Srinivasa Ramanujan : The Man Who Saw Infinity, Beautiful Mind & 1729


ramanujanKnowledge Series which kick started with The Great Abraham Lincoln, continues with another Great Man in his own right and one of the greatest Mathematical Genius of all time whose contributions still stun the academia even 90 years after this death…Srinivasa Ramanujan “The Beautiful Mind.” Remember the amazing movie based on the life of John Nash, another Brilliant Mathematician, got an inspiration to borrow their title to aptly address another mathematical genius.

The Man Who Saw Infinity is a great movie based on the life of the stellar mathematician and autodidact Srinivasa Ramanujan. The movie is based on the book of the same name by author by Robert Kanigel.  Based on the book, the movie chronicles the rise of Ramanujan through his collaboration with mentor G H Hardy, an eminent and one of the foremost Mathematicians, who fosters g-h-hardy-6the genius of Ramanujan on a global level. The preview of the movie will come a bit later considering the movie was really special with great performances all round esp. Jeremy Irons and very well directed by Matt Brown. The movie is certainly up there for Oscars in Best Supporting Role for Jeremy, Best Director & Best Picture categories. Last year there was a fantastic movie on another brilliant Mathematician Alan Turing, The Imitation Game played by my favorite British Actor and one of the most versatile actors presently, Benedict Cumberbatch.

Side: Photo G H Hardy thefamouspeople.com 

41dT+4sPACL._SX316_BO1,204,203,200_Hey Dude I thought it was Tom Hardy…

Well both are great but Benedict just inches out (more on this at a later date)

An equation means nothing to me unless it expresses thought of GOD “ Srinivasa Ramanujan

Ramanujan’s contribution in mathematics is paramount in Mathematical Analysis, Number Theory, Infinite Series including his breakthrough in theory of partition of numbers which is both iconic and legendary.

Hey whats theory of partition numbers ?

Lets consider the number 3

It can be expressed as 3, 2+1, 1+1+1 while 4 can be expressed as 4 can be expressed as 4, 3 + 1, 2 + 2, 2 + 1 + 1, and 1 + 1 + 1 + 1. It simple for small number but Ramanujan devised a formula which could accurately estimate the number of partitions of huge numbers wherein partitions add up-to to billions. This was a stellar achievement at that point of time considering the best minds in the world in Trinity College, Cambridge could not achieve the same feat. His mathematics is used in such complex theoretical physics like string theory

Srinivasa Ramanujan will forever be known for his Beautiful Mind…Man from very humble origins bestowed by nature with supernatural intelligence, foresight and Mathematical acumen.

Its is very difficult to highlight Ramanujan’s all accomplishments here but lets look into the Iconic No. 1729.

Ramanujan Number…1729

I found a very good description of the essence of this number on the website rohitn.com

1729 came to be known as Ramanujan number, after an interesting incident that took place between Ramanujan & his mentor, G. H. Hardy.

RamanujanCambridgeHardy was paying a visit to Ramanujan, who was ill and undergoing treatment at Putney (London). Hardy mentioned to him that he rode a taxi cab, whose number was 1729. “…the number seemed to me rather a dull one”, he added. It is said about Ramanujan that the numbers 1 – 10000 were his “personal friends”. He could effortlessly tell you their factors, divisors, how the number can be split & the each part of the number can be squared/cubed, etc. to produce interesting numbers, and much more.
Interestingly enough, Ramanujan replied to Hardy’s comment, saying that 1729 is not a dull number at all. It is the smallest number that can be written as sum of 2 cubes, in 2 different ways. . Photo Source: en.wikipedia.org

This is what Ramanujan meant…

Ramanujan number 1729

After Hardy related this incident to his colleagues, this number became well known and was called as Ramanujan Number.

Later on, numbers having similar property were all called as Ramanujan Numbers & the problem of finding such numbers came to be known as TaxiCab(2) problem. That is, solution toTaxiCab(2) yielded numbers of the kind

a^3 + b^3 = c^3 + d^3

Here are a few numbers of this kind :

Ramanujan numbers

Numbers of the kind a^3 + b^3 = m^3 + n^3 = x^3 + y^3 are now known as Ramanujan Triples. The corresponding problem is known as TaxiCab(3).
Numbers of the kind a^3 + b^3 = c^3 + d^4 = w^3 + x^3 = y^3 + z^3 are known as Ramanujan Quadruples or corresponding problem is known as TaxiCab (4), and so on

A very good perspective shared by Rohit and worthy to be highlighted here.

A good artcile to read is listed below.

More will follow up on the superlative genius. List of great mathematicians is here. http://www.famous-mathematicians.com/srinivasa-ramanujan/

http://www.britannica.com/biography/Srinivasa-Ramanujan

 

 


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