What was Ramanujan's IQ
|San-José State University|
Department of Economics
U. Tornado Alley
a mathematician shining
Had he turned up in a city of learning from a family of well-known mathematicians that his accomplishments would still have been astonishing, but he was born into a poor family with no notable professional achievements in a part of the world where hardly any of the nature of his talents could even understand. The obstacles to his achieving his goal of becoming a professional mathematician were insurmountable by assessment. Yet he did and people all over the world still wonder about the achievements of Srinivasa Ramanujan.Ramanujan was born on December 22, 1887 in Erode, a small town in Madras state (now Tamil Nadu) in southern India. His father was a secretary in a tissue store. The family was a Brahmin and Ramanujan's maternal grandfather was a minor officer in a local court. So the family was poor but socially significant. Ramanujan was born in this grandfather's house erode inside. His mother and father soon after his birth moved with him to a house in the city of Kumbakonam and Ramanujan grew up there.
Ramanujan's family sometimes took in student boarders and it was through these that Ramanujan was first introduced to formal mathematics. One of the boarders gave him a trigonometry text when he was twelve and Ramanujan worked it out alone within a year.
When Ramanujan was sixteen and still in high school, an older friend who knew of his precocious math talent gave him synopsis George Carr's the basic results in pure and applied mathematics. This two-volume encyclopedic volume contained six thousand theorems in every field of mathematics. As Ramanujan read and worked his way through these theorems, he discovered that he could derive results that were not in Carr. This was the beginning of Ramanujan's mathematical productions and set the tone for his mathematical career.
The city of Madras, now called Chennai
The British East India Company began establishing a presence on the Coromandel coast of the Bay of Bengal in southern India in the 17th century. The company obtained permission from local rulers to build a fort there. The company chose a site north of the mouth of the Cooum River where a fishing village called Madraspatnam was located. The fort was called Fort St. George.
There were other villages like Mylapore in the area that were temple cities. The area was a low lying flat no more than 23 feet above sea level. Rice was the main product, but there were cotton waxes and weavers to convert the cotton into cloth. East India Company encouraged the weavers and merchants to settle north of the fort. Fort St. George was occupied by the British merchants and was used as a white city known. The area were Tamil merchants and weavers settled were considered black city known. Later the area George Town called.
The city around Fort St. George grew up became known as Madras after the fishing village of Madraspatnam which was originally on the site. However, the Tamil speakers named the city Chennaipatnam and newer Chennai.
The city grew and the British controlled the region and all of India. The region was known as the Madras State for a long period of time. After independence, it became known as Tamil Nadu.
After the East India Company took full control of the region, some British merchants built summer houses in the districts southwest and west of the fort (Nungambakkam, Adyar and Kilpauk).
Over time there developed ethno-religious-linguistic enclaves in the city. Mylapore and Triplicane were Brahmin. Chepauk to the south of the island formed by the branching of the Cooum River became Muslim. Royapuram to the north of the fort beyond Black City (George Town) became an area of Christian settlement. West of Royapuram in an area known as Washermanpet became an area where weavers lived. Weavers also lived in the Chintadripet area to the southwest of the fort and beyond the island in the Cooum River.
In modern times an industrial park was created at Guindy, about four miles southwest of the fort across the Adyar River.
Demographics of Madras (Chennai)
|The linguistic structure|
from the population of Madras,
Tamil, Telugu, and Malayam are languages in the Dravidian family. Urdu is a language closely related to Hindi but containing elements of Persian and Arabic. For more on the Urdu style see Urdu. About 17% of the population speak English as a second language. The population is predominantly Hindu in religion, but there are small Muslim and Christian minorities.
