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Ramanujan's Deathbed Conjecture Finally Proven
jomama717 writes "Another chapter in the fascinating life of Srinivasa Ramanujan appears to be complete: '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.'"
I can't wait to see what the elite-math-folks around here post below here.
2 + 2 = 5, for very large values of 2
It must have been something you assimilated. . . .
Just imagine the contributions he might have made if he had lived. Such a shame.
It's just a hunch, but I have a feeling, unlike say technology, that mathematics is one of those fields where discoveries aren't always inevitable. Either someone thinks up of some things or they don't.
I wonder what would happen if US colleges (or even earlier in our educational system) let students have free reign, and really specialize. If over in India this man had been nurtured in college, and allowed to stay in math courses (or even better conduct his own lines of study), might he have had a more enjoyable or productive life? If we recognize genius and cultivate it, what might grow in that garden?
Or gently shaking his head in confirmation.
Ono's team did not prove the Ramanujan Conjecture. It was proven a long time ago, in 1974 by Deligne as part of his proof of the Weil conjectures
Yes as if you have been to Indian colleges. I really hate people just shooting from their behind.
I studied at IIT Delhi and Columbia. At Columbia easy to score an A in every subject and at IIT I got one A barely.
Trying getting into an undergraduate course in IIT, you will know the worth of good Indian colleges. Sometime, Google the number of IITians and IIM graduates in high position in USA, it will open you mind.
The summary suggests that Ramanujan wrote down some results that were conjectures until now. He wrote down many results, few if any on his deathbed, and most of them have already been verified for years, though some were still open until recently. Apparently the actual article is about the closing of the last few ones only.
"What lies behind us, and what lies before us are tiny matters compared to what lies within us." Ralph Waldo Emerson
Hi AC,
I know about four sentences of a whole lot of stuff. It's like it's a party game, you can drop a key word or two, but the min any actual specialist asks you a question, you're hosed.
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I'm lost, he apparently wrote a bunch of stuff on his deathbed and sent it all to Mr. Hardy.
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I suspect that you're quite wrong. The man was a mathematical prodigy. I don't think it was a matter of choice at all, but rather some sort of unique wiring
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I suspect that you're quite wrong.
I might be wrong.
But, what if I am right?
The man was a mathematical prodigy.
Mathematical prodigy or any other type of prodigy means nothing, so far as the brain goes.
The grey matter in between your ears contains similar amount of chemicals as the ones inside the head of those so-called "prodigies".
I don't think it was a matter of choice at all, but rather some sort of unique wiring
Unless it is proven that that deceased Indian math genius suffered from some acute type of "savant syndrome", I seriously doubt his brain has any "unique wiring" of any kind.
My view is that it's more of a "will" - the will to think, to explore, to use as much brain capacity as the brain can provide, without any negative effect.
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Whenever I read submissions like this, I wonder why they put a sentence like "genius in flunked out of ...". Unless the area they were a genius in was the same one he/she failed at, it seems kind of flame-bait - trying to start an "school is useless - look at these outliers" discussion.
Ramanujan was brilliant at mathematics, and there is no denying that. But like any school/college, his was made for the average person. Sure, it would be great if education was tailored to each individual's aptitude. But we don't have a good way of finding out what that is directly yet. Instead, we throw a bunch of subjects at students, and they figure out where there relative strengths are. And they focus on one or two areas where their natural aptitude lies (or more realistically, where their job prospects and abilities/interests combine to give "best" results; best being chosen by the student. Some may chase money, others fame, others just want to solve interesting problems - applications/paycheck be damned).
And discovering outliers early is hard when the teachers themselves are not much better at their subjects than the students. If some kindergarten student started using calculus for loading of building blocks, it won't be much use if her teacher doesn't realize that what she is doing is phenomenal (especially since the child will have her own notations/symbols). Obviously, that is an extreme example, but the point remains - outliers will have a tough time in the current system.
Alternatively, we can let everyone do what they find interesting, but a majority of students will just spend time doing "fun" things like sports - which is not necessarily bad. But as long as we have the current system where you starve if you can't hold down a job doing "productive things", I think the educational system prepares most people for such a world.
Outliers are great - and can help speed up society's progress significantly. But at the end of the day, they are just that - outliers. If you design a system to help the outliers, most people (myself included) would wind up getting a very bad outcome - because most people aren't phenomenally skilled at anything (and no, being the best me I can be doesn't cut it). And if you have a lot of starving deadbeats on the street (instead of the mediocre, but holding down a job majority) I expect society to completely break down - and that won't help the outliers either.
