Srinivasa Ramanujan, an Indian mathematician was born in 22nd December, 1887 in Madras, India. Like Sophie Germain, he received no formal Education in mathematics but made important contributions to advancement of mathematics.
His chief contribution in mathematics lies mainly in analysis, game theory and infinite series. He made in depth analysis in order to solve various mathematical problems by bringing to Light new and novel ideas that gave impetus to progress of game theory. Such was his mathematical genius that he discovered his own theorems. It was because of his keen insight and natural intelligence that he came up with infinite series for π.
This series made up the basis of certain algorithms that are used today. One such remarkable instance is when he solved the bivariate problem of his roommate at spur of moment with a novel answer that solved the whole class of problems through continued fraction. Besides that he also led to draw some formerly unknown identities such as by linking coefficients of and providing identities for hyperbolic secant.
He also described in detail the mock theta function, a concept of mock modular form in mathematics. Initially, this concept remained an enigma but now it has been identified as holomorphic parts of maass forms. His numerous assertions in mathematics or concepts opened up new vistas of mathematical research for instance his conjecture of size of tau function that has distinct modular form in theory of modular forms. His papers became an inspiration with later mathematicians such as G. N. Watson, B. M. Wilson and Bruce Berndt to explore what Ramanujan discovered and to refine his work. His contribution towards development of mathematics particularly game theory remains unrivaled as it was based upon pure natural talent and enthusiasm. In recognition of his achievements, his birth date 22 December is celebrated in India as Mathematics Day. It would not be wrong to assume that he was first Indian mathematician who gained acknowledgment only because of his innate genius and talent.
Continued fraction
Continued fraction, expression of a number as the sum of an integer and a quotient , the denominator of which is the sum of an integer and a quotient, and so on. In general,
where a0, a1, a2, … and b0, b1, b2, … are all integers.
In a simple continued fraction (SCF), all the bi are equal to 1 and all the ai are positive integers. An SCF is written, in the compact form, [a0; a1, a2, a3, …]. If the number of terms ai is finite, the SCF is said to terminate, and it represents a rational number; for example, 802/251 = [3; 5, 8, 6]. If the number of these terms is infinite, the SCF does not terminate, and it represents an irrational number; for example, Square root of√23 = [4; 1, 3, 1, 8], in which the bar spans a sequence of terms that repeats indefinitely. A nonterminating SCF in which a sequence of terms recurs represents an irrational number that is a root of a quadratic equation with rational coefficients. Nonterminating SCFs that represent numbers such as π or e can be evaluated after any given number of terms to obtain a rational approximation to the irrational quantity.
His Publications
It was after his first publication in the “Journal of the Indian Mathematical Society” that he gained recognition as genius mathematician. With collaboration of English mathematician G. H. Hardy, with whom he came in contact with during his visit to England, he brought forward his divergent series that later stimulated research in that given area thus refining the contribution of Ramanujan. Both also worked on new asymptotic formula that gave rise to method of analytical number theory also called as “Circle Method” in mathematics.
It was during his visit to England that he got worldwide recognition after publication of his mathematical work in European journals. He also achieved the distinction of becoming second Indian, who was elected as Fellow of Royal Society of London in 1918.
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Srinivasa Ramanujan was an Indian mathematician who made extraordinary contributions to number theory, analysis, and infinite series. He had no formal training in mathematics, but he was able to produce highly original work that has had a profound impact on the development of mathematics.
Ramanujan was born in Erode, Tamil Nadu, India, on December 22, 1887. He was the son of a clerk in the Local Government office. Ramanujan showed an early interest in mathematics, and he taught himself from books that he borrowed from the local library. In 1903, he entered the Government College at Kumbakonam, where he studied mathematics and physics.
In 1907, Ramanujan graduated from the Government College at Kumbakonam with a first-class degree in mathematics. He then applied to the Indian Institute of Technology Madras, but he was rejected because he did not have a high enough score on the entrance exam.
Ramanujan then decided to study for the Indian Civil Service exam. However, he failed the exam twice. In 1910, he gave up on his dream of becoming a civil servant and decided to focus on mathematics.
In 1913, Ramanujan wrote a letter to the English mathematician G.H. Hardy, in which he shared some of his mathematical discoveries. Hardy was impressed by Ramanujan’s work, and he invited Ramanujan to come to England to study at Cambridge University.
Ramanujan arrived in England in 1914. He worked with Hardy and other mathematicians at Cambridge, and he made significant contributions to number theory, analysis, and infinite series.
In 1917, Ramanujan was elected a Fellow of the Royal Society, the highest honor that can be bestowed on a scientist in the United Kingdom. He was the first Indian to be elected to the Royal Society.
Ramanujan married Janaki Ammal in 1909. They had no children.
Ramanujan suffered from poor Health throughout his life. He was diagnosed with tuberculosis in 1917, and he died in 1920 at the age of 32.
Ramanujan’s work has had a profound impact on the development of mathematics. He is considered one of the greatest mathematicians of all time. His work has been used to solve problems in physics, chemistry, and engineering.
Ramanujan has been the subject of numerous books, articles, and films. He has also been honored with a postage stamp, a commemorative coin, and a museum in his hometown of Erode.
Ramanujan’s work is still being studied and used by mathematicians today. He is a true genius, and his work will continue to inspire and amaze mathematicians for generations to come.
Here are some of Ramanujan’s most famous results:
Ramanujan’s prime number theorem: This theorem gives an asymptotic formula for the number of primes less than or equal to a given number.
Ramanujan’s theta function: This function is a modular form that has been used to study the distribution of prime numbers.
Ramanujan’s mock theta functions: These functions are similar to the theta function, but they have no modular properties.
Ramanujan’s continued fraction expansions for À and Euler’s constant: These expansions are very accurate and have been used to calculate À and Euler’s constant to millions of digits.
Ramanujan’s work is truly remarkable, and it is a testament to his genius. His work has had a profound impact on the development of mathematics, and it will continue to inspire and amaze mathematicians for generations to come.
Here are some frequently asked questions and short answers about the topic of mathematics:
What is mathematics? Mathematics is the science that deals with the logic of shape, quantity, and arrangement. Math is all around us, in everything we do. It is the building block for everything in our daily lives, including mobile devices, architecture (ancient and modern), art, Money, engineering, and even Sports.
Who are some famous mathematicians? Some famous mathematicians include Pythagoras, Euclid, Archimedes, Rene Descartes, Blaise Pascal, Sir Isaac Newton, Gottfried Wilhelm Leibniz, Leonhard Euler, Srinivasa Ramanujan, David Hilbert, Alan Turing, John von Neumann, and Andrew Wiles.
What are some famous mathematical equations? Some famous mathematical equations include the Pythagorean theorem, the quadratic formula, the equation for the circle, and the equation for the line.
What are some famous mathematical concepts? Some famous mathematical concepts include pi, e, the golden ratio, and infinity.
What are some famous mathematical problems? Some famous mathematical problems include Fermat’s Last Theorem, the Goldbach Conjecture, and the P versus NP problem.
What are some famous mathematical applications? Some famous mathematical applications include cryptography, computer science, and engineering.
What are some famous mathematical discoveries? Some famous mathematical discoveries include the discovery of zero, the discovery of calculus, and the discovery of group theory.
What are some famous mathematical controversies? Some famous mathematical controversies include the controversy over the foundations of mathematics, the controversy over the Riemann Hypothesis, and the controversy over the existence of Fermat’s Last Theorem.
What are some famous mathematical quotes? Some famous mathematical quotes include “Mathematics is the language of the universe,” “Mathematics is the queen of the sciences,” and “Mathematics is the art of reasoning correctly.”
