, an illness then widespread in Madras, rather than tuberculosis. He had two episodes of dysentery before he left India. When not properly treated, dysentery can lie dormant for years and lead to hepatic amoebiasis, whose diagnosis was not then well established. At the time, if properly diagnosed, amoebiasis was a treatable and often curable disease; for instance, British soldiers who had contracted the disease during the First World War were being successfully cured of amoebiasis around the time Ramanujan left England.

//source : Wikipedia

Charles Darwin

Charles Darwin : Writer of The Descent of Man


Charles Darwin, in full Charles Robert Darwin, (born February 12, 1809, Shrewsbury, Shropshire, England—died April 19, 1882, Downe, Kent), English naturalist whose scientific theory of evolution by natural selection became the foundation of modern evolutionary studies. An affable country gentleman, Darwin at first shocked religious Victorian society by suggesting that animals and humans shared a common ancestry. However, his nonreligious biology appealed to the rising class of professional scientists, and by the time of his death evolutionary imagery had spread through all of science, literature, and politics. Darwin, himself an agnostic, was accorded the ultimate British accolade of burial in Westminster Abbey, London.

Darwin formulated his bold theory in private in 1837–39, after returning from a voyage around the world aboard HMS Beagle, but it was not until two decades later that he finally gave it full public expression in On the Origin of Species (1859), a book that has deeply influenced modern Western society and thought.

Top Questions About Darwin

Charles Darwin’s theory of evolution by natural selection is the foundation upon which modern evolutionary theory is built. The theory was outlined in Darwin’s seminal work On the Origin of Species, published in 1859. Although Victorian England (and the rest of the world) was slow to embrace natural selection as the mechanism that drives evolution, the concept of evolution itself gained widespread traction by the end of Darwin’s life.
Charles Darwin’s theory of evolution had three main components: that variation occurred randomly among members of a species; that an individual’s traits could be inherited by its progeny; and that the struggle for existence would allow only those with favorable traits to survive. Although many of his ideas have been borne out by modern science, Darwin didn’t get everything right: traces of Jean-Baptiste Lamarck’s outdated theory of evolution remained in Darwin’s own. He was also unable to correctly establish how traits were inherited, which wasn’t clarified until the rediscovery of Gregor Mendel’s work with peas.
Growing up, Charles Darwin was always attracted to the sciences. In 1825 his father sent him to the University of Edinburgh to study medicine. There he was exposed to many of the dissenting ideas of the time, including those of Robert Edmond Grant, a former student of the French evolutionist Jean-Baptiste Lamarck. He transferred to Christ’s College, Cambridge, in 1828, where his mentors mostly endorsed the idea of providential design. A botany professor suggested he join a voyage on the HMS Beagle—a trip that would provide him with much of his evidence for the theory of evolution by natural selection.

Darwin formulated his bold theory in private in 1837–39, after returning from a voyage around the world aboard HMS Beagle, but it was not until two decades later that he finally gave it full public expression in On the Origin of Species (1859), a book that has deeply influenced modern Western society and thought.

Charles Darwin's

HMS Beagle voyage A map of Charles Darwin’s voyage on the HMS Beagle in 1831–36

Early life and education

Darwin was the second son of society doctor Robert Waring Darwin and of Susannah Wedgwood, daughter of the Unitarian pottery industrialist Josiah Wedgwood. Darwin’s other grandfather, Erasmus Darwin, a freethinking physician and poet fashionable before the French Revolution, was author of Zoonomia; or the Laws of Organic Life (1794–96). Darwin’s mother died when he was eight, and he was cared for by his three elder sisters. The boy stood in awe of his overbearing father, whose astute medical observations taught him much about human psychology. But he hated the rote learning of Classics at the traditional Anglican Shrewsbury School, where he studied between 1818 and 1825. Science was then considered dehumanizing in English public schools, and for dabbling in chemistry Darwin was condemned by his headmaster (and nicknamed “Gas” by his schoolmates).

His father, considering the 16-year-old a wastrel interested only in game shooting, sent him to study medicine at Edinburgh University in 1825. Later in life, Darwin gave the impression that he had learned little during his two years at Edinburgh. In fact, it was a formative experience. There was no better science education in a British university. He was taught to understand the chemistry of cooling rocks on the primitive Earth and how to classify plants by the modern “natural system.” At the Edinburgh Museum he was taught to stuff birds by John Edmonstone, a freed South American slave, and to identify the rock strata and colonial flora and fauna.

More crucially, the university’s radical students exposed the teenager to the latest Continental sciences. Edinburgh attracted English Dissenters who were barred from graduating at the Anglican universities of Oxford and Cambridge, and at student societies Darwin heard freethinkers deny the Divine design of human facial anatomy and argue that animals shared all the human mental faculties. One talk, on the mind as the product of a material brain, was officially censored, for such materialism was considered subversive in the conservative decades after the French Revolution. Darwin was witnessing the social penalties of holding deviant views. As he collected sea slugs and sea pens on nearby shores, he was accompanied by Robert Edmond Grant, a radical evolutionist and disciple of the French biologist Jean-Baptiste Lamarck. An expert on sponges, Grant became Darwin’s mentor, teaching him about the growth and relationships of primitive marine invertebrates, which Grant believed held the key to unlocking the mysteries surrounding the origin of more-complex creatures. Darwin, encouraged to tackle the larger questions of life through a study of invertebrate zoology, made his own observations on the larval sea mat (Flustra) and announced his findings at the student societies.

The young Darwin learned much in Edinburgh’s rich intellectual environment, but not medicine: he loathed anatomy, and (pre-chloroform) surgery sickened him. His freethinking father, shrewdly realizing that the church was a better calling for an aimless naturalist, switched him to Christ’s College, Cambridge, in 1828. In a complete change of environment, Darwin was now educated as an Anglican gentleman. He took his horse, indulged his drinking, shooting, and beetle-collecting passions with other squires’ sons, and managed 10th place in the Bachelor of Arts degree in 1831. Here he was shown the conservative side of botany by a young professor, the Reverend John Stevens Henslow, while that doyen of Providential design in the animal world, the Reverend Adam Sedgwick, took Darwin to Wales in 1831 on a geologic field trip.

Fired by Alexander von Humboldt’s account of the South American jungles in his Personal Narrative of Travels, Darwin jumped at Henslow’s suggestion of a voyage to Tierra del Fuego, at the southern tip of South America, aboard a rebuilt brig, HMS Beagle. Darwin would not sail as a lowly surgeon-naturalist but as a self-financed gentleman companion to the 26-year-old captain, Robert Fitzroy, an aristocrat who feared the loneliness of command. Fitzroy’s was to be an imperial-evangelical voyage: he planned to survey coastal Patagonia to facilitate British trade and return three “savages” previously brought to England from Tierra del Fuego and Christianized. Darwin equipped himself with weapons, books (Fitzroy gave him the first volume of Principles of Geology, by Charles Lyell), and advice on preserving carcasses from London Zoo’s experts. The Beagle sailed from England on December 27, 1831.