5 ms·

aahhh just another one of Ramanujan's random identities that he divined from the minds of the gods. reading these has been a reliable way for mathematicians to

aahhh just another one of Ramanujan's random identities that he divined from the minds of the gods. reading these has been a reliable way for mathematicians to humble themselves since 1900. he often wouldn't (or wasn't able to) prove them. they were just assertions that, much more often than not, turned out to be accurate.

Crazyontap 6y ago
I don't understand what you mean. He couldn't have just come up with that huge equation on the page out of thin air? Surely there would be a method for coming up with such assertions (maybe only known to him though)
- shmerl 6y ago
  According to him it wasn't a method, but an insight. So if you like to phrase it that way, you could say it he came up with it "out of thin air".
- dharma1 6y ago
  "Ramanujan said that, throughout his life, he repeatedly dreamed of a Hindu goddess known as Namagiri. She presented him with complex mathematical formulas over and over, which he could then test and verify upon waking. Once such example was the infinite series for Pi: Describing one of his many insightful math dreams, Ramanujan said: "While asleep I had an unusual experience. There was a red screen formed by flowing blood as it were. I was observing it. Suddenly a hand began to write on the screen. I became all attention. That hand wrote a number of results in elliptic integrals. They stuck to my mind. As soon as I woke up, I committed them to writing...""
  - emmanueloga_ 6y ago
    Reminds me of TempleOS, "created by American programmer Terry A. Davis, who developed it alone over the course of a decade after a series of prophetic episodes that he later described as a revelation from God."
  - laichzeit0 6y ago
    I think this kind of explanation irritates many people for some reason. As if things just can't be that way, there must be a repeatable, reproducible recipe that someone else could follow, and if they did, they would get the same results as Ramanujan. I think maybe because it flies in the face of everyone that claims 10x developers are not possible. Or that some people are just genetically gifted and there's nothing you could possibly do that would get you within a hundred yards of them no matter how much hard work you put in, or how good your teachers were, etc. (thinking about John von Neumann here). It's sort of depressing to think that there's almost a different species of man amongst us. It's undeniable though.
    - PartiallyTyped 6y ago
      There have been quite a few such people in history. It's really humbling to know that Galois did what he did at just 20, Gödel was just a year older than me when he broke PM, Neumann could solve problems faster than what it took a person to write a program on the computer to solve the problem and the computer running. While genetics play a huge role, nurture plays a large role as well [1]. [1] https://www.psychologytoday.com/us/articles/200507/the-grandmaster-experiment https://www.psychologytoday.com/us/articles/200507/the-grand...
    - maaaaattttt 6y ago
      I for one find the fact that such people existed very exciting. It means that some possible configuration of our physiology allows for amazing capabilities. Maybe nurturing has to do with it too, but the point is that it is possible. Maybe one day (in a distant future most likely) the general population will have access to such mental prowess. This would then be another kind of singularity!
    - psychoslave 6y ago
      > I think this kind of explanation irritates many people for some reason. As if things just can't be that way, there must be a repeatable, reproducible recipe that someone else could follow, and if they did, they would get the same results as Ramanujan. Oh, there is an easy recipe : just emulate the universe as it was back then and observe Ramanujan. As we know, having a recipe doesn’t mean we have the resources to implement it. There are several movies on Ramanujan as well as biographic books. Apart from the tragic path of is life, these material also depict him not only as gifted but as a compulsively working his maths. So that’s no wonder he would even dream about it. And of course, you can model that as the result of unconscious thoughts throwing the result of problems that