Unless you're a doctor or a lawyer, your Indian degree is less than worthless.
Hmm... nice choice there - especially since doctors and lawyers can't generally practice in other countries based on their Indian degrees. On the other hand, a lot of Indian engineers (or engineers from most countries) can take up jobs wherever they get the opportunity. Bitter much?
There's no way to know because he's dead, but there's certainly a body of evidence suggesting neurological differences between genius level mathemetic prodigies to suggest that a poor young man from an Indian village who literally taught himself 100 years worth of mathematics was in possession of cognitive abilities beyond the average person's.
The amount of grey matter is an obscenely crude way to measure intelligence. What I find interesting is your need to make the man average and ordinary. Does the possibility that some have greater cognitive capacity than others bother you?
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Not really buying it.
If you got a kiddo with a 150+ IQ, your lectures on Gilgamesh will be wasted. End Of Story.
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Chimp grey matter contains similar amount of chemicals as the ones inside the head of those so-called prodigies. Chimp DNA is pretty similar to human DNA too. A chimp is not going to equal Ramanujan in math despite how much willpower it has. They just don't have the ability.
So your argument is just as silly as those "you can do anything if you just try hard enough" bullshit cliches.
If you think it's so simple, go ask the top athletes/musicians why they aren't all number one despite most of them spending much of their life training, practicing etc. You think it's because they lack willpower to push themselves to their limits? They're not trying hard enough?
I may not know my exact max limits, but I know that no matter how much I try I am never going to run as fast as Usain Bolt, and I'm never going to be as good at math as Ramanujan. Thinking otherwise is foolishness or hubris even.
I'm all for people trying to improve themselves and others, but I'm against spreading bullshit. The world would be a better place if more humans fully realized and admitted how crap they were, but still persisted in helping and bettering others despite their limitations.
The grey matter in between your ears contains similar amount of chemicals as the ones inside the head of those so-called "prodigies".
So if I put your brain in a blender, it should work the same afterwards right? Silly argument.
Unless it is proven that that deceased Indian math genius suffered from some acute type of "savant syndrome", I seriously doubt his brain has any "unique wiring" of any kind.
Perhaps not unique in that you'd see a difference on a brain scanner at the macro level, but I think it's more about being wired right or wrong. Look at people playing chess, the poor players aren't making any less of an effort but they're just overlooking moves or forgetting what paths they have and haven't explored or miscalculating because they don't see the piece is pinned. Your average player has an early botched Pentium and flaky non-ECC RAM, the grandmasters an Xeon with RAS features and ECC RAM. They very rarely think wrong or remember wrong, of course there's also training but I think it's also a lot what you're given from nature's side. It doesn't help if the same number of neurons are firing if in one brain it only leads to noise and nonsense and in the other to answers and solutions.
Live today, because you never know what tomorrow brings
He said exactly the opposite. He said: the wiring is important. O_o
The only difference between Srinivasa Ramanujan and 99.99999% of the human race is that he opted to use his brain power as much as it could be sustained.
If only you were lucky enough to have a brain half as good as his, you'd realise that your hypothesis was a load of utter bollocks.
There's no way to know because he's dead, but there's certainly a body of evidence suggesting neurological differences between genius level mathemetic prodigies to suggest that a poor young man from an Indian village who literally taught himself 100 years worth of mathematics was in possession of cognitive abilities beyond the average person's.
The amount of grey matter is an obscenely crude way to measure intelligence. What I find interesting is your need to make the man average and ordinary. Does the possibility that some have greater cognitive capacity than others bother you?
Or maybe he was just more motivated than average. How many people would want to spend all their best moments in life on math?
"The grey matter in between your ears contains similar amount of chemicals as the ones inside the head of those so-called "prodigies"." Interestingly, the grey matter between our ears contains largely the same chemicals as the matter between the ears of most vertebrates, and in smaller amounts than some other mammals. As far as reductionism goes, I think you've taken it to a pretty absurd level.
"Be nice, veer left, and never stop thinking" Iain Banks - Walking On Glass
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If only the rest of 99.99999% of the human population can do the same - becoming a galaxy-roaming race wouldn't stay merely a dream for long.
Ah, the old "omniscience == omnipotence" fallacy again.
You seem very sure about outcome of it. I'd say: "If only the rest of 99.99999% of the human population can do the same - possibility of becoming a galaxy-roaming race wouldn't stay merely a guess for long."
He said exactly the opposite. He said: the wiring is important. O_o
No, just reading comprehension fail on your end. The post I replied to by Taco Cowboy clearly argued it wasn't and that it is only a "will" to use your full mind.