Poverty and the math education of Ramanujan
As mentioned earlier, Ramanujan's family was poor but considerable. He was able to go to the local high school where he received training in basic math. By students boarding with his family he was introduced to more advanced mathetics and started learning on his own. When he graduated from high school he took a competition in which he earned such good grades that he was given a scholarship to a local college, the Government College at Kumbakonan. There his mathematical development continued well, but he was not much interested in the other subjects. In part, this was a matter of him being so fascinated with mathematics that he didn't want to spend his time thinking about other academic subject. Also, some of the subjects were positively distatsteful to Ramanujan, particularly psychology, which was probably really physiology. His course in psychology included the dissection of frogs. Ramanujan was a devout Hindu and was appalled at what he perceived as senseless and immoral cruelty. When the year-end exams came he did very well in math but he left the other subjects and consequently lost his scholarship.
Ramanujan was able to complete a year at another college, Pachiappa College in 1906, thanks to another scholarship. (This scholarship was cut in half when another student applied for a scholarship available and the only one shared between the two of them.) However, in the exams at the end of 1907 he failed again due to poor performance on subjects otherwise than math.
Despite his academic failure, Ramanujan threw himself into the pursuit of new results in mathematics. He worked long and hard. A friend of Ramanujan known as Sandow had the following conversation with Ramanujan:
Sandow: Ramanju, they all call you a genius.
Ramanujan: What! I am a genius! Looking at my elbow, it will tell you the story.
Sandow: What is all this, Ramanju? Why is it so rough and black?
Ramanujan: My elbow has turned rough and black when it made a genius of mine! Night and day I do my calculations on slate. It's too slow to look for a rag to wipe it off with. I wipe the slate with my elbow almost every few minutes.
Sandow: So you are a mountain of industry. Why use a slate when you have to do so much calculation? Why not use paper?
Ramanujan: When food itself is a problem, how can I raise capital for paper? I can request four packages of paper every month.
Sandow goes on to inquire how Ramanujan gets money for food. Ramanujan was a devout Hindu and believed in the gods and goddesses of Hinduism. The story he relates shows how Ramanujan's culture came through it members to his resource. To the extent that the gods and goddesses are straight, personifications of aspects of this culture can be the gods and goddesses that he believed came in to his aid.
At first, Ramanujan was under pressure from his parents to find some means of support in life. In 1907, Ramanujan sought an interview with a man who was a MP collector of income with the Madras Civil Service. His name was Ramaswamy Ayyar and he was a founder of the Indian Mathematical Society. In the interview, Ramanujan told Ayyar of his interest in mathematics and showed him one of his notebooks containing the results Ramanujan had found. When Ramanujan explained to Ayyar that he wanted a job while a secretary told Ayyar that Ramanujan could lose his math talent role as a secretary. Ramanujan was confused, but Ayyar said he would find a way to make him work as a secretary without helping. Ayyar gave Ramanujan a letter of recommendation to take to another Professor Ayyar who happened to have been Ramanujan's instructor in the past.
It was not until December of 1910 that Ramanujan followed through on Ramasway Ayyar's instructions. When Ramanujan took this letter of recommendation to Professor Seshu Ayyar, Professor Ayyar passed it on with a note of introduction to Ramachandra Rao who was a government official and the President of the Indian Mathematical Society. Rao asked to see Ramanujan's notebook. After slipping through it for a few minutes, Rao realized that Ramanujan had found results unknown to other mathematicians. Rao then found where Ramanujan lived. It was in the district in Madras near the beach known as Triplicane. Rao informed Ramanujan that he would receive some money each month to take care of his expenses. This enabled Ramanujan to do his mathematical explores day and night. He took breaks for an evening walk on the beach and for sleep.
In February of 1912, Ramanujan became sufficiently unsure of his future that he secured a clerical position with the Madras Port Trust Bureau. His wages were 25 rupees a month.
Ramanujan worked in the Port Trust Office for only one year. During this time he seems to have found time to work on math because some sheets of this work accidentally got sent to the trust supervisor's port office along with some official papers.
