Srinivasa Ramanujan (Greatest Mathematician)
Quick facts.
Born: 22 Dec 1887, Erode
Died: 26 Apr 1920 (32 years), Kumbakonam
Cause of death: Amoebiasis
Spouse: Janakiammal (m. 1909–1920)
Parents: Komalatammal, Kuppuswamy Srinivasa Iyengar
Siblings: Sadagopan Ramanujan
Education
Government Arts College
Pachaiyappa's College
Trinity College (1914–1916),
University of Cambridge (1916)
Known for Ramanujan's sum:
Landau–Ramanujan constant
Mock theta functions
Ramanujan's congruences
Ramanujan conjecture
Ramanujan prime
Ramanujan–Soldner constant
Ramanujan theta function
Rogers–Ramanujan identities
Ramanujan's master theorem
Hardy–Ramanujan asymptotic formula
Ramanujan–Sato series
Awards
Fellow of the Royal Society (1918)
Scientific career
Fields: Mathematics
Institutions: University of Cambridge
Thesis : Highly Composite Numbers (1916)
Academic advisors:
G. H. Hardy
J. E. Littlewood
Ramanujan's contributions to mathematics continue to inspire and influence researchers, and his life story remains a testament to the power of intuitive mathematical genius. He is regarded as one of the greatest mathematicians of the 20th century.
Srinivasa Ramanujan, born on December 22, 1887, in Erode, Tamil Nadu, India, was an exceptional Indian mathematician renowned for his substantial contributions to various branches of mathematics, including mathematical analysis, number theory, infinite series, and continued fractions. Despite limited formal training in mathematics, Ramanujan's innate mathematical talent became evident during his early years.
Ramanujan excelled in mathematics at the Town Higher Secondary School in Kumbakonam, where he struggled with subjects other than math. His self-taught journey began at the age of 15 when he discovered George Shoobridge Carr's "Synopsis of Elementary Results in Pure and Applied Mathematics." This compilation, dating no later than 1860, fueled his intellectual curiosity, leading him to not only master but surpass Carr's theorems with his own innovative ideas. Although he secured a scholarship to the University of Madras in 1903, he lost it the following year due to his exclusive focus on mathematics.
Throughout his life, Ramanujan faced financial challenges, compelling him to navigate a path through employment struggles. In 1909, he entered into an arranged marriage with Janaki Ammal. Despite the financial difficulties, government official Ramachandra Rao recognized Ramanujan's mathematical prowess and supported his research for a time. However, Ramanujan, driven by a desire for self-sufficiency, eventually secured a clerical position with the Madras Port Trust.
Ramanujan's international recognition began in 1911 when he published his first papers in the Journal of the Indian Mathematical Society. A pivotal moment came in 1913 when he corresponded with British mathematician G. H. Hardy, leading to a special scholarship and grant from the University of Madras and Trinity College, Cambridge, respectively. Overcoming religious objections, Ramanujan arrived in England in 1914, collaborating with Hardy and expanding his mathematical repertoire.
His collaboration with G. H. Hardy was instrumental in gaining recognition within the mathematical community. Despite differences in their backgrounds, they produced significant mathematical results together. Ramanujan's profound knowledge spanned continued fractions, the Riemann series, elliptic integrals, hypergeometric series, and his innovative theory of divergent series called Ramanujan summation. Despite being unfamiliar with modern mathematical developments, he made substantial contributions.
His expertise in the partition of numbers—expressing a positive integer as the sum of positive integers—furthered his acclaim. Ramanujan's papers were published in English and European journals, leading to his election to the Royal Society of London in 1918.
In 1917, Ramanujan contracted tuberculosis, prompting his return to India in 1919. Despite ongoing health struggles, he continued working on mathematical problems until his untimely death in 1920 at the age of 32. He left behind three notebooks and a "lost notebook" containing unpublished results that continue to captivate mathematicians.
Ramanujan's math is applied in modern computing (pi calculation algorithms), physics (string theory, black holes, quantum mechanics via partition functions), cryptography (number theory), computer science (Ramanujan graphs for network design), and algebraic geometry, with his concepts like infinite series, partition theory, and theta functions underpinning breakthroughs in theoretical physics and pure mathematics, even inspiring AI formula discovery via the Ramanujan Machine
Key Applications
Computer Science & Algorithms:
Pi (π) Calculation: His rapid-convergence infinite series for \(\pi \) form the basis for high-precision algorithms used in modern computers.
Ramanujan Graphs: Used as "expanders" in network design and computer science for efficient data routing.
Physics:
Quantum Gravity & String Theory: His mock theta functions and partition identities help predict black hole entropy and critical dimensions in string theory.
Statistical Mechanics: Partition functions for atomic nuclei are calculated using his formulas.
Number Theory & Cryptography:
Deep connections between his partition identities and number theory have implications for modern cryptography.
Pure Mathematics:
Algebraic Geometry: His partition identities reveal surprising links to curves and surfaces.
Representation Theory: Influenced the theory of Galois representations and the Langlands program, relevant to Fermat's Last Theorem.
Other Areas:
Feynman Diagrams: Higher-dimensional versions of his Master Theorem appear in quantum physics.
Ramanujan Machine: An AI project uses his work to discover new mathematical formulas.
Examples of Specific Concepts
Hardy-Ramanujan Asymptotic Formula: For integer partitions, applied in physics.
Mock Theta Functions: Crucial for quantum physics and black hole physics.
Ramanujan's Master Theorem: Used for definite integrals and infinite series.
1729 is the famous Hardy-Ramanujan number, the smallest positive integer expressible as the sum of two cubes in two different ways:
Original handwritten by Ramanujan.
Srinivasa Ramanujan's life story, marked by resilience and dedication to mathematics, has inspired numerous books, documentaries, and movies. His extraordinary journey from a self-taught mathematician in India to an internationally recognized genius underscores his enduring legacy in the world of mathematics.
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