Live today, because you never know what tomorrow brings
Why do people want to make this into a debate on his mental state? I think he took a phenomenal ability and used it to the fullest extent that his personal circumstances allowed. He certainly didn't wallow in an aspie tank, moaning about how brilliant he was and wasting his too short life on comic book trivia.
I don't think he has any comprehension problems.
You come off as the sort of asshole who thinks, "I could be Batman... but I just can't be bothered with pushups."
Disagree entirely. A little cross-training is generally good for the brain as a whole - look at the classic Feynman story where he decided to do a biology class to expand his horizons (he went to the library and asked for a "map of a cat").
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There are absolutely kids who do this, even today. Most of them will never come near the level Ramanujan was operating on.
Whenever I read submissions like this, I wonder why they put a sentence like "genius in flunked out of ...".
Let's look at the sentence in question: "spent so much time thinking about math that he flunked out of college in India twice" -- and you went off on a many-paragraph rant, when the only things that the sentence showed were that he was more interested in mathematics (some might rather say obsessed with) than the baseline, and perhaps that the school system was not set up to handle him. It does not contain an indictment of the school system, and only you thought it did, then went off on a massive rant about it. While your rant is not incorrect, and I see no problem with your conclusions, your introduction to the subject came straight from left field.
"You're right," Fisheye says. "I should have set it on 'whip' or 'chop.'"
Ramanujan is pretty near the top of my list of most admirable humans. His widely encompassing spirituality, the incredible way he developed his own native ability, and his focused obsession which hindered his college learning, are all themes that resonate strongly with me. The story of his life is at once a triumph of the individual human spirit and a tragedy of the life of one of the very finest of us being cut short.
Well, maybe it's luck. Much of it could be.
We all have strategies we approach problems with, in maths and puzzles as in life. Some strategies are better fits for certain sorts of problems than others. To some degree you can change your mental strategies, but once you're set in them, it becomes an expensive proposition. Like assumptions, methods are hard to change once you've built a lot of genuinely useful stuff on them. Maybe we have different aptitude for certain strategies, but it may also be affected by e.g. which strategies we happened to adopt when we learned our first words.
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But there's value to a well rounded education. In part because it lets you work with others and function in society better. While some great works are done almost solely by an individual (like the Principia) most are done via collaboration.
Also it allows you to see things more cross-domain. Knowledge of things in more than just one area can let you see connections that you might otherwise miss, and to see applications for things that otherwise might just seem to exist in a vacuum.
Hyper-focused education is not necessarily a good idea. Particularly since, as you note, people may not make the best choices as to what to focus on.
OK, so what have you accomplished lately that utilized your brain to its full, Ramanujan-like potential?
He just lacked the will to fully comprehend the thread and your post ;).
Hi Elucido, answering your stupid question : "How many people would want to spend all their best moments in life on math?" You can safely asume that statistically, many people (especially, in India, MANY, would want to spend ther ..... on math, but not that MANY are geniuses, Please refrain yourself from posting this STUPID questions, where do you want to arrive ?
But, what if I am right?
If you're right, then should I flog myself in a closet for hours every day for having such poor character that I can't unlock this potential I'm supposed to have?
I mean, come on. I'm pretty damned smart. IQ somewhere in the 160 range, but I know damned well my limits. For example, anagrams escape me for reasons I don't understand unless I run through an algorithm on paper. In high school, there were others who could hand me my ass in chess, math, creative writing, history, you name it. My "gift" (seems more like a curse every day) is complex systems and algorithms. Debugging and working out things with computers is where I'm very skilled.
Let's face it. Some people are better at other things than other people. There is no mystical magical "will" that's going to unlock some mystical magical untapped potential.
I work with people who are unable to think abstractly. It's not just some math-phobia or other character defect. IANAPsychologist, but I've observed them in numerous scenarios and pressured them in different ways, and it's just not happening for them. I'm talking about being unable to understand what a variable is. The idea of a symbol without a fixed, concrete value or a symbol with a value that's defined somewhere else that can change is beyond them. They are very, very aware of their inability to think abstractly, too. I am not being conceited, and if you think I am, go back and re-read where I talk about my limits. Folks like you that preach this "willpower is everything" bullshit are why we can't have nice things.
Your attitude is a caustic one that only makes things more difficult. To get back to my co-workers, for all I know, they very well could understand a variable and even progress to having an understanding of algebra given sufficient time, but this idea that they lack sufficient willpower or virtue to just "get it" shuts them down before they even begin. And they've been hearing your message from other people like you their entire lives.
