National Mathematics Day 22nd December

Today ( December 22, 2025) is the 138th birthday to Srinivasa Ramanujan, a self-taught Indian mathematical genius. 

Srinivasa Ramanujan, the mathematical genius, credited his groundbreaking discoveries to divine inspiration, particularly from Namagiri Thayar, the goddess he revered.

For him, mathematics wasn't just numbers and equations; it was a spiritual pursuit, a way to decode the cosmic language of the universe.

    

He once said, 'An equation means nothing to me unless it expresses a thought of God.' His faith guided him to insights that still baffle mathematicians, proving that when intellect is aligned with spirituality, the results can be truly infinite.

Birthversary: S. Ramanujan (Dec. 22, 1887 -- April 26, 1920)

National Mathematics Day of India ! 

I have not trodden through the conventional regular course which is followed in a university course, but I am striking out a new path for myself. "

This is what Srinivasa Ramanujan wrote in a letter introducing himself to the famous and esteemed British mathematician G. H. Hardy, in January 1913. Ramanujan was a self-taught mathematician working as a clerk in a post office in India when he wrote to Hardy at the University of Cambridge. What happened next became an inspiring tale of how an untrained genius could become accepted as one of the greatest mathematical minds of his time. Hardy invited Ramanujan to Cambridge, and on March 17, 1914 Ramanujan set sail for England to start one of the most fascinating collaborations in the history of maths.

Srinivasa Ramanujan hailed as an all-time great mathematician, like Euler, Gauss or Jacobi, for his natural genius, has left behind 3900 original theorems, despite his lack of formal education and a short life-span.

When Ramanujan arrived in England he worked with Hardy on a range of mathematical topics. He arrived with little formal training, and had devised his very own way of writing mathematics that other mathematicians had never seen before.

One of these papers, written with Hardy, astonished the mathematical community as it gave a way to reliably calculate numbers that had eluded mathematicians for centuries – partition numbers. This paper was one of those quoted in his nomination to be elected as a Fellow of the Royals Society, a high honour for any scientist.

G. H. Hardy says 

"The limitations of his knowledge were as startling as its profundity. Here was a man who could work out modular equations and theorems…to orders unheard of, whose mastery of continued fraction was… beyond that of any mathematician in the world, who had found for himself the functional equation of zeta function and the dominant terms of many of the most famous problems in analytical theory of numbers; and yet he had never heard of a doubly periodic function or of Cauchy’s theorem, and had indeed but the vaguest idea of what a function of complex variable was…”

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.

The romanticism rubbed off on the number 1729, which plays a central role in the Hardy-Ramanujan story. "I remember once going to see [Ramanujan] when he was ill at Putney," Hardy wrote later. "I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. 'No', he replied, 'it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.'" What Ramanujan meant is that

 

The anecdote gained the number 1729 fame in mathematical circles, but until recently people believed its curious property was just another random fact Ramanujan carried about in his brain — much like a train spotter remembers train arrival times. 

There is another interesting twist to this story. While Ramanujan was working in the abstract realms of number theory, physicists studying real-world phenomena began developing the theory of quantum mechanics. Although a triumph in its own right, it soon became clear that the resulting quantum physics clashed with existing physical theories in an unredeemable way. The rift still hasn't been healed and presents the biggest problem of twenty-first century physics. One attempt at rescuing the situation was the development, started in the 1960s, of string theory, a prime candidate for a "theory of everything" uniting the disparate strands of modern physics.

A curious prediction of string theory is that the world we live in consists of more than the three spatial dimensions we can see. The extra dimensions, the ones we can't see, are rolled up tightly in tiny little spaces too small for us to perceive. The theory dictates that those tiny little spaces have a particular geometric structure. There's a class of geometric objects, called Calabi-Yau manifolds, which fits the bill. And one of the simplest classes of Calabi-Yau manifolds comes from, wait for it, K3 surfaces, which Ramanujan was the first to discover.

Ramanujan could never have dreamt of this development, of course. He was a whiz with formulas and his aim was to construct those near counter-examples to Fermat's last theorem. So he developed a theory to find these near misses, without recognising that the machine he was building, those formulas that he was writing down, would be useful for anyone, ever, in the future.

His discoveries and his analytical theory of numbers , his works on elliptic functions, infinite series and continued fractions outstandingly declare his mathematical class and calibre . He was around 33 years old  on April 26th ,1920  when he died from tuberculosis complication.

Many of his mathematical discoveries were based on pure intuition – but most of them were later proved to be true.

He once said, “An equation for me has no meaning, unless it represents a thought of God.”

Ramanujan’s obsession with fractions, divergent series, elliptic integrals and hypergeometric series made him desperate to gain recognition from established mathematicians around the world. 

 Hardy invited Ramanujan to Cambridge but as brahmin he would not cross the ocean and his mother scoffed at the idea of the journey to foreign land. Going to a foreign land, especially crossing the sea, was “sinful”, akin to discarding the sacred thread, eating beef, or marrying a widow.

Some time later his mother had a dream, in  the dream, his mother had seen herself surrounded by Europeans and heard the goddess Namagiri commanding her to stand no longer between her son and the fulfillment of his life’s purpose.

While mathematicians in the West were trained to systematically prove each of their theorems, with extensive workings but Ramanujan was a man of deep faith and intuition. Once, Ramanujan was asked about a new equation he had derived. His reply was:

It was goddess Namagiri, the presiding deity of a shrine in Namakkal who had appeared in my dream and helped me solve that problem.

In the spring of 1917, Ramanujan fell ill. He had been following a rigid brahmin diet discipline since 1914 where he wouldn’t eat anything prepared by a flesh eater or in the utensils used in its cooking. The War was in its full swing and England was bereft of customary Indian condiments for cooking. His inadequate intake of food along with cold weather and coughing added to his sickness. He was in and out of sanatoria for the rest of his stay in Cambridge. By early 1919 Ramanujan seemed to have recovered sufficiently and decided to travel back to India.  Sadly, Ramanujan’s recovery was short-lived. His illness returned and he died, aged just 32, on April 26, 1920, leaving him only a short time to benefit from his fellowship of the Royal Society and fellowship of Trinity.

Hardy considered his friend’s demise as a loss too much to bear and live with. In a eulogy organized by the Fellows of Royal Society in remembrance of Ramanujan, Hardy who was a non-believer expressed his gratitude to the ‘Lord’ for the honor to work with both Ramanujan and Littlewood in his lifetime. “There are no proofs that can determine the outcome in matters of the heart,” Hardy said.