## Leonhard Euler

The Man Who Knew Infinity Review

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The first ever film we have chosen to review for the Math Chronicles details the life of one of the most original and productive mathematicians of the Twentieth Century despite receiving no formal training in pure mathematics and only living for 32 years. That’s right - he is the Indian mathematician Srinivasa Ramanujan (1887-1920), who made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions in a way that is still studied by academics and aspiring mathematicians today. As recently as 2011, his “lost notebook” which detailed his work in the last year of his life, inspired calculations for the entropy of black holes. The film in question is The Man Who Knew Infinity, a 2015 movie by director Matt Brown based on Robert Kanigel’s book by the same name.

Frame #1: Ramanujan is working on his theorems in his dorm room in Trinity College.

The film is overwhelmingly accurate in its portrayal of Ramanujan’s life and his relationship with his advisors G. H. Hardy (1877-1947) and John Littlewood (1885-1977). The story begins in Madras, India where Ramanujan tries to find work in order to save enough money for his mother Komalatammal and wife Janaki to move in with him. He frequently writes letters regarding his theorems and formulas to established mathematicians in the United Kingdom, only to be ignored. Speaking on his continuous rejection, psychologist Hans Eyesenck would say: "He tried to interest the leading professional mathematicians in his work but failed for the most part. What he had to show them was too novel, too unfamiliar, and additionally presented in unusual ways; they could not be bothered." He rarely if ever proved his work, and the fact that India was under British rule in his lifetime subjected him to the racist dismissal of the British mathematical community.

Frame #2: Ramanujan is talking with Littlewood while Hardy is listening.

Except for one person: G. H. Hardy. Hardy was an influential mathematician from Trinity College, Cambridge, and had seen the potential in Ramanujan, who was soon invited to England by him. Ramanujan agreed to take the trip although it meant leaving his family behind and betraying his deep-rooted Hindi beliefs which forbade him from overseas travel in order to achieve his dreams of getting his work published. I will not spoil your enjoyment of the movie by revealing any further details; however, the rest of the movie is a breathtaking portrayal of life in Cambridge during the First World War. Death, illness, and prejudice against Ramanujan’s lack of formal education and Indian nationality surround both the setting of the movie and Ramanujan’s life in itself. He struggles to adapt to his life in England and strives along with Hardy for his work to be acknowledged by the Cambridge mathematical community. His work is intuitive and without rigorous proof, which leads to disagreements between himself and Hardy, the latter believing his work will be ridiculed if they refuse to provide concrete evidence. Despite such setbacks, the film has its moments of shining optimism: Ramanujan goes on to establish a legacy that will far outlive him with more certainty and acclaim each passing year.

Frame #3: Hardy is lecturing Ramanujan in his office at Cambridge.

The mathematics behind Ramanujan’s work is explained, although rather superficially, throughout the movie with an emphasis on partitions. A topic of number theory, partitions are ways in which an integer n can be written as a sum of positive integers. For example, 4 can be partitioned in 5 distinct ways: 4, 3 + 1, 2 + 2, and 2 + 1 + 1. This is simple enough, but the calculations get increasingly complicated. The integer 100 has 190569292 partitions. Ramanujan attempts to find a simple formula in order to calculate the number of partitions of any given number throughout the movie, a task deemed to be impossible by the overwhelming majority of the mathematical community. There is also reference to infinite series and Highly Composite Numbers, the first mathematical paper ever published by Ramanujan. We suggest you watch the movie in order to find what exactly Ramanujan came up with, and even better, take a look at these mathematical topics yourself. I guarantee you will not quite forget the number 1729 after seeing the movie as well!

Overall, I would recommend The Man Who Knew Infinity to anyone interested in Ramanujan’s life and work. The movie is a whirlwind of pain, excitement, and uncertainty set in 1910's Cambridge with familiar names such as the eminent philosopher Bertrand Russel. A clear sense of direction, and charming history is present. Not every relationship is properly explored in the movie, and especially the bond between Ramanujan and his wife falls relatively flat. Nonetheless, such complaints can be attributed to the relatively short run time of the movie at 108 minutes, and the director’s artistic decision to not “overly fictionalize” the narrative by filling missing spots of Ramanujan’s life with inaccurate scenes. This movie is a great starting point to Ramanujan’s life, and I would recommend the books “Modern mathematics: 1900 to 1950” by Michael J. Bradley and “The music of the Primes: Searching to Solve the Greatest Mystery in Mathematics” by Marcus du Sautoy if you’re searching for more, both of which are present at our school’s library!

I want to conclude this pseudo-review with a quote from Hardy in his obituary of Ramanujan written in 1920: “His insight into formulae was quite amazing, and altogether beyond anything I have met with in any European mathematician. It is perhaps useless to speculate as to his history had he been introduced to modern ideas and methods at sixteen instead of at twenty-six. It is not extravagant to suppose that he might have become the greatest mathematician of his time. What he actually did is wonderful enough… when the researches which his work has suggested have been completed, it will probably seem a good deal more wonderful than it does today.” And in fact, 101 years after his death, the work of Ramanujan is as relevant as ever, if not more.

References

Hans Eysenck (1995). Genius, p. 197. Cambridge University Press, ISBN 0-521-48508-8.

Hardy, G. H. (June 1920). "Obituary, S. Ramanujan". Nature. 105 (7): 494–495. Bibcode:1920Natur.105..494H. doi:10.1038/105494a0. S2CID 4174904.

“The Man Who Knew Infinity.” IMDb, IMDb, www.imdb.com/title/tt0787524/.