100-year-old deathbed dreams of mathematician proved true

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While on his death bed, the brilliant Indian mathematician Srinivasa Ramanujan cryptically wrote down functions he said came to him in dreams, with a hunch about how they behaved. Now 100 years later, researchers say they’ve proved he was right.


“We’ve solved the problems from his last mysterious letters. For people who work in this area of math, the problem has been open for 90 years,” Emory University mathematician Ken Ono said.

Ramanujan, a self-taught mathematician born in a rural village in South India, spent so much time thinking about math that he flunked out of college in India twice, Ono said.

But he sent mathematicians letters describing his work, and one of the most preeminent ones, English mathematician G. H. Hardy, recognized the Indian boy’s genius and invited him to Cambridge University in England to study. While there, Ramanujan published more than 30 papers and was inducted into the Royal Society.

“For a brief window of time, five years, he lit the world of math on fire,” Ono told LiveScience.

But the cold weather eventually weakened Ramanujan’s health, and when he was dying, he went home to India.

It was on his deathbed in 1920 that he described mysterious functions that mimicked theta functions, or modular forms, in a letter to Hardy. Like trigonometric functions such as sine and cosine, theta functions have a repeating pattern, but the pattern is much more complex and subtle than a simple sine curve. Theta functions are also “super-symmetric,” meaning that if a specific type of mathematical function called a Moebius transformation is applied to the functions, they turn into themselves. Because they are so symmetric these theta functions are useful in many types of mathematics and physics, including string theory.

Written By: LiveScience
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20 COMMENTS

  1. I’ve never understood what motivates the varying oscillations between say an electron and a photon in string theory. I can kind of grasp the very basic idea of string theory but not why we would need the subatomic variations; quarks, leptons, electrons, muons, etc. I picture a universe as a permanent lightning bolt all twisted and gnarled, when I think about it as a string.

    I have to see it, I see nothing in numbers.

  2. In reply to #2 by Consilience:

    Yes, you left out the bit about “Ramanujan, a devout Hindu, thought these patterns were revealed to him by the goddess Namagiri.”

    I think historical thinkers, being typically embedded and habitualised in reactionary societies, tend to be limited in their choice of metaphor for expressing sources of their inspiration.

    Likely modern scientific insights into mind would have allowed for more precise expression, leading these thinkers to quantifiable self-knowledge as well as resulting in a better legacy to future generations.

    But on the other hand, often these thinkers achieve focus (to self-teach for example) as a reaction against their reactive society, a specific focus which ironically would be lost if society was more enlightened as to allow multiple means of fulfilment.

    But yet on the other hand, multiple means of fulfilment allows choice towards ‘ultimate’ fulfilment of potential etc. – motivating an ‘ultimate’ focus.

    Ramanujan probably would have been even more profoundly seminal if he would have had access to modern scientific, particularly mathematically presented, insights into mind to gauge and express himself by.

  3. I’ve never understood what motivates the varying oscillations between say an electron and a
    photon in string theory.

    Although a string can manifest as any particle type under the right circumstances, electron-photon oscillation doesn’t occur; indeed, that violates charge conservation. Pre-ST physics has a more illuminating example: that of an electron and positron annihilating and 2 photons forming. In ST, this is a case of two strings joining at one end of each, then rebounding with changed properties.

    I can kind of grasp the very basic idea of string theory but not why we would need the subatomic variations; quarks, leptons, electrons, muons, etc. I picture a universe as a permanent lightning bolt all twisted and gnarled, when I think about it as a string.

    String theory says not that the universe itself is a single string, but that individual particles are strings. The different particle types emerge from the quantum numbers of how the string is excited; effectively, what note it plays as it vibrates.

    I have to see it, I see nothing in numbers.

    That’s too bad, because the numbers are the only way to even describe what makes one string an electron, never mind to prove that that is so.

  4. Srinivasa Ramanujan! my childhood hero.

    I was born in the same village (Erode) nearly after 100 years since he was born. In my 3th Standard (Year 3 in UK), apparently my maths teacher told my mom I am not up to the standard and that I am performing poorly in arithmetic. My mom told her that, it is not possible as I was born in the same village as Ramanujan.

    After decades, in my early 20s, I won the Ramanujan Scholarship to study at Cambridge. That was one of my proudest days in life. But I did decide to go to Bristol instead and transferred my scholarship funds to Bristol. My mom till date, complains about that. I should have gone to Cambridge apparently, because none of her neighbours know where or what “Bristol” is! :)

  5. Also, of interest, Hinduism being a polytheist religion, has millions of gods & goddesses. One of the reasons why the numbers of gods/goddesses exploded is Kuladeivam (Tamil) or Kuladevata(Sanskrit). It stands for “family deity, that is either a god or a goddess” within Hinduism. This is more prevalent in the South India.

