Guest Author Professor Satish Bhatnagar, Ph.D. – WHAT RAMANUJAN MEANS TO YOU?
This was the title of my keynote address that I delivered on Dec. 22, 2020 (10 AM, IST) at the one-day conference on the History and Development of Mathematics. This conference was organized and onlined by the Mathematics Department of Maharshi Dayanand University, Rohtak, Haryana (est.1976). Mainly, it was a mathematical celebration of the 133rd birth anniversary of Ramanujan. In 2012, his birthday (Dec. 22, 1887) was declared as the National Mathematics Day by Prime Minister Manmohan Singh. My guess is that Manmohan Singh was also prompted by TP Srinivasan (1932 – 2013), his long-time friend and a distinguished mathematician. Incidentally, my Economics colleague and I (in Panjab University Evening College Shimla) had hosted a lunch for the Singhs and Srinivasan at our residence in Nov. 1964 when they were holidaying in Shimla. This reflective article is extracted from this address, and elaborated on in a few places.
First of all, I explained that the Humanistic History of Mathematics, my current area of research, is the study of the History of Mathematics (HoM) integrated with history in general, political systems, philosophy and organized religions. Therefore, during the address, I interjected these disciplines at every opportunity. The very first moment came when I greeted the audience and told them of my addressing them from Las Vegas, the Entertainment Capital of the World. I refer to Las Vegas as the Indrapastha(the present region around old Delhi – not too far from Rohtak!) of the Mahabharata era (c. 800 BC). Thus, sciences and mathematics were highly developed in the India of the Mahabharata era as evidenced by the description of grandiose palaces, weapons of mass destruction, and entertainment centers etc. Mathematics is one of the indexes of affluence and power of a nation.
I pointed out that though this conference is about HoM too, but to the best of my knowledge, HoM is not taught in any regular course in India! This has to change – and the sooner the better. This absence is a reflection of the lack of interest in the general history especially amongst the Hindu masses and the intelligentsia alike (80% of India’s population). It is no wonder that the leading nations in HoM are the ones that build economic empires and colonize the world with trade and the sale of armaments etc. – namely, the UK, France, Germany, Japan and the USA. The total autonomy of Indian colleges and universities (in the public and private sectors) alone can bring innovation in academic programs and in the production of seminal and indigenous research of the caliber of Nobel Prizes and Fields Medals.
What Ramanujan Means To You? is not a rhetorical question. I wanted the participants to ponder over it as to how and why Ramanujan’s achievements have any relevance today. Otherwise, it is pointless to celebrate a life if it cannot be connected with the present. I also raised the questions: Why has another Ramanujan not been born in India yet? Is the Indian educational system flexible enough, say, to let an 18-year old get a PhD? I told the story of a 13-year old student currently enrolled at UNLV who already has four associate degrees from a community college!
The focus of my address was on my thesis, On the Making of Ramanujan. Its gist is that Ramanujan practiced Bhakti (devotional) yoga at a very deep level, and pursued mathematics with equanimity of mind – not at all concerned or competitive – who is doing what etc. Eventually, there came a point in his life when there was a confluence or a resonance effect between these two streams. It took place when Ramanujan’s brain cells were over activated due to constant fever caused by the TB (Tuberculosis Bacteria). What now follows are five salient phases of his short life span of 32 years.
A. Seeding of the Bhakti Yoga (1887 – 1898 )
Ramanujan’s initiation into Bhakti yoga was subliminal – watching people daily, especially his mother worshipping the family goddess and singing in temples. He was the first born. In Dec. 1889, Ramanujan contracted smallpox, but he did not die, like the 4,000 others who did in one district. For a child, it was natural to start believing that his survival was due to his mother’s divine faith. Again, in 1889, his mother gave birth to a son, but he died before completing a year. Imagine his mother’s anguish and her becoming protective of Ramanujan. I can fully identify with this scenario as I witnessed my wife undergoing this experience in 1980 – her memory of that event remains vivid.
‘Unfortunately’, this happened to Ramanujan’s mother twice again – in 1891 and 1894; a girl and a boy were born – both died within a year!! At such a point in life, people either lose their faith in their belief systems or become more devout. His mother remained steadfast. Ramanujan learned about the Bhakti traditions, worship rituals, and puranas (secondary Hindu scriptures). He was 11 years old when his mother gave birth to a boy in 1898, and yet another boy in 1905! These two boys not only survived the dreaded first year, but they outlived Ramanujan. His parents took the births of these two sons as divine blessings, and that cemented down in Ramanujan’s life. Subsequently, he always credited every deep mathematics theorem to his family goddess, Namagiri Thayar (Goddess Mahalakshmi) of Namakkal. He often said, “An equation for me has no meaning unless it expresses a thought of God. Great things in life are the results of yoga (Bhakti yoga is one of the many) while physically engaged in any chore.
B. Dips in Mathematics (1897-1904)
The genius of Ramanujan in mathematics through the age of 11 is not known. There are no anecdotal stories – the reason being that he was raised in a small town and in Tamil culture that forbade any show-off. After the 1857 uprising in India, the British had iron fist control over Indians by enforcing punitive legislation that broke the will of the people. Total submission was the only way to survive. Such was the state of mind of the people living in the eastern and southern parts of India. Thus the compliant regions were duly ‘rewarded’ – like, in 1857, universities were started in Calcutta (Kolkata), Bombay (Mumbai) and Madras (Chennai). For a relative perspective, the first university in Haryana state was established in Kurukshetra in 1957 – ten years after India’s independence!
