Thursday, January 27, 2022

The Man Who Knew Infinity: Ramanujan, the Genius and his Significance

 

This piece is not meant to be a review of the Hollywood release The Man who Knew Infinity, though I would certainly, in my humble capacity, laud it for its cinematic prowess and sensibilities, and indeed, even recommend one and all to watch it. The screenplay and the performances were interesting and fairly gripping without being too dramatic, and the music was very appealing too. As someone has written on the mathematics blog of Columbia University, the movie is “extremely good, infinitely better than the most recent high profile film about a mathematician”, the reference to that other movie which The Man who Knew Infinity is infinitely better than being Alan Turing: The Enigma. This piece seeks to explore the movie for what it has to offer in terms of the intellectual discourse (without giving many spoilers!), which in itself, may interest some to watch it, and further still, what Ramanujan the man still means to mathematics and even Indian nationalism ands the history of scientific research in India.

I had first heard of the great Indian mathematician Ramanujan as a Class V student when some of my friends and I were chosen to participate in a mathematics competition named after him, which was conducted by my school in Delhi (Modern School Vasant Vihar). While I did have an interest in history even back then, I don’t recall trying to find out more about him.

However, in more recent times, the Hollywood movie The Man who Knew Infinity has etched Ramanujan in my consciousness for posterity for the sheer brilliance of the film, which narrates the story of an unqualified Indian clerk from a humble background who was a young, self-taught mathematician, and who, by the stroke of destiny, made it to the University of Cambridge to rub shoulders with that mathematical genius GH Hardy (who became his mentor), John Littlewood and Bertrand Russell. Ramanujan was, as the movie depicts, in many ways, overawed by that great British university and in some ways, found himself to be a misfit, including in the context of his staunch vegetarianism.

One very interesting facet of the movie on an Indian for an Indian viewer was the fact that the topic itself was quite offbeat in our Indian context (though certainly not by Hollywood standards), as making a film on the life of a true-life mathematician (different from science-fiction movies) is quite interesting, that too of a genius who battled many odds, not the least of them being racism. Bollywood, for one, would do well to take a leaf out of this creativity in selecting topics. We have had well-made biopics of sports personalities like Milkha Singh, Mary Kom and Paan Singh Tomar, and looking at some of our scientific geniuses like CV Raman, Salim Ali, S. Chandrashekhar, Vikram Sarabhai, JC Bose and Homi Bhabha as well may not be a bad idea, and celebrating our scientists can go a long way in helping India achieve its potential in scientific research and promote a scientific temperament, as discussed here. In fact, in this context, I’m glad that one of the producers of the film was Manjul Bhargava, an Indian-American mathematician who  learnt Sanskrit and employed Sanskrit texts by ancient Indian mathematicians*, along with the work of Western mathematicians, to come up with brilliant new findings in the field of mathematics to win the Field Medal, the equivalent of a Nobel Prize in the discipline of mathematics, and Bhargava is an accomplished tabla player too, having learnt to play the tabla from none other than a maestro like Zakir Hussain.

Another aspect of the film that struck me was the interface between science and religion, of the possible divinity in the concept of infinity, and how Ramanujan claimed divine inspiration for his mathematical theorems, which appeals to me as someone who is both a believer in God and a science-lover, as have been many great scientists like Galileo, Newton, Einstein, Faraday, Mendel, Francis Collins, Rosalind Franklin (America’s first female astronomer), Abdus Salam (a practising Ahmedia physicist exiled from Pakistan who won the Nobel Prize) and APJ Abdul Kalam as also many other Indian scientists. This theme of the interface between science and religion was well explored in the Dan Brown novel The Lost Symbol (interestingly giving considerable space to Hinduism and Islam** other than Christianity), which has been among my favourite books.

And yes, last but not the least, the ideological and intellectual challenge to jingoistic nationalism in the context of the First World War when the likes of Hardy and Russell refused to support the British war effort (the First World War wasn’t even about territorial integrity but competition for colonies), was something that struck me, and I’ve suggested what to make of it in our Indian context in some detail here.