S.R. Ranganathans in the book Ramanujan: The Man and the Mathematician there is no mention of the story that Ramanujan operated two adding machines at once, one with each hand. This story may have emerged from someone for whom mathematics only meant arithmetic and could only imagine in that way what a mathematical genius could do.
During Ramanujan's period of work with the Port Trust Office, a friend of his saw him gathering up pieces of wrapping paper. Ramanujan explained to him that it was for doing his math. When Ramanujan did not have plain paper, he used written on paper and wrote about writing colored in red.
Perhaps the most misleading aspect of Ramanujan’s brief biographies is that they leave the impression that the climate and lack of usable food in England were ruining the health of the vegetarian Ramanujan. Those factors were not good for his health, but his health was precarious long before he traveled to England. His health may have been weak due to health conditions in southern India and due to genetic factors. His mother bore some children who did not survive childhood. His generally poor health may have contributed to his tuberculosis contraction.
A student who knew Ramanujan at Pachaiyappa College 1906-1907, Radhakrishna Ayyar, had some interesting observations from Ramanujan. Ayyar observed that Ramanujan was appropriate and soft of qualities as one would expect from someone who was not physically active. Ayyar said that when Ramanujan focused on any mental task, the pupils of his eyes would disappear. Ayyar and others noticed that Ramanujan's eyes looked intensely piercing. However, Ramanujan was not withdrawn and reticent. He was a great company and liked talking about religion and philosphy as well as math. He was a rather religious Hindu and considered the god Narashima of special meaning for him.
In 1909 Ayyar lived in the Triplicane district of Madras. One day Ramanujan arrived at Ayyar's residence by horse cart. He was very sick and his landlord in George Town (another district of Madras) asked him to come to the market with friends who could look after him. Ayyar gave Ramanujan his bed and tried to take take from him, but Ramanujan was a difficult patient refusing what his caretaker thought would be useful. Ayyar took Ramanujan to a doctor who said Ramanujan should be sent home to his family because he would need constant care. When Ayyar put Ramanujan on the train for Kumbakonam Ramanujan intrusted Ayyar with two notebooks and gave him instructions on what to do with them when he, Ramanujan died. Fortunately, Ramanujan recovered. By 1911, Ramanujan had returned to Madras. Ayyar noted that at that time he had a hand in putting Ramanujan in touch with Ramachandra Rao, who granted Ramanujan a monthly salary of 20-25 rupees per month, which enabled Ramanujan to work on his mathematical research unimpaired.
Ramanujan's family and friends
The image of Ramanujan's personality that comes from the memories of those who knew him is one of a genius, shy, and humble person who was devoutly devoted as well as being devoted to mathematics. He was a devoted and devoted son to his mother and only contradicted her on rare occasions. To his school mates, he was someone who could entertain them with recitations of religious philosohy, but could also tell them about scientific matters such as astronomy.
An anecdote sourced from a friend indicates an unusually ingenious personality. Ramanujan was at a point in his college career sharing a room with two other students who were brothers. Ramanujan and a brother stayed up late talking about astronomy. The other brother, angry at letting his sleep distrubed, dumped a pot of water on Ramanujan's head and said the dousing was to cool off Ramanujan's overheated brain. Instead of responding with violent retaliation, Ramanujan announced that he had just been bathed in the Ganges River.
Ramanujan's mother found him a wife in 1909. She was only nine years old at the time and will have to stay with her family through puberty. Even if she came to Ramanujan's family home, his mother would not let the couple sleep in the same bed together for several years. They never had children and it is possible that the marriage never went through. Still, Ramanujan was apparently quite fond of his wife, Janaki. When Ramanujan, who was brought back to India from England by his mother, met him without bringing Janaki and Ramanujan was upset at this. Later at home, because of his illnesses, Ramanujan's mother asked him to send Janaki back to her family and Ramanujan refused to do so.