I have to say that some of the best moments of my life were calculating the area under the curve by tactile measurement.
Put a towel under the door.
The man was a mathematical prodigy.
Einstein was a mathematical prodigy. We preserved his brain for post-mortem study and it is unquestionably different from the average brain.
How much was the thinking shaping the brain and how much was the brain shaping the thinking isn't something we can determine, but his brain was definitely different. And, like Ramanujan, he had a reputation for never ceasing to think.
There's room for both. Put a few "sythetist" type thinkers in with of a whole bunch of specialists and you've got a pretty amazing combination. Some people are better suited to specialty, while others excel at being a "jack of all trades". We obviously can't all be a DaVinci but those who are really make an impact.
"Growing old is inevitable; growing up is optional."
I suspect that you're quite wrong.
I might be wrong.
But, what if I am right?
Get over yourself :-)
Oh for fuck sake.
I am from India, and I really don't give FUCK about your IITs and IIMs. Tell me what your IIT created in last 100 years? Can you give me one programming language? One successfully business idea?
Other than producing bots, they are not doing anything.
And just because they are the elite institutions, with about a million students fighting for one seat, you are going to have the best getting in. I wonder how many are best getting out of there.
> How many people would want to spend all their best moments in life on math?
Is this slashdot? Never mind.
>Or maybe he was just more motivated than average. How many people would want to spend all their best moments in life on math?
Anyone who's brain was more capable of math than other tasks. People gravitate to what they're good at.
Captcha:Reasons
I did quite well in math by almost any measure, but I wouldn't say I'm anywhere near the level Ramanujan achieved at. Sure, I read books on math and such and didn't get out much, but I wouldn't have called myself a particularly hard worker. For the most part performing a few standard deviations above my peers in my areas of talent was fairly effortless. No doubt for me to achieve at a world-class level would have required considerable effort, but for most people no amount of effort would have made that possible.
I'm fairly convinced that talent is something you're born with. Sure, you can choose to develop it more or less, and somebody who auditions for the violin after days of continuous practice will outperform somebody who doesn't even bother to show up for the audition. However, those with extraordinary talent will easily outperform those without it almost completely without regard to effort expended.
I used to teach English as a Second Language in Peru. Of the several hundred students that I had, they all had varying amounts of aptitude and interest, except for two. There was a brother and sister who to save their lives were absolutely unable to grasp something as simple as "Where" in English could mean the same thing as "Donde" in Spanish. I tried using Quechua as an example, (River/Mayo/Rio) but that was even worse. Very nice, intelligent kids, perfectly able to function normally in any other aspect of life, but utterly without any ability to learn more than their native language.
"Think about how stupid the average person is. Now, realise that half of them are dumber than that." - George Carlin
A lot of us mathematicians.
Chimp grey matter contains similar amount of chemicals as the ones inside the head of those so-called prodigies. Chimp DNA is pretty similar to human DNA too. A chimp is not going to equal Ramanujan in math despite how much willpower it has. They just don't have the ability.
So your argument is just as silly as those "you can do anything if you just try hard enough" bullshit cliches.
If you think it's so simple, go ask the top athletes/musicians why they aren't all number one despite most of them spending much of their life training, practicing etc. You think it's because they lack willpower to push themselves to their limits? They're not trying hard enough?
I may not know my exact max limits, but I know that no matter how much I try I am never going to run as fast as Usain Bolt, and I'm never going to be as good at math as Ramanujan. Thinking otherwise is foolishness or hubris even.
I'm all for people trying to improve themselves and others, but I'm against spreading bullshit. The world would be a better place if more humans fully realized and admitted how crap they were, but still persisted in helping and bettering others despite their limitations.
Thanks, we all have the potential to improve ourselves and accomplish great things (in our own way within our own limitations). But to compare ourselves to others and say we are equal in all things as individuals is just irrational. Ramajam might have been a terrible, terrible gardner, father, comedian, or teacher, I wouldn't know though.
P.S. math is only good enough to kind of model some of the universe some of the time. It is by no means the absolute truth or gateway to universal understanding itself. Its great that there are people who can dedicate their lives to it and specialize in it. But this alone will not create enlightenment.
Srinivasa Ramanujan was given a brain, a brain that is not that different from the one we have in between our own ears.
The only difference between Srinivasa Ramanujan and 99.99999% of the human race is that he opted to use his brain power as much as it could be sustained.
If only the rest of 99.99999% of the human population can do the same - becoming a galaxy-roaming race wouldn't stay merely a dream for long.