Ramanujan the man remains an interesting character in the history of mathematics for his sheer presence of mind. While the most famous incident in this regard is portrayed slightly inaccurately in the movie, I am producing it here quoting from a blog by Jonathan Borwein, Laureate Professor of Mathematics, University of Newcastle-

“There is one famous anecdote about Ramanujan that even a non-mathematician can appreciate. In 1917 Ramanujan was hospitalised in London.”

“Hardy took a cab to visit him. Not being good at small talk all Hardy could think to say was that the number of his cab, 1,729, was uninteresting.

Ramanujan replied that quite to the contrary it was the smallest number expressible as a sum of two cubes in two distinct ways:

1,729 = 123 + 13 = 103 + 93

This is now known as Ramanujan’s taxi-cab number.”

Ramanujan’s presence of mind! He also had a romantic streak about him, not only in terms of his love for his wife, but also in terms of how fascinating his life-journey was.

As Borwein puts it, Ramanujan is “generally viewed by mathematicians as one of the two most romantic figures in our discipline”, the other one being the French mathematician Évariste Galois, who died in a duel with another man over a woman he loved, and the woman was also interestingly a mathematician.

Ramanujan’s work has not only played a pivotal role in the field of pure mathematics, also having its actual applications in technology, but he also helped shape a sense of self-worth in our then colonised nation, even among those who were irreligious and were hence not necessarily as drawn to India’s philosophical achievements in the sphere of spirituality or theology (Ramanujan’s own deep religiosity is irrelevant to this), and Borwen points out that one such person, according to Nobel Laureate S. Chandrashekhar, was none other than Pandit Jawaharlal Nehru (an agnostic and a science-lover to the extent that Australian diplomat Walter Crocker mentions how Nehru once pointed out a factual error made by a Nobel Laurete scientist in an in-person interaction between the two, where Crocker was also present), who, after our independence, along with Maulana Abul Kalam Azad, laid the foundation of the IITs and the Indian Council for Scientific Research, other than many laboratories and India’s nuclear and space programmes. (While both Nehru and Azad had their flaws and made errors of judgment, both have been victims of much false and unjustified criticism, as discussed in some detail here and here.) This is not surprising, for Chandrasekhar had this to narrate about Nehru’s attitude to Ramanujan, and about Ramanujan himself, in the book ‘Ramanujan: Essays and Surveys’-

“During the late forties after the war, Sir Alagappa Chhettiar (as he was then) wrote to me inquiring if I might be useful for him to found a mathematical institute in Madras named after Ramanujan. I enthusiastically supported the idea; and when I returned to India briefly in 1951, the Ramanujan Institute had been founded a few months earlier. Its first director, T. Vijayaraghavan was one of the most talented among Hardy’s former students; he died at a comparatively early age in 1955. C.T. Rajagopal, a student of Ananda Rao, took over the directorship from him. Already at that time the financial status of the institute was shaky, since Alagappa Chettiar’s fortune was melting away.

In April 1957, when Alagappa Chettiar died, the fate of the Institute hung in the balance; Rajagopal wrote to me that the Institute ‘will cease to exist on the first of next month,’ whereupon I wrote to the Prime Minister (Jawaharlal Nehru), explaining the origin of the Institute and the seriousness of its condition. Nehru’s prompt answer was refreshing: ‘Even if you had not put in your strong recommendation in favour of the Ramanujan Institute of Mathematics, I would not have liked anything to happen to which put an end to it. Now that you have also written to me on this subject, I shall keep in touch with this matter and I think I can assure you that the Institute would be carried on.’ And it was…”

“There is very little more I can say. My own view, sixty-six years after my first knowing of his name, is that India and the Indian scientific community were extremely fortunate in having before them the example of Ramanujan. It is hopeless to try to emulate him. But he was there even as the Everest is there.” (emphasis mine)

And with this coming from a Nobel Laureate like S. Chandrasekhar, there’s very little I am left with to say too!