were fed to the mind during awaken time. So, the magic recipe is practice, practice, and practice even more. > I think maybe because it flies in the face of everyone that claims 10x developers are not possible. On what metrics? The ability to be able to throw impressive "magical" code and being able to work efficiently with the rest of a team will not necessarily come together, for example. > Or that some people are just genetically gifted and there's nothing you could possibly do that would get you within a hundred yards of them no matter how much hard work you put in, or how good your teachers were, etc. “Be yourself; everyone else is already taken.” is generally attributed to Oscar Wilde. Every life is genetically gifted, but not all lives encounter the environment that enables to thrives this gift – unfortunately. Also no one is perfect. Many aspect of human life are not only dependent on how performant you are individually, so being really "too ahead" can be actually a severe handicap – at least if it doesn’t come with equal excellence into convincing other to trust you. And so depression is not something you can expect to be out of the realm of gifted evoked here.
  - texteller 6y ago
    Recently visited the "Ramanujan Museum" in India which showcases his original works: * Where we could see his family goddess - Sri Namakkal Namagiri Thayaar who he credited for his works: http://casualwalker.com/wp-content/uploads/2019/08/Ramanujan_Museum_Srinivasa_Ramanujan_00023.jpg http://casualwalker.com/wp-content/uploads/2019/08/Ramanujan... * His desk where he made his early mathematical findings: http://casualwalker.com/wp-content/uploads/2019/08/Ramanujan_Museum_Srinivasa_Ramanujan_00273.jpg http://casualwalker.com/wp-content/uploads/2019/08/Ramanujan... * Check the full photo coverage about Ramanujan and his fascinating works at: http://casualwalker.com/museum-for-the-man-who-knew-infinity-ramanujan-museum-royapuram-chennai-travel-guide http://casualwalker.com/museum-for-the-man-who-knew-infinity...
  - inglor_cz 6y ago
    Another famous mathematician, Paul Erdős, took Ritalin and Benzedrine and when he stopped for a month (to win a bet), he complained like this: "Before, when I looked at a piece of blank paper my mind was filled with ideas. Now all I see is a blank piece of paper."
Blammar 6y ago
I have read (though can't find the source) that Ramanujan had access to a black board, chalk, and just the paper in his notebooks -- no other paper. So he did his derivations and proofs on the blackboard, and just wrote down the result in his notebook and then erased the blackboard. He knew he didn't have room for anything else in his notebooks.
- qart 6y ago
  Not a blackboard, but just a slate. Paper was too expensive for him, so he used it only to write down results. Source: https://www.quantamagazine.org/three-puzzles-inspired-by-ramanujan-20160714/ https://www.quantamagazine.org/three-puzzles-inspired-by-ram...
  - cpach 6y ago
    That’s very fascinating. I guess it still is the case for many people in the world, that paper is too expensive. Whereas for many of us it’s readily available in massive, one might even say infinite, quantities.
- wglb 6y ago
  It is talked about in his biography "The Man who Knew Infinity"
- SamBam 6y ago
  An actual, literal case (instead of a cop-out) of "a truly marvelous proof, which this margin is too narrow to contain."
alquemist 6y ago
How would a mere mortal could possibly divine equations like this? There is a method behind it. The formulas are derived from the study of relatively simple ODEs, in this example f'(x) = x.f(x) + 1 and g'(x) = x.g(x) − 1. The latter was solved 100 years prior by Jacobi. While the solutions are non-trivial, they are fairly compact, accessible to a high schooler. The presentation linked from the blog is pretty good at unveiling the magic. This is to say that, with proper guidance, the kid down the street can too become as cool as Ramanujan. https://math.ucr.edu/home/baez/ramanujan/ramanujan_whittier_web.pdf https://math.ucr.edu/home/baez/ramanujan/ramanujan_whittier_...
- sorokod 6y ago
  Proving statements that are known to be true requires a different skillset from coming up with true statements.
Der_Einzige 6y ago
I am a strong atheist, but I have a hard time calling Ramanujan a liar when he says that god (or a god) give him his knowledge...

