National Mathematics Day ,December 22,“An equation for me has no meaning, unless it expresses a thought of God.While asleep, I had an unusual experience".Ramanujan Mathematician,1729,

    

Ramanujan

Indian mathematician Srinivasa Ramanujan, Indian Young Mathematician,was born in Erode, India, on December 22, 1887, and passed away in 26 April 1920 (aged 32)Kumbakonam, Tanjore District, Madras Presidency, British India (now Thanjavur district,Tamil Nadu, India). Among his many contributions to the theory of numbers are his groundbreaking findings regarding the characteristics of the partition function.Srinivasa Ramanujan was a self-taught Indian mathematician known for his pioneering work in number theory, continuous fractions, infinite series, and mathematical analysis. Despite having no formal experience in advanced mathematics, he created astonishing ideas and formulas that have had a long-term impact on the discipline.He was introduced to the realm of mathematics by G. S. Carr's book "Synopsis of Elementary Results in Pure Mathematics". He devised his own theories and methods, which he published in what became known as Ramanujan's Frayed Notebooks, which other great mathematicians read and edited on numerous occasions. Prof. G. H. Hardy (Trinity College, Cambridge) assisted Ramanujan's formal presentation to the world, believing him to be the best mathematician based only on talent.Despite his short life and lack of formal university education, Ramanujan left behind around 4,000 original theorems, placing him alongside world greats such as Euler, Jacobi, and Gauss.It was G. H. Hardy's 'Orders of Infinity' that Ramanujan discovered. In a letter to him he cited 120 formulas and theorems. Hardy arranged him a trip to London for him as soon as he realized how brilliant he was.National Mathematics Day is marked every year on December 22, the birth anniversary of Srinivasa Ramanujan.Ramanujan-Hardy Collaboration: His collaboration with the British mathematician G.H. Hardy at Cambridge University made his genius known to the world. Hardy saw him as a natural genius on par with greats such as Euler and Gauss.

He is known for the Ramanujan number, which is 1729 with example:

The Story: In 1919, Ramanujan was hospitalized, and mathematician G.H. Hardy paid him a visit. Hardy noted that he had arrived in a taxi with the number 1729 and commented that it appeared to be an uninteresting number. Ramanujan quickly replied: "No, that is a pretty fascinating number. It is the smallest integer that can be expressed as the sum of two cubes in two separate ways.

1729 = 1^3 + 12^3 = 9^3 + 10^3 

This attribute makes 1729 the first number in mathematics to be recognized as a taxicab number 1729, which implies it can be written as the sum of two cubes in two different ways.The incident demonstrates Ramanujan's deep and intuitive understanding of numbers, even in seemingly insignificant contexts. This property of 1729 is explored in number theory and has sparked additional research into related numerical properties.Srinivasa Ramanujan's approach to mathematical problem solving was based mostly on intuition. Unlike traditional mathematicians, who relied primarily on formal proofs and established methodologies, Ramanujan frequently arrived to discoveries and formulas by deep intuition and instinct, which he attributed to his religious views and devotion to the goddess Namagiri.

1.Discovery Without Formal Proof 

2.Innate Number Sense

3.Mock Theta Functions

4.Role of Spirituality

5.Collaboration with G.H. Hardy:G.H. Hardy (born February 7, 1877, Cranleigh, Surrey, England—died December 1, 1947, Cambridge, Cambridgeshire) was a prominent English pure mathematician who primarily worked in analysis and number theory.From 1906 to 1919, he lectured there on mathematics. In 1912, Hardy and John E. Littlewood published the first of a series of papers that made fundamental contributions to many areas of mathematics, including Diophantine analysis theory, divergent series summation (see infinite series), Fourier series, the Riemann zeta function, and prime distribution. The partnership between Hardy and Littlewood is one of the most well-known in twentieth-century mathematics.Award was received Copley Medal (1947)

The Impact of His Intuition: While Ramanujan's lack of formal training meant that parts of his work needed to be refined, his intuitive approach resulted in revolutionary discoveries that would not have been possible using conventional methods. His intuition-driven findings continue to motivate mathematicians to explore unknown territory in mathematics.Srinivasa Ramanujan's contributions to mathematics have had a significant impact on civilization since they advanced the field and shaped modern applications in science, technology, and other areas. His work has had a wide-ranging impact, with much of it still evolving and finding new uses.Contributions to Number Theory;Example: Cryptographic algorithms, such as RSA encryption, rely on number theory to protect sensitive information.

Infinite Series and Calculations;Example: His series for is used in algorithms for calculating digits of in computational mathematics.This has applications in fields requiring precise computations, such as computer science, engineering, and simulations.Example: Physicists use mock theta functions to explore the behavior of black holes and study the geometry of spacetime.Contributions to Data Science and Machine Learning;Example: Algorithms inspired by partition theory help improve data compression and pattern recognition.Example: His achievements encourage mathematical education and research in India and globally, fostering a new generation of thinkers.

Conclusion 

Ramanujan's mathematics not only advanced theoretical understanding, but also established the framework for practical applications that still impact society today. His legacy continues to have an impact on technology, science, cryptography, and education, illustrating his genius's lasting significance.