*The genuinely documented achievements of ancient Indian mathematicians and scientists must be promoted and celebrated, but promoting an un-historical history of science that conveniently undermines the scientific creativity of all non-Hindu civilisations (to claim in a baseless fashion that all knowledge was “stolen” from here) and promotes Hindu religious texts as undisputed history, with supposedly much science in them, doesn’t bode well for promoting a scientific temperament. Going by the Jewish texts, even Solomon had a flying vehicle (there are similar references in ancient Egyptian and Greek lore too), and many science-fiction stories by writers like Joules Verne have mentioned things really invented later, but that does not mean those stories were true when they were written, nor does referring to real places like Delhi or Mumbai or Hastinapur or Kurukshetra in a story make that story true, and as Karan Thapar, whether you love him or hate him, logically points out – “how do you account for the fact the scientific knowledge and achievements you are boasting of have been lost, if not also long forgotten, and there is no trace of any records to substantiate they ever occurred?”. Rather than spreading awareness about the documented scientific achievements of our civilisation, by boasting of scientific achievements from religious lore, we would only largely make a laughing stock of ourselves! There are indeed such counterparts among Muslim rightists, including the celebrity-preacher Zakir Naik, too, talking of religious lore being scientific (not a very good idea), as discussed in this article.

**Terrorism, and even terrorism citing a theological basis, is not a Muslim monopoly. As you can see here, very many instances of terrorism globally, even in the name of religion, have been carried out by those identifying themselves as Christians, Jews, Sikhs, Hindus and even Buddhists, the victims of the acts of terrorists from each of these religious groupings not always being Muslims. However, just like most people of these religious groupings are not terrorists or supporters of terrorism, and they do not believe that their religion preaches terrorism, the same is the case with most Muslims (and not supporting terrorism applies to even most of those Muslims with other regressive and not-so-liberal attitudes on issues like gender and homosexuality).

It is possible to quote any scripture (allegedly out of context according to its liberal adherents) to justify malpractices, like some verses in the Bible namely Deuteronomy 13:12-15, Samuel 15:3, Leviticus 24:16 and Matthew 10:34 seemingly advocate violence against “non-believers” and the Purusha Sukta of the Rigved, an ancient Hindu scripture, is taken by some to justify caste discrimination, but these verses do not define the entire religion. This article mentioning an anecdote from the British parliament does make an interesting read in this regard, as does this video make an interesting watch in this connection. There are Quranic verses like 2:2565:25:85:326:1086:15110:9949:1360:8 and 109:6 preaching peace, religious tolerance and human brotherhood, as does the letter from Prophet Muhammad to the Christian monks of St Catherine’s monastery and there are episodes from Prophet Muhammad’s life, as per Islamic lore, indicative of such an approach too, such as his allowing a woman to throw garbage at him daily and his succeeding in ideologically, winning over her by way of humanitarian affection. Those suggesting that peaceful verses in the Quran are superseded by violent verses (which the vast majority of practising Muslims globally regard as contextual) would do well to note that verse 109:6 appears towards the end of the book, and preaches nothing but peace, and the Quran and Hadiths devote considerable space to talking about honesty (there’s an anecdote of Prophet Muhammad punishing a Muslim for stealing from a Jewish gentleman’s house), kindness, forgiveness, humility and striving for socioeconomic egalitarianism.

Very many mainstream Muslims do indeed believe that Islam is the only religion that can lead to God since the advent of Prophet Muhammad, as mainstream Christians believe the same for Christianity since the advent of Jesus, but that doesn’t entail intolerance towards those of other faiths. To explain this with an analogy, if a certain coaching centre (analogous to Islam or Christianity, going by the mainstream interpretation) claims it is the only one that can get students admitted into say, IIT (analogous to heaven), and even encourages its students to get students of other coaching centres and those not taking any coaching to join that particular coaching centre, it cannot be equated with forcing others to join their institute or killing those not willing to do so. In fact, both the Bible and the Quran preach the message of peaceful coexistence with other religious groups (the relevant verses in the context of the Quran have already been cited, and  Rom. 12:18 and 1 Tim 2:2  may be cited in the context of the Bible).