Ramanujan's journey across the deep, dark sea to England
The clique of Ramanujan fans who had worked to find him funds to live on soon began to look for ways to send him to England where he could be in contact with mathematicians who were at his level were. They urged him to send samples of his work to mathematicians in Great Britain.
A letter was written that contained a selection of about a hundred theorems that Ramanujan had discovered. The text of the letter may well have been drawn by some supporters in Madras because it did not display the usual extreme humility of Ramanujan himself about his work. Copies of the letter were sent to three mathematicians in England. Two of the recipients did not deign to reply and may not even read the letter. The other recipient was George Hardy from Cambridge University, one of the top mathematicians of his day. Robust and a colleague, John Edensor Littlewood, edited through the claimed theorems to check their validity. Not all were correct, but most were. This exercise convinced Robust that Ramanujan was a superlative mathematician. Robust then set to find a way to bring Ramanujan to Cambridge. In February of 1913 Robust, Ramanujan wrote a letter expressing Ramanujan's interest in the work. He also started to pull robust strings in order to get Ramanujan support for his work. Authorities at the University of Madras provided Ramanujan with a research grant that paid him at a rate more than twice what he had earned as a secretary.It was not an easy matter for the university to do this because Ramanujan had not received a degree.
Getting Ramanujan out of India was no easy matter either. There is a prohibition against crossing the deep dark sea in Hindu theology and Ramanujan was a devout Hindu. The first request by Robust to Ramanujan for him to come to Cambridge was rejected. Probably this refusal was his assumption would have involved not only his going against his own religious principles, but also it would have involved disobeying his religiously religious mother.
In robust England a campaign began to bring Ramanujan to Cambridge. An English scholar named Neville who was persuaded to India for a visit to visit Ramanujan in Madras and in the encouage he went to come to England.
As soon as Ramanujan's trip to England was arranged the clique of his friends began to admire him for preparing the trip. They thought, unfortunately, as it failed, that Ramanujan needed an English style of dress. A friend took Ramanujan to various stores in the sidecar of his motorcycle to get the clothes. His friends prevailed upon Ramanujan to get his haircut in the European style and left his turban for a hat. All of this change in style made Ramanujan uncomfortable, and the inconvenience continued during his temporary stay in England and was unnecessary. The people he had contact with in England would have been perfectly comfortable with Ramanujan wearing a turban instead of a hat.
Although Ramanujan reluctantly acquiesed to a European style of dress, he was adamant about not changing the food he would eat. As a Hindu he would not eat any meat, eggs or fats that involved killing animals.
Ramanujan left Madras in March of 1914. Ramanujan's friends in India arranged for him to be provided with a vegetarian meal on his ships trip to England. Ramanujan, however, did not trust the purity of the meals prepared by non-Hindus. For this reason in England he cooked his own meals. However, since finding vegetables in the wintertime in England, difficult and took time, Ramanujans was not getting the nourishment that he needed. Even with ingredients, the existing Ramanujan diet would have suffered from his pre-intense preoccupation with mathematical research. The bottom line was that his health was deteriorating and he was contracting tuberculosis.
Ramanujan was a rare creature touched by inspiration and not really competent to take care of. When Ramanujan complained about being cold in his bed at night, his friends had to explain to him that the problem was that he slept on the bed, as he did in India, and slept on his bed under the covers.
There are other examples of Ramanujan's difficulty dealing with the elements of ordinary life. As soon as when he was cooking a meal for friends he was so confused at a guest who does not want a third helping of a dish that immediately he left his apartment with his guest sitting there and not seen for a few days. Another problem Ramanujan had was that he was teased by the students at Cambridge University for being so shy.
Ramanujan was celebrated by the scientific institution of Great Britain. He was awarded a Bachelor of Arts (B.A.) degree in 1916 solely for his mathematical studies. In December of 1917 he was elected to the London Mathematical Society. He was inducted into the royal society as a fellow in 1918 at the age of 30, an extremely young age for such an honor and he was one of the few so honored non-British to be. There were some who were reluctant to pile such honors on a foreigner and a young one on that. Some referred to Ramanujan as that hindu calculator. Near the end of 1918 he became a Fellow of the Trinity College of Cambridge University. He was the first so honored Indian to be.
