The number 1729 is called hardy ramanujan number in his honor, following an incident pertaining to a taxi with this number. At age 15 srinivasa ramanujan obtained a mathematics book containing. On the occasion of the 125th birth anniversary of the famous indian mathematician srinivasa ramanujan, the tata institute. Ramanujans 1729 taxi number lends new discovery in. In honor of the ramanujan hardy conversation, the smallest number expressible as the sum of two cubes in different ways is known as the taxicab number and is denoted as. At first glance, it is remarkable that ramanujan knew the properties of the number 1729. When ramanujan was a year old his mother took him to the town of kumbakonam, about 160 km nearer madras. Thus, one of his two closest mathematical friends in madras did have a copy of mathewss book, and ramanujan intimates that this source was well known to both of them. The romanticism rubbed off on the number 1729, which plays a central role in the hardy ramanujan story. Pdf contributions of srinivasa ramanujan to number theory. Mathematician ramanujan biographical book pdf download free. Ramanujans mock theta functions and some recent developments. Number 1729, rather a dull number, ramanujan immediately. It is a taxicab number, and is variously known as ramanujans number and the hardyramanujan number, after an anecdote of the british mathematician g.
A common anecdote about ramanujan during this time relates how hardy arrived at ramanujans house in a cab numbered 1729, a number he claimed to be totally uninteresting. Carr, in three notebooks, between the years 1903 1914, before he left for england. Ramanujan replied that 1729 was not a boring number at all. Ramanujan came upon the number 1729 during a search for integer nearsolutions of the diophantine equation. The ramanujan prime, the ramanujan theta function, partition formulae, and mock theta functions, have opened entire new areas of work and inspired a vast amount of further research. Ramanujan is said to have stated on the spot that, on the contrary, it was actually a very interesting number mathematically, being the smallest number representable in two different ways as a sum of two cubes. Ramanujan has 22 books on goodreads with 12308 ratings. Srinivasa ramanujan was a famous indian mathematician who lived during the british rule in india.
A taxicab number is the smallest number that can be expressed as the sum of two positive cubes in n distinct ways. Oct 16, 2015 one day, hardy visited ramanujan at the hospital as he regularly had before, stepping out of a black cab with the number 1729, rather a dull one, hardy said as he met ramanujan. Ramanujan was born in his grandmother s house in erode, a small village about 400 km southwest of madras. Srinivasa ramanujan frs 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. The number 1729 has since become known as the hardy ramanujan. Ramanujan was sent to kangeyam primary school in kumbakonam at the age of seven. In this book, we examine chapters 1015 in ramanujans second note book. Apr 26, 2018 the smallest nontrivial taxicab number, i. A note on mathematics genius srinivasa ramanujan, frs article pdf available in international journal of information technology and decision making january 2014 with 42,753 reads. The subjects examined in this book have a rich history dating back to euler and jacobi, and. How a rather dull taxi number inspired ramanujan to make a. Ramanujan studies and works with godfrey hardy 1916. Srinivasa ramanujan was one of indias greatest mathematical geniuses.
It is the smallest number expressible as a sum of two cubes in two different ways. As ramanujan pointed out, 1729 is the smallest number to meet such conditions. Once, hardy visited ramanujan in hospital and observed, just to make conversation, that the taxi in which he had arrived had the number 1729, which was. Library of congress cataloging in publication data.
Srinivasa ramanujan 18871920 was a mathematical genius who changed the world of mathematics in his short life. Watson stored at the wren library at trinity college, cambridge. The problem about the number 1729 is now often called the taxicab. The history of the notebooks, in brief, is the following. Ramanujans notebooks the institute of mathematical sciences. The number was also found in one of ramanujan s notebooks dated years. Ramanujans notebooks were compiled approximately in the years. June 1, 20 ramanujan educational institutions palwal india 17hardy ramanujan taxicab numbers a common anecdote about ramanujan relateshow hardy arrived at ramanujans house in acab numbered 1729, a number he claimed to betotally uninteresting. Biography of srinivasa ramanujan, mathematical genius. The man who knew infinity ramanujan college of management.
