12 DecNational Mathematics Day
Category : Academic
The Man who truly knew infinity
Solving an enigma that is Srinivasa Ramanujan
Ramanujan was a pure mathematician of the 20th century mentored by G.H. Hardy. Math for Ramanujan was all about writing down ‘the thoughts of Gods’ while for his mentor who was an atheist, it was a religious substitute. Despite the varied perceptions, the unique relationship of this mentor and the mentee often described as ‘two men talking mathematics’ is celebrated to this day. In fact, his mentor on an occasion or two has compared the mathematical proficiency of Ramanujan to that of Euler and Jacobi.
A few books and a few movies based on this Indian Clerk (Ramanujan introducing himself as an Indian Clerk in his letters to British mathematicians seeking opportunities to pursue mathematics despite having no formal training) who had his way with numbers that made many mathematic experts to deem him as one of the best number theorists of the early 20th century. Ramanujan was a self-taught mathematician who mastered trigonometry at the tender age of 12 and proved over 5000 theorems at the age of 16. The makings of this genius transpired even before he shared his ‘cryptic’ partition numbers.
The Pattern of Ramanujan’s Partition Numbers
A partition of a number is the combination of integers adding up to that particular number. For instance, 4 = 3+1 = 2+2 = 2+1+1 = 1+1+1+1, so the partition number of 4 is 5. The number 100 exhibits over 190 million partitions while the partition number of 10 is 42 which makes the simple pattern complicated. Though not definite, Ramanujan had approximated a formula in the year 1918 that helped him present his ‘partition numbers.’ He determined that numbers ending in 4 and 9 have partition numbers that are divisible by 5. Further, he was able to apply his number theory for partition numbers divisible by 7 and 11 as well. Though he did not prove it, he reached a conclusion that the partition numbers had ‘simple properties.
This number puzzle that originated in the work of Srinivasa Ramanujan close to a century ago has been recently solved. And it is astonishing to find that Ramanujan’s partition numbers will hold the key to advancements in Particle Physics and computer security. In fact, partition numbers have already been used to understand the various ways particles can arrange themselves. They have also been used in the encryption of credit card information shared online. One can only imagine the wonders these numbers would create in the future.
Ramanujan's Lost Notebook
It is very intriguing to note that Ramanujan’s work is being applied in understanding the black holes. In his last letter to G. H. Hardy in 1920, Ramanujan described the examples of mock theta functions. These are also found in his lost notebook (that consists of unordered sheets of paper written in Ramanujan's distinctive handwriting containing more than six hundred mathematical formulas consecutively listed.)
A mock theta function is a mock modular form of weight ½ while a mock modular form is the holomorphic part of a harmonic weak Maass form. Mathematical experts have determined and proved that certain mock modular forms generate functions of BPS states (Bogomol'nyi–Prasad–Sommerfield state) in certain supersymmetric string theories that find relevance to the study of black holes with an outlook of quantum gravity (because the string theory predicts that the proposed messenger particle of the gravitational force known as the ‘graviton’ is a string with wave amplitude zero.) Though quite unclear and unestablished, it is the testament of Ramanujan’s proficiency in the field of mathematics that was way radical considering the fact he made these observations in the early 20th century. Reminiscing Ramanujan fascinates us with the many possibilities of the advancements of today being experienced back in the early 20th century if the mathematical genius would have lived beyond his age of 32.