By Ramanujan's health in 1919 had deteriorated to the point where he could no longer work in England and needed the care and comfort of his family in Madras. He returned to India in 1919. His disease was incurable and he died in 1920 at the age of 32. His death is usually attributed to tuberculosis, but apparently he also suffered from liver disease.
Ramanujan's mathematical way
Ramanujan's way of doing mathematics evolved from his introduction to higher mathematics through trigonometry and Carrs to the volume of six thousand theorems. In trigonometry one can derive sets of formulas (identities). Ramanujan looked for such formulas that I saw in Carr's volume. Ramanujan generated formulas that he believed to be true on the basis of intuition and the examination of a few special cases. He generally didnt provide rigorous evidence of his results. In general, he was not strong in making such rigorous evidence.
Ramanujan, for example, looked for the limits of endless rows. Such a series became the preferred way of computing the mathematical constant π.
For k = 0 the result is 3.14159273, because k = 1 it is 3.141592654. The value of π to 14 decimal places is 3.141592653589793, so Ramanujan's formula provided a result that is accurate to 9 places on the second step. Collectively, Ramanujan had 17 series formulas for the reciprocal of π. There is no way anyone could have created such a formula without a touch of genius.
Ramanujan had a special interest in persistent fractions; i.e. effectively endless fracture structures. For examples of the evaluation of infinite series and continued fractions, see series and fractions.
More recent Ramanujan evaluated definitive integrals. In the times computer software like Maple and Mathematica have been created to do such evaluationations. These software packages do symbolic computation by manipulating strings of symbols until a configuration is found that corresponds to a known result.
Ramanujan and Asperger's Syndrome
Lions 1943 Kanner published a description of a behavior pattern that appears to be that of an identifiable subgroup of the human population. This pattern included
- excessive withdrawal of contact with other people that included noncommunication either through residual dumb or using language in a way that did not involve communication with others
- an obsession with preserving the semeness of their environment
- a fascination with physical objects
- the holding back of facial expressions that reveal no inner feeling
This pattern was called autism known. Later it was recognized that there is not just a single pattern but rather a collection or spectrum of related disorders. It was also recognized that although many autistic people are of very limited functionality that can be identified as delayed there some who are of normal or even above normal abilities.
In the same 1943 year that Kanner marked autism, Hans Asperger of Austria identified another related population group who have some characteristics related to the autistic but are generally quite good at working in human society but another one Mode of operation than to have the general population. Asperger's study was a lost track for about half a century. It was rediscovered and given prominence when psychologist found that Asperger's work had relevance to some people's understanding of extraordinary ability and creativity. Those people came to be known as Asperger's Syndrome people.
The UK National Autistic Society provides the following estimates of proportions of the various autistic patterns in the general population.
in the population
(Inability to learn
With IQ below 70
Or high work
Some scholars believe that Srinivasa Ramanujan had Asperger's Syndrome. The type of Asperger's syndrome and its relation to the spectrum of autism has not yet been decided. High working autistic people and Asperger's syndrome have one social handicap in common, but Asperger's syndrome people appear to have no impairment of their language skills, although they may tend to speak to them at people rather than opposite. Asperger's people can have remarkable skills and yet lack a certain common sense about the world elements of life.
In the case of Ramanujan, there were elements of his early life that fit the pattern of Asperger's Syndrome like his beginning to speak relatively late. His neglect of the non-mathematical subjects in his college work that led to his loss of his desperatedly required scholarship could be an example of a lack of common sense or just poor judgment. In England, when he failed to find he had to sleep on a bed under the covers, be another example of a lack of common sense. His neglect of his health would be another more serious example of a lack of common sense.
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