Hardy later described his collaboration with ramanujan as the one romantic incident in my life. A note on mathematics genius srinivasa ramanujan, frs. The purpose of this paper is to introduce some of the contributions of srinivasa ramanujan to number theory. What he had to show them was too novel, too unfamiliar, and additionally presented in. Ramanujans astonishing knowledge of 1729 thatsmaths. Hardy is the british mathematician who first appreciated the full extent of ramanujan s talent, knew him well personally, and had a fruitful mathematical collaboration with him. Some things you probably did not know about 1729 and the man who knew infinity. You should attend if you are a student or faculty from academic institution interested to learn the influence of ramanujan in number theory. Taxicab number simple english wikipedia, the free encyclopedia. He was not a formal mathematician but made his part to factorial stuff, number theory and continued fractions. This number is now called the hardyramanujan number, and the smallest numbers that can be expressed as the sum of two cubes in n different ways have been dubbed. On 1st october 1892 ramanujan was enrolled at local school.
Hardy visiting his friend srinivasa ramanujan while. Life and work of the mathemagician srinivasa ramanujan. Pdf this paper brings representations of 1729, a famous hardyramanujan number in. A taxicab number is the name given by mathematicians to a series of special numbers. Ramanujan had noted down the results of his researches, without proofs, as in a synopsis of elementary results, a book on pure mathematics, by g.
It is the smallest number expressible as the sum of two cubes in two different ways. Ramanujan hardy number 1729 hardy arrived in a cab numbered 1729 he commented that the number was uninteresting instantly ramanujan claimed that it was the smallest natural number which can be written as sum of cubes in 2 ways 18. Duration july 25 august 6, 2016 number of participants for the course will be limited to fifty. Ramanujan s lost notebook is the manuscript in which the indian mathematician srinivasa ramanujan recorded the mathematical discoveries of the last year 19191920 of his life. He made substantial contributions to the analytical theory of numbers and worked on elliptic functions, continued fractions, and infinite series. It is 1729, found by mathemagician srinivas ramanujan, 1729 is said to be the enchantment number, since it is the sole number which can be communicated, as the entirety of sum. The story begins like thisthe number derives its name from the following story g. In a famous anecdote, hardy took a cab to visit ramanujan.
Once, in the taxi from london, hardy noticed its number, 1729. Ramanujan is said to have stated on the spot that, on the contrary, it was actually a very interesting number mathematically, being the smallest number representable in two. Nearly all his claims have now been proven correct. Picking up where others left off, beginning with the great english mathematician g. The digits of the hardy ramanujan number 1729 as 7 x 2 x 9 1 125. Srinivasa ramanujan iyengar december 22, 1887 april 26, 1920 was an indian mathematician. Its whereabouts were unknown to all but a few mathematicians until it was rediscovered by george andrews in 1976, in a box of effects of g. Galois died at twentyone, abel at twentyseven, ramanujan. Srinivasa ramanujan frs was an indian mathematician who lived during the british rule in. This particular example of 1729 was made famous in the early 20th century by a story involving srinivasa ramanujan. No mathematician should ever allow him to forget that mathematics, more than any other art or science, is a young mans game. The hardy ramanujan number, which ramanujan stated was the smallest number that can be expressed as the sum of cubed numbers in two different ways. Ramanujan said, no, it is a very interesting number. Pdf a note on mathematics genius srinivasa ramanujan, frs.
Apr 28, 2016 some things you probably did not know about 1729 and the man who knew infinity. According to a wellknown story, hardy rode a taxicab with that number on his w. Input input from keyboard, a positive integer n less than or equal to 1,000,000output output to the screen a table of ramanujan numbers less than. Srinivasa ramanujan, born december 22, 1887, erode, indiadied april 26, 1920, kumbakonam, indian mathematician whose contributions to the theory of numbers include pioneering discoveries of the properties of the partition function. Why is the number 1729 known as the ramanujan number.
Some of his work and biography can be seen in following books. Most of ramanujan s work in number theory arose out of \q\series and theta functions. Ramanujan, in turn, replied that the taxi number 1729, was the smallest number that can be shown as the sum of two cubes two di erent ways. On the occasion of the 125th birth anniversary of the famous indian mathematician srinivasa. However, they are all in the spirit of his mathematics. Hi, i have a programming assignment to display all the ramanujan numbers less than n in a table output. He made mention of the number of the taxi that he was in, stating that it was such an uninteresting number. It has nothing to do with taxis, but the name comes from a wellknown conversation that took place between two famous mathematicians. He further added to hardys comment, that 1729 is not a dull number at all. Ramanujan number 1729 pdf 1729 is the natural number following 1728 and preceding 1730. A ramanujan number is a number which is expressible as the sum of two cubes in two different ways. The smallest number that can be expressed as the sum of two cubes in. The number derives its name from the following story g. Thetoptenmost fascinatingformulasin ramanujanslostnotebook george e.