Speaking of apostates of Islam (“ex-Muslims”) criticising their former religion, there is a fairly well-known website run by an apostate and basher of Islam who has even offered a cash prize to anyone who can disprove his allegations against Prophet Muhammad (but there are books by apostates of other religions criticizing their former religions too, the most famous one being ‘Why I Am Not a Christian’ by Bertrand Russell, and there’s also ‘Why I am Not a Hindu’ by Kancha Ilaiah, levelling very strong allegations), but practically, he is the judge of the debate, or to go by what he is saying, the “readership” of the website, a rather non-defined entity. In fact, he has acknowledged that he came across a Muslim who “intelligently argued his case and never descended to logical fallacies or insults” and while that Islam-basher “did not manage to convince him to leave Islam”, that Muslim earned his “utmost respect”, which implies that practically, the Islam-basher is the judge of the debate. Likewise, that Islam-basher has mentioned with reference to a scholar of Islam he debated with, that the latter was “a learned man, a moderate Muslim and a good human being” and someone he (the Islam-basher) has “utmost respect for”. So, that Islam-basher’s critique of Islam, whether valid or invalid, has no relevance in terms of making blanket stereotypes about the people we know as Muslims or even practising Muslims. By the way, that Islam-basher bashes Judaism too. And it is worth mentioning that I have encountered several practising Muslims on discussion groups on the social media, who have, in a very calm and composed fashion, logically refuted the allegations against Islam on such websites. Indeed, as you can see here and here, there are several other apostates of Islam who have stated that while they personally left Islam thinking that the extremist interpretations are correct and moderate ones wrong (as is the case with apostates of many other religions), they have equally explicitly emphasized that that does not in the least mean that they believe that most people identifying themselves as practising Muslims support violence against innocent people.

And in fact, even speaking of the West, a report submitted by Europol, the criminal intelligence agency of the European Union, showed that only 3 out of the 249 terrorist attacks (amounting to about 1.2%) carried out in Europe in 2010 were carried out by Muslims. Even in the United States, most terrorist attacks from 1980 to 2005 were not carried out by Muslims. And no, I am not in the least seeking to undermine the heinousness of the crimes committed by some in the name of Islam by pointing to others having committed similar crimes under other ideological banners, for a more highlighted wrongdoing is no less of a wrongdoing than a less highlighted wrongdoing, but only to point out that viewing only Muslims as villains, and that too, all or even most of them, would indeed be grossly incorrect. However, despite jihadist terrorists being a microscopic minority of Muslims, Islamist terrorism has become a bigger global threat for its well-coordinated international network since the 1990s, with the US-backed Islamist resistance to the Soviet invasion of Afghanistan having signalled its rise. And, let us not forget that when we had the Charlie Hebdo attacks in Paris, the victims included Ahmed Merabet, a Muslim police officer who died fighting the terrorists (and by the way, there are more French Muslims in the local police, including those who have died fighting jihadist terrorists, than in the Al Qaeda unit in their country), Mustapha Ourad, a Muslim who was one of the magazine staff members killed in that attack and there was Lassana Bathily, a Muslim shopkeeper who gave sanctuary to many innocent civilians during the hostage crisis in Paris that followed. Even in the context of the more recent attacks in Paris, a Muslim security guard Zouheir, risking his own life, prevented one suicide bomber from entering a packed football stadium. More recently, Kenyan Muslims very laudably protected fellow bus commuters, who were Christians, from jihadist terrorists, and Kurdish, Emirati, Iraqi and Syrian Muslims have also been fighting the ISIS.  In India too, most of the terrorism is not by Muslims, as you can see here and here.