    In case of Ramanujan, it was Namagiri, most probably inherited from his paternal lineage. Most often than not, these gods/goddesses are considered to be re-incarnates of existing gods/goddesses or of elements relating to nature. Even today, more new gods/goddesses get added to the list. People who have the same Kuladeivam seldom get involved. Probably a method to stop intermarriage between distant cousins I suppose.

    I do not know if adds to the conflicts or dilutes the conflicts. Someone once said, the reason Hinduism survived the christian & muslim onslaught is because to them yahweh or allah is just another god/goddess.

    In my case, my dad’s kuladeivam is the re-incarnate of Shiva, the bird, Painted Bush Quail & my mom’s kuladeivam is the goddess of earth. They both have their own temples, traditions, literature, music etc.

    I cannot believe, how could anyone growing up in such a situation can take faith seriously. But they still do. And even crazier is the attempt to convert hinduism to a monotheistic religion. The concept of Ram Janmabhoomi, the land of Rama is abhorrent not to only rationalist/atheists like me, but millions of faithful across the country whose gods/goddesses are trivialized by the worshiper of Rama, a despicable, misogynist character of fiction. And the Hindu Nationalist Party (BJP/RSS) portray Rama as the only true god and others as pagan.

  6. Science and dreams-

    Now Kekulé’s account of his “dreams” is admittedly florid and imprecise; it’s not clear if he slept or was just in a deep reverie (though he later called these “dreams” and surely he ought to know best). But in many other cases, there is no such uncertainty. Agassiz’s dream correctly predicting the structure of a fossil fish, Loewi’s dream of an experiment to prove nerve impulses propagate chemically, Howe’s dream leading to the modern sewing machine, Einstein’s dream of sledding near the speed of light, Ramanujan’s mathematical dreams, Parkinson’s dream of the M9 fire-controller that turned the tide against the Luftwaffe–all these and more show dreams to be just as useful in hard science and technology as they unquestionably are in the arts, humanities, and soft sciences.

  7. Consilience,
    It’s unfortunate that people just don’t understand that the human brain, although flawed, is also very powerful.

    Dreaming sometimes is a good way to solve problems and come up with creative solutions. There have been times when I was dreaming (in a relaxed state) in which I visualized design solutions for a project at work. I simply sketch it out and get to work. Frequently I have visualized projects that would take too long for me to humanly produce in a decent amount of time. I have actually had several animated dreams, painted entire gallery shows, etc. It’s very frustrating that my mind works so quickly and freely, but my body can’t keep up.

    If I can do this, someone who is skilled at mathematics certainly can have dreams solving problems too.

  8. In reply to #5 by Jos Gibbons:

    I’ve never understood what motivates the varying oscillations between say an electron and a
    photon in string theory.

    Although a string can manifest as any particle type under the right circumstances, electron-photon oscillation doesn’t occur; indeed, that violates charge conservation. Pre-ST physics has a more illuminating example: that of an electron and positron annihilating and 2 photons forming. In ST, this is a case of two strings joining at one end of each, then rebounding with changed properties.

    I can kind of grasp the very basic idea of string theory but not why we would need the subatomic variations; quarks, leptons, electrons, muons, etc. I picture a universe as a permanent lightning bolt all twisted and gnarled, when I think about it as a string.

    String theory says not that the universe itself is a single string, but that individual particles are strings. The different particle types emerge from the quantum numbers of how the string is excited; effectively, what note it plays as it vibrates.

    I have to see it, I see nothing in numbers.

    That’s too bad, because the numbers are the only way to even describe what makes one string an electron, never mind to prove that that is so.

    I am totally in the dark, mathematically speaking. I can’t event recall how to do long division. Same with words, I usually have to write most longer words a few times until I recognize the shape. Spell check has saved my life at work.

  9. Me neither. All these ‘theta functions, super symmetric , Moebius transformations” give me a headache but I’m with you on praise for a wonderful achievement – All hail Namagiri!

    In reply to #3 by aquilacane:*

    I’ve never understood what motivates the varying oscillations between say an electron and a photon in string theory. I can kind of grasp the very basic idea of string theory but not why we would need the subatomic variations; quarks, leptons, electrons, muons, etc. I picture a universe as a permanent lightning bolt all twisted and gnarled, when I think about it as a string.

    I have to see it, I see nothing in numbers.

  10. In reply to #12 by QuestioningKat:

    Consilience,
    It’s unfortunate that people just don’t understand that the human brain, although flawed, is also very powerful.

    Dreaming sometimes is a good way to solve problems and come up with creative solutions. There have been times when I was dreaming (in a relaxed state) in which I visualized design solutions for a project at work. I simply sketch it out and get to work. Frequently I have visualized projects that would take too long for me to humanly produce in a decent amount of time. I have actually had several animated dreams, painted entire gallery shows, etc. It’s very frustrating that my mind works so quickly and freely, but my body can’t keep up.

    If I can do this, someone who is skilled at mathematics certainly can have dreams solving problems too.

    I have no memory of my dreams but I day dream like a bastard and solve things that way, sometimes when driving.

  11. In reply to #4 by Vin2:

    I think historical thinkers, being typically embedded and habitualised in reactionary societies, tend to be limited in their choice of metaphor for expressing sources of their inspiration.

    Likely modern scientific insights into mind would have allowed for more precise expression, leading these thinkers to quantifiable self-knowledge as well as resulting in a better legacy to future generations.

    But on the other hand, often these thinkers achieve focus (to self-teach for example) as a reaction against their reactive society, a specific focus which ironically would be lost if society was more enlightened as to allow multiple means of fulfilment.

    But yet on the other hand, multiple means of fulfilment allows choice towards ‘ultimate’ fulfilment of potential etc. – motivating an ‘ultimate’ focus.

    Ramanujan probably would have been even more profoundly seminal if he would have had access to modern scientific, particularly mathematically presented, insights into mind to gauge and express himself by.

    Eh… or maybe the goddess doesn’t actually need to exist to affect him. As a mental construct it could have aided him, in which case it would be accurate to attribute the goddess. It is also accurate to attribute LSD and dreams to many scientific discoveries, such as DNA’s double helix, circuit boards, and how nerves work.

    When Tesla (another fan of Hinduism) hallucinated the electric motor, in a different culture he may have attributed the vision to a supernatural force. He may have used that belief to further his vision, but instead he saw it as an intrinsic gift. The same goes for Alan Turing’s visions. These great leaps forward necessarily skip a few tedious steps. The brain is powerful that way. Just discerning an image or sound is an amazing event, and some people simply see the numbers as we see our environment. How they experience these things is an enigma to the rest of us, but I’m not entirely sure we all see colors the same. Unique minds may make use of unique circumstances, and he may have been without his abilities in the absence of Hinduism. That’s possible.

  12. In reply to #19 by This Is Not A Meme:

    In reply to #4 by Vin2:

    Eh… or maybe the goddess doesn’t actually need to exist to affect him.

    I hope I didn’t say or imply (as your tagging above of ‘Eh..or’ onto my comment implies?) that the goddess exists (I will accept a rebuke if you can point to where I did imply the goddess exists, otherwise please pause and reflect more before you contrive accusation in future).

    As a mental construct it could have aided him, in which case it would be accurate to attribute the goddess. It is also accurate to attribute LSD and dreams to many scientific discoveries, such as DNA’s double helix, circuit boards, and how nerves work.

    i somewhat disagree with how you define accuracy of attribution: mental construct goddesses, LSD and dreams also require other rather critical and painstaking effort as input before they can yield any synthesis otherwise you would have proportionally more discoveries being made by people using LSD. etc., and none or far fewer being made by people who don’t.

    It is like you are saying islamic science is not possible without islam while not only ignoring the relay of the scientific knowledge baton from other civilisation, but also that proportionately fewer people from all walks of life who practice islam make great scientific discoveries compared to infidel scientists.

    Unique minds may make use of unique circumstances, and he may have been without his abilities in the absence of Hinduism. That’s possible.

    I did cover this point (and your preamble which i haven’t quoted above because i don’t accept religion is equivalent to synthesia, or physiological variation that contributes to insight, in the same way the specific usefulness of imaginary number (complex number) is not equivalent to the arbitrary instrumentality of religion.

    In my last comment, I explored reasonable alternatives to conclude how it would on balance likely be better not to be influenced by religion, so showing anything intrinsic in Ramanujan would likely flourish better without religion. Religion stifled Ramanujan abilities like smoking curtailes the performance of an athlete (people don’t need to accept cancer to be great athletes) because secular alternatives being openly eclectic and contingent upon reality outnumber and prolifically outshine any religiously contingent construct.

  13. In reply to #3 by aquilacane:

    I’ve never understood what motivates the varying oscillations between say an electron and a photon in string theory. I can kind of grasp the very basic idea of string theory but not why we would need the subatomic variations; quarks, leptons, electrons, muons, etc. I picture a universe as a permanent lightning bolt all twisted and gnarled, when I think about it as a string.

    I have to see it, I see nothing in numbers.

    Can you picture: Ratios and relative sizes? Distances? Angles? Three teapots?

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