Seshu aiyar, ramanujan s mathematics teacher at the government college at kumbakonam, claims that he had suggested to ramanujan that he read hardys tract 8, p. Ramanujan is elected fellow of the royal society f. Srinivasa ramanujan mathematician 1729 gh hardy what ive been doing all morning is that ive been trying to come up with some numerically interesting factoid about the number 125. One day, hardy visited ramanujan at the hospital as he regularly had before, stepping out of a black cab with the number 1729, rather a dull one, hardy said as he met ramanujan. The number was also found in one of ramanujan s notebooks dated years before the incident. Ramanujan is recognized as one of the great number theorists of the twentieth century. Material recently uncovered in the library of trinity college, cambridge shows that the story was not simply a charming tale dreamed up by hardy. This is a famous story about one of indias great mathematical genius shri. 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.
Ramanujans notebooks the history of the notebooks, in brief, is the following. Carr a synopsis of elementary results a book on pure. Hardy was very superstitious due to his such nature when he entered into ramanujan s room, he quoted that he had just came in a taxi cab having number 1729 which seemed to him an unlucky number but at. Ramanujan did not leave us proofs of the thousands of theorems he recorded in his notebooks, and so it cannot be claimed that many of the proofs given in this book are those found by ramanujan. Ramanujan books pdf it is this photograph which appears in hardys book, ramanujan. One feels that ramanujan is ready to leave the subject of highly composite numbers, and to come back to another favourite topic, identities. Highly composite numbers 121 75, the number of representations of n by some other quadratic forms is considered, but no longer its maximal order. In this lesson, learn about his very interesting and unusual life and all the. He is considered to be one of the most talented mathematicians in recent history. A biographical film in tamil language, based on ramanujan s life, was released in. Here now is the first book to provide an introduction to his work in number theory.
Dec 26, 2018 the hardyramanujan number, which ramanujan stated was the smallest number that can be expressed as the sum of cubed numbers in two different ways. During his school days, he impressed his classmates, senior students and teachers with his extraordinary intuition and astounding pro. Hardy, who brought ramanujan to cambridge in 1914, ono has devoted his mathematical career to understanding how in his short life, ramanujan was able to discover so many deep mathematical truths, which ramanujan believed had been sent to him as visions from a hindu goddess. Ramanujan gave the two positive cubes in two different ways. The number 1,729 is not one to make the average persons pulse race, but it is the subject of one of the most remarkable stories in the history of. His father worked in kumbakonam as a clerk in a cloth merchant s shop. When he got there, he told ramanujan that the cabs number, 1729, was rather a dull one. It is a taxicab number, and is variously known as ramanujans number and. Dec 17, 2014 ramanujan hardy number 1729 hardy arrived in a cab numbered 1729 he commented that the number was uninteresting instantly ramanujan claimed that it was the smallest natural number which can be written as sum of cubes in 2 ways 18. Lacking any topic of conversation hardy made mention that the number 1729 was. A discovery of the taxi cab number 1729 research india.
Ramanujan writes, if you see the last paragraph in mathews sic theory of numbers you will find the statement hence we conclude that gausss approximation was too great. First hand testimony and insightful thoughts on ramanujan s background and way of doing mathematics can be found in hardys lecture indian mathematician ramanujan. Hardy when he visited indian mathematician srinivasa ramanujan in hospital. Ramanujan was born in his grandmothers house in erode, a small village about 400 km southwest of madras now chennai. Hardy ramanujan number once hardy visited to putney where ramanujan was hospitalized. Why 1729 a magic number is known as ramanujan number. Ramanujan returned to india in 1919, still feeble, and died the following year, aged only 32. Srinivasa ramanujan simple english wikipedia, the free. For an exposition of ramanujans proof, see shapiro 14, section 9.
A common anecdote about ramanujan during this time relates how hardy arrived at ramanujan s house in a cab numbered 1729, a number he claimed to be totally uninteresting. The ramanujan cubes sorry hardy, 1729 is hardly a story. Srinivasa ramanujan english version mactutor history of. His fathers name was kuppuswami and mothers name was komalatammal. May 12, 2016 at first glance, it is remarkable that ramanujan knew the properties of the number 1729.
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