It is not as though communalists under any banner, except arguably those actually resorting to killing innocent civilians, should be dehumanized or can never be logically made to modify their views, as the must-watch movie Road to Sangam, based on a true story, demonstrates, and to draw an analogy, you can see this video of a Muslim who initially wanted to become a terrorist wanting to blow up Jewish civilians but changed his standpoint about Israel for the better after visiting that country. It is also not as though Muslims are another species  that can’t be rationally engaged with, the way some extreme anti-Muslim rightists almost make them out to be, portraying Muslims in general as cruel, slimy, backstabbing and aggressive (many Muslims whom the non-Muslim readers would know personally would not exhibit such traits if the non-Muslim readers were to analyze dispassionately, rather than making baseless presumptions, and indeed, most Indian Muslims are of Hindu ancestry and so, they share the same genes as the Hindus – Hindu religious lore also refers to treacherous human beings like the Kauravas wanting to burn the Pandavas in a wax palace; so, treachery was not unknown to India before the advent of Islam, as royal family feuds among the Nanda and Gupta rulers also demonstrate, and some of the worst atrocities in history have been committed by the likes of Hitler and Stalin, who were not Muslims, nor was Chengiz Khan who was an animist), but like many people in other communities in different contexts, some (not all) Muslims are in the stranglehold of anachronistic ideas like a global pan-Muslim fraternity and the upholding of Islamic law, other than having prejudiced notions in the form of an exaggerated sense of victimhood, and I have dealt with how to ideologically combat Muslim extremism in some depth in this article.

Sacrificing animals as a religious ritual is indeed not exclusive to Muslims, and ‘bali’ has existed among Hindus too, something Gautam Buddha (who lived centuries before Jesus and Muhammad) had opposed (and even Emperor Ashok the Great consumed meat of peacocks, which he stopped after embracing Buddhism, though interestingly, Buddhists in China, Japan, Bhutan, Vietnam etc. do consume meat, as do most Sikhs, Christians, Jews and Parsis, and what is halal for Muslims in terms of dietary regulations and the mode of slaughtering some animals is identical to what is kosher for Jews and several sects of Christians, and that is true for the practice of circumcision for males as well, which even has health benefits), and still continues in many Hindu temples across India, especially in West Bengal during the Navratri season. Also, it may interest some to know that the story of Prophet Abraham associated with Id-ul-Zuha is found in the Old Testament of the Bible too, which the Jews and Christians also believe in (those regarded as prophets by the Jews are regarded as prophets by the Christians too, with the addition of Jesus, and those regarded as prophets by the Christians are regarded as prophets by the Muslims as well, with the addition of Muhammad). And obviously, not all of Arab cuisine is non-vegetarian either, with Arab vegetarian dishes like strained yogurt using labneh cheese and sweet dishes like zlabia, popular in South Asia as jalebi!

There are also misplaced notions of Muslims potentially outnumbering Hindus in India, though the Muslim population growth rate is declining (not the population itself, which cannot decline usually for any community), and the population growth rate of Keralite Muslims is less than UPite Hindus, for instance, and yes, even otherwise, if someone sees Muslims potentially outnumbering Hindus in India as a real problem, they should appeal to the Indian government to legally impose a two-child norm for all Indian citizens, irrespective of religion, rather than just generate unnecessary hatred for an entire community and divide the nation. Many Hindus criticize Muslims for having many children because they practise polygamy as permitted by their faith (though census reports have established that Hindus are more polygamous than Muslims, even though it is illegal for the former, and I myself know a Hindu electrician in Delhi who has engaged in bigamy), even though that actually doesn’t make a difference to the number of children as long as the number of reproductive women remains the same. Four women would respectively give birth to the number of children they would, irrespective of whether they are married to one man or four different men! In fact, polygamy is not prohibited by Hinduism as a faith (and, in fact, it was outlawed for Hindus only after independence, and Nehru faced stern opposition for the same from orthodox Hindus). The Puranic lore is full of multiple marriages by a single man – to quote some prominent examples, Krishna had thousands of wives, prominent among whom were Rukmini, Satyabhama and Jambvati; his father Vasudev had two wives, Devki (Krishna‘s mother) and Rohini (Balram‘s mother) and Ram‘s father Dashrath had three wives, besides even Bheem having a wife other than Draupadi (Gatodkach‘s mother) and Arjun too had several, including Krishna‘s sister Subhadra. In fact, the law mandating monogamy for Hindus was introduced only after independence! Also, Islam mandates a limit of four wives and a responsibility of the husband to look after his multiple wives (if he has multiple wives in the first place) equally well, though I do agree that even this is anachronistic today. As for harems, these too have not been a monopoly of Muslim rulers, and the practice has existed among Hindu rulers too, such as in South India, and even among Buddhist rulers in Sri Lanka. And there are indeed many Hindus too, particularly in rural areas and in several cases, even among the urban educated class, who have several children even if they are monogamous. Many educated Hindus who have been public figures, like former president V.V. Giri, former prime minister Narasimha Rao and our very own Lalu Prasad Yadav have all had many children, and even Narendra Modi is the third of his parents‘ six children.