Ramanujan’s young mind was ignited when he got hold of SL Loney’s classic book on Trigonometry and GS Carr’s book containing thousands of theorems. Had Ramanujan not seen these English textbooks, then his mathematics talents might not have received bursts of oxygen. He was so much fired up by mathematics that he neglected the study of other subjects. Consequently, he failed twice (1906, 1907) in the college FA exam. According to one source, he failed in math too as his solutions were beyond the understanding of his examiners! The reason he did not fail in high school was that the examiners there could follow his solutions!
C. Wilderness Years (1904 -1910)
Without the FA diploma, 20- year old Ramanujan had no steady job, but tutored math to survive. He lived in depression and dejection, and moved around. Such periods of soul-searching for one’s identity and purpose in life are common traits amongst the geniuses. A common social practice in India was to get a disillusioned boy married with a belief that sex life (started with married life in that era – unlike today) would reset his life on a normal course. I know so many of my childhood friends who were married in their teen years. Siddhart (who became Buddha) was also married under similar circumstances Ramanujan was 21 and his wife was 10 years old when they were married in 1909. The strength of a joint family system lies in its support system. For his spiritual affirmation, my guess is that Ramanujan may have met/heard of Raman Maharishi (1879- 1950), a great Tamil yogi.
D. Budding Mathematician in India (1910 – 1914)
Around 1910, Ramanujan’s mathematical prowess came to the attention of V. Ramaswamy Aiyer of Madras University, a founder of the Indian Mathematical Society (1907). He showed Ramanujan’s work to his English colleagues. One of the English professors sent Ramanujan’s papers to mathematicians in the UK – Principle of Associativity at work. At this point, Ramanujan had already published some research papers before leaving India in 1914. Some English mathematicians did not believe that it was Ramanujan who did this work, and some did not understand his math – a common fate of a genius amongst the average – a human paradox. Anyway, Ramanujan was now out of depression. Hindus strongly give such a credit to the wife for bringing about a transformation!
E. Mathematical Explosions in Cambridge (1914 – 1919) and Fever Yoga in India (1919 – 1920)
Before World War II, Cambridge University (UK) dominated by GH Hardy (1877 – 1947) and Gottingen University (Germany) dominated by David Hilbert (1862 – 1943) were the two great centers of mathematics in the world – at the same time the greatest political powers (mind the connection!) It goes to the credit of GH Hardy and the Cambridge University administration for admitting and supporting Ramanujan as an exceptional case. Hardy and Littlewood (1885 – 1977) polished Ramanujan mathematically as he was a bit of a rough diamond until then. The speed of Ramanujan’s ability to learn the foundations of mathematics cannot be explained except by the yogic power that Ramanujan harnessed subconsciously. Apart from problems that engaged Hardy and Littlewood, he produced great mathematics independently. His research productivity seems to have accelerated during his illness.
Ramanujan contracted TB within 2-3 years after his arrival in London/Cambridge in 1914. As a matter of fact TB was raging in the urban population of western Europe due to indiscriminate industrialization without proper ventilation in damp climate, no protective gears, and no understanding of TB. Anyway, mathematics including Mock Theta functions that Ramanujan produced in the last 2-3 years of his life remained beyond the understanding of the world class mathematicians for the next 50 years! For Ramanujan, mathematics was meditation and meditation was mathematics! He did not die, but rather, he flamed out mathematically.
1. Ramanujan’s full name is Srinivas Ramanujan Iyenger. The longer a person is remembered after their death, the shorter gets their name – like Confucius, Buddha, Alexander, Gandhi. Hindu nomenclature is based upon horoscopes. Iyenger is a Tamilian Brahmin caste. His parents must have chosen the name in consultation with their family priest. Srinivas(a) = Sri (God) + Nivas (lives, dwells) means the one who dwells in God. Ramanujan = Ram (God) + Anuj(an) (younger or dear) means one close or dear to God. Ram is not necessarily the hero of the epic of Ramanyana. This, Ramanujan lived up to his name! I try to live up to my name, Satish (means God of Truth or Gandhi’s Truth is God! It is very challenging.
2. In order to demonstrate a contrast between math and sciences, I said that in science and technology, the principle, Necessity is the Mother of Invention works – like, finding a vaccine for the pandemic due to the Covid-19 virus. However, in pure mathematics, some results are proved way ahead of their applications, if any. Ramanujan’s Mock Theta functions are such examples.
3. I explicitly posed the following questions: Can we duplicate Ramanujan? My answer is NO.
Can we identify, nurture, encourage someone to approximate Ramanujan ? Yes, to some extent.
Here is my way of doing it. At the end of the address, I announced a donation of Rs one lac (100,000) as the seed money for recognizing the top student in the traditional MSc (Math) program – starting from the previous five years, 2016 -2020. The award of Rs 5000 will be given in the name of my late friend, Manohar Lal Gogna, a self-made person, solid math professor and teacher, who had a big heart for his students, friends and relatives.
4. Finally, Before getting into the substance of my address, I told the audience that in order to make this address memorable for all of us, please email me or put in the chat your questions or comments after the talk. The top three questions will be awarded Rs 500 to 1,000 with a citation. No one submitted any question! That speaks a lot!
Guest author Satish C. Bhatnagar is a mathematics professor at UNLV that he joined in 1974. He is the author of ten non-fiction books in six different genres.
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