Our brains may all have the same matter, but that doesn't mean we all have the same abilities or aptitudes. Trust me, I hate the misconception that high level mathematics is accessible only to geniuses, but it's also not as simple as "you can be Gauss if only you try." That's not true. Not everyone can come up with calculus; not everyone can come up with general relativity.
As for Ramanujan, the British mathematician G. H. Hardy, when ranking mathematicians based on talent from 1 to 100 placed himself at 25, David Hilbert at 85, and Ramanujan at 100. To get some perspective, Hilbert was an incredibly influential mathematician who almost beat Einstein to general relativity, and he wasn't even a physicist! That's how talented Ramanujan apparently was. So no, the difference between him and "99.99999% of the human race" is NOT that he "opted to use his brain power as much as it could be sustained."
Your second quote is from Pyramids, not Small Gods - Sorry to be pedantic!
If you actually attempt to read Ramanujan's work, it becomes obvious pretty quickly that there is more than just motivation involved in his genius. Check out some of his generating functions if you don't think this is true and honestly ask yourself "could I have thought of this"? There is absolutely nothing "obvious" to the rest of us mere mortals, about why his incredibly complicated equations should be so incredibly accurate.
I personally doubt his inspiration came from God, and suspect it derives from a remarkably able and unique set of neuronal pathways. Nonetheless, where ever it came from, it is nothing short of amazing and something I could have never conceived of myself. Sadly, judging from the comments here, which I had hoped might actually lead to an indication of where and exactly how his conjectures were "proven" won't likely found among /. readers like myself. Perhaps this point is most profoundly made by the fact that true importance of such news never actually gets mentioned in the article or in discussions about it.
They say that if you are one step ahead, you are smart. If you are two steps ahead, you are a genius. If you are three steps ahead, you are a crackpot. In trying to understand Ramanujan's work, I would venture to guess that he was likely at least 4 or 5 steps ahead.
It is a testament to Ramanujan's genius that when W. H.Hardy, who was himself an extraordinarily gifted mathematical genius, was asked what his greatest contribution to mathematics was, he replied "discovering Ramanaujan".
Let's face it, our brains may look like Ramanujan's, but at a molecular and inter-neuronal level the similarity ends. One only has to try to work through Ramanujan's work to quickly understand this first hand.
Anyone know where the results in the article have been or are being published and further commented upon by the mathematical community?
Srinivasa Ramanujan was given a brain, a brain that is not that different from the one we have in between our own ears.
There's another comment in this thread with a link to Harvard that says you're wrong. According to the article, creative people's brains aren't normal. They're closer to the brains of madmen. And yes, it applies to me as well, I'm nowhere near normal.
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Indeed -- From study, it seems that Albert Einstein's brain may have better enabled him to make his discovery's on the workings of space and time.
“Although the overall size and asymmetrical shape of Einstein’s brain were normal, the prefrontal, somatosensory, primary motor, parietal, temporal and occipital cortices were extraordinary,” said Falk, the Hale G. Smith Professor of Anthropology at Florida State.
“These may have provided the neurological underpinnings for some of his visuospatial and mathematical abilities, for instance.”
-- http://www.examiner.com/article/differences-albert-einstein-s-brain-may-explain-his-genius
Not all brains are the same and when extraordinary ability is granted to such a narrow focus such as mathematics, I would have to guess that the cause would have a physical cause rather than simply "putting his brain to use more than 99.9999999999% of us"
Why are plant cells so efficient at harvesting light and how can we duplicate that ability?
They're not.
http://en.wikipedia.org/wiki/Photosynthetic_efficiency
http://en.wikipedia.org/wiki/Solar_cell_efficiency
I can believe this. Intelligence isn't an absolute value. Sure, you can take a whole bunch of measures and add them up, but the fact is that your brain is a complex organ capable of doing all kinds of things, and it can do all of them to varying degrees.
I'm married to somebody who is fairly intelligent, but due to a recent stroke she went through a period of time where her vocabulary was all of about 20 words. Now she struggles but does fairly well verbally, but still struggles with written language. However, in most areas of intelligence she was always every bit as proficient as before the stroke, which has created all kinds of struggles. People assume that a lack of better than an elementary school vocabulary translates into a lack of "intelligence."
People think about the mind like it is some kind of mystical thing, but it is really just a big modular computer. If you damage part of it, that manifests itself in particular ways. It only stands to reason that due to environment or genetics that parts can also be enhanced. Having seen the effects of brain damage first hand I'm convinced that basically everybody is born "brain damaged" relative to others in various ways, and the only things that differ are manifestation and degree.
Yes indeed, I stand corrected, that'll teach me to overuse Ctrl-V!
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The