Also, there are some who accuse Muslims of being the only community that carries out inter-cousin marriages, but that is true for Parsis as well and Hindu lore mentions Abhimanyu marrying his maternal uncle Balram‘s daughter (though this is a South Indian folk adaptation not to be found in the Puranic lore, it shows that the idea hasn‘t always been abhorrent in Hindu societies) and Rajasthani folklore has it that Prithviraj Chauhan too eloped with his cousin and while even this is contested by historians, he has never been looked down upon for the same, and even today, this practice exists in South Indian Hindu societies.

An allegation often leveled against Islam and Muslim societies is sexism. It should be noted that Prophet Muhammad’s wife Khadijah was a successful businesswoman, and the world’s oldest existing university, which is in Morocco and dates back to 859 AD, was set up by Fatima al Fihri, a well-educated Muslim woman. Prophet Muhammad is even believed to have mandated education for all, irrespective of gender, as you can see here and here, and in fact, the education cutting across gender lines even includes physical education. Interestingly, Prophet Muhammad himself is believed to have said that children (he did not specify only boys) must be taught archery, horse-riding and swimming. In fact, a woman, Nusaybah bint Ka’ab, fought in his army, just as Hindu lore refers to Arjun’s wife Chitrangada as an ace fighter and how Kaikeyi and Madri were ace charioteers. This article discusses in some detail the freedoms accorded to women by Islam and early Muslim societies, and how they partook in war, diplomacy, business and several other fields of life, and how the veil came in later as a norm in Muslim history.  Currently, many Kurdish Muslim women are bravely fighting the ISIS, and there was news of an Iraqi Kurdish woman, Rehana, killing over a hundred ISIS terrorists. Major Mariam Al Mansouri, a female fighter pilot from the UAE, has also been involved in anti-ISIS operations. While one would not assert that Islam or any other major global religion (and in this, we include the oriental faiths as much as the Abrahamic religions) is completely free from patriarchy (with all due respect to everyone’s religious sentiments), this mindset of prohibiting girls’ education represents a deeply patriarchal mindset among these ultra-conservative terrorists hailing from tribal Pashtun communities in Pakistan and Afghanistan, but has no basis in Islamic theology, and very many people across the globe who have identified themselves as Muslims have educated their daughters.

No Muslim-majority country (but for parts of them ruled by militias like the Taliban and ISIS), not even Saudi Arabia, has legally imposed wearing burqas (though only Iran has imposed headscarves; however, as regards wearing burqas, it must be noted that the Quran does not ordain it, nor do quotations attributed to Prophet Muhammad of undisputed authenticity), or prohibited women from driving (though only Saudi Arabia, other than militia-ruled regions, has imposed a ban on women driving, but a Saudi cleric also declared that there was nothing in the Islamic texts that prohibits women from driving. In Dubai in the United Arab Emirates, another Islamic state which largely follows the same Wahabi sect of Islam as Saudi Arabia, there are women-run family taxis, and Laleh Seddigh, an Iranian Muslim woman, is among the best car-racers globally, competing with men.

 

 

Originally published on Khurpi. 

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