Crazyontap 6y ago

I don't understand what you mean. He couldn't have just come up with that huge equation on the page out of thin air? Surely there would be a method for coming up with such assertions (maybe only known to him though)

shmerl 6y ago
According to him it wasn't a method, but an insight. So if you like to phrase it that way, you could say it he came up with it "out of thin air".
dharma1 6y ago
"Ramanujan said that, throughout his life, he repeatedly dreamed of a Hindu goddess known as Namagiri. She presented him with complex mathematical formulas over and over, which he could then test and verify upon waking. Once such example was the infinite series for Pi: Describing one of his many insightful math dreams, Ramanujan said: "While asleep I had an unusual experience. There was a red screen formed by flowing blood as it were. I was observing it. Suddenly a hand began to write on the screen. I became all attention. That hand wrote a number of results in elliptic integrals. They stuck to my mind. As soon as I woke up, I committed them to writing...""
- emmanueloga_ 6y ago
  Reminds me of TempleOS, "created by American programmer Terry A. Davis, who developed it alone over the course of a decade after a series of prophetic episodes that he later described as a revelation from God."
- laichzeit0 6y ago
  I think this kind of explanation irritates many people for some reason. As if things just can't be that way, there must be a repeatable, reproducible recipe that someone else could follow, and if they did, they would get the same results as Ramanujan. I think maybe because it flies in the face of everyone that claims 10x developers are not possible. Or that some people are just genetically gifted and there's nothing you could possibly do that would get you within a hundred yards of them no matter how much hard work you put in, or how good your teachers were, etc. (thinking about John von Neumann here). It's sort of depressing to think that there's almost a different species of man amongst us. It's undeniable though.
  - PartiallyTyped 6y ago
    There have been quite a few such people in history. It's really humbling to know that Galois did what he did at just 20, Gödel was just a year older than me when he broke PM, Neumann could solve problems faster than what it took a person to write a program on the computer to solve the problem and the computer running. While genetics play a huge role, nurture plays a large role as well [1]. [1] https://www.psychologytoday.com/us/articles/200507/the-grandmaster-experiment https://www.psychologytoday.com/us/articles/200507/the-grand...
  - maaaaattttt 6y ago
    I for one find the fact that such people existed very exciting. It means that some possible configuration of our physiology allows for amazing capabilities. Maybe nurturing has to do with it too, but the point is that it is possible. Maybe one day (in a distant future most likely) the general population will have access to such mental prowess. This would then be another kind of singularity!
  - psychoslave 6y ago
    > I think this kind of explanation irritates many people for some reason. As if things just can't be that way, there must be a repeatable, reproducible recipe that someone else could follow, and if they did, they would get the same results as Ramanujan. Oh, there is an easy recipe : just emulate the universe as it was back then and observe Ramanujan. As we know, having a recipe doesn’t mean we have the resources to implement it. There are several movies on Ramanujan as well as biographic books. Apart from the tragic path of is life, these material also depict him not only as gifted but as a compulsively working his maths. So that’s no wonder he would even dream about it. And of course, you can model that as the result of unconscious thoughts throwing the result of problems that were fed to the mind during awaken time. So, the magic recipe is practice, practice, and practice even more. > I think maybe because it flies in the face of everyone that claims 10x developers are not possible. On what metrics? The ability to be able to throw impressive "magical" code and being able to work efficiently with the rest of a team will not necessarily come together, for example. > Or that some people are just genetically gifted and there's nothing you could possibly do that would get you within a hundred yards of them no matter how much hard work you put in, or how good your teachers were, etc. “Be yourself; everyone else is already taken.” is generally attributed to Oscar Wilde. Every life is genetically gifted, but not all lives encounter the environment that enables to thrives this gift – unfortunately. Also no one is perfect. Many aspect of human life are not only dependent on how performant you are individually, so being really "too ahead" can be actually a severe handicap – at least if it doesn’t come with equal excellence into convincing other to trust you. And so depression is not something you can expect to be out of the realm of gifted evoked here.
- texteller 6y ago
  Recently visited the "Ramanujan Museum" in India which showcases his original works: * Where we could see his family goddess - Sri Namakkal Namagiri Thayaar who he credited for his works: http://casualwalker.com/wp-content/uploads/2019/08/Ramanujan_Museum_Srinivasa_Ramanujan_00023.jpg http://casualwalker.com/wp-content/uploads/2019/08/Ramanujan... * His desk where he made his early mathematical findings: http://casualwalker.com/wp-content/uploads/2019/08/Ramanujan_Museum_Srinivasa_Ramanujan_00273.jpg http://casualwalker.com/wp-content/uploads/2019/08/Ramanujan... * Check the full photo coverage about Ramanujan and his fascinating works at: http://casualwalker.com/museum-for-the-man-who-knew-infinity-ramanujan-museum-royapuram-chennai-travel-guide http://casualwalker.com/museum-for-the-man-who-knew-infinity...
- inglor_cz 6y ago
  Another famous mathematician, Paul Erdős, took Ritalin and Benzedrine and when he stopped for a month (to win a bet), he complained like this: "Before, when I looked at a piece of blank paper my mind was filled with ideas. Now all I see is a blank piece of paper."

Blammar 6y ago

I have read (though can't find the source) that Ramanujan had access to a black board, chalk, and just the paper in his notebooks -- no other paper. So he did his derivations and proofs on the blackboard, and just wrote down the result in his notebook and then erased the blackboard. He knew he didn't have room for anything else in his notebooks.

qart 6y ago
Not a blackboard, but just a slate. Paper was too expensive for him, so he used it only to write down results. Source: https://www.quantamagazine.org/three-puzzles-inspired-by-ramanujan-20160714/ https://www.quantamagazine.org/three-puzzles-inspired-by-ram...
- cpach 6y ago
  That’s very fascinating. I guess it still is the case for many people in the world, that paper is too expensive. Whereas for many of us it’s readily available in massive, one might even say infinite, quantities.
wglb 6y ago
It is talked about in his biography "The Man who Knew Infinity"
SamBam 6y ago
An actual, literal case (instead of a cop-out) of "a truly marvelous proof, which this margin is too narrow to contain."

alquemist 6y ago

How would a mere mortal could possibly divine equations like this? There is a method behind it. The formulas are derived from the study of relatively simple ODEs, in this example f'(x) = x.f(x) + 1 and g'(x) = x.g(x) − 1. The latter was solved 100 years prior by Jacobi. While the solutions are non-trivial, they are fairly compact, accessible to a high schooler. The presentation linked from the blog is pretty good at unveiling the magic. This is to say that, with proper guidance, the kid down the street can too become as cool as Ramanujan. https://math.ucr.edu/home/baez/ramanujan/ramanujan_whittier_web.pdf https://math.ucr.edu/home/baez/ramanujan/ramanujan_whittier_...

sorokod 6y ago
Proving statements that are known to be true requires a different skillset from coming up with true statements.

Der_Einzige 6y ago

I am a strong atheist, but I have a hard time calling Ramanujan a liar when he says that god (or a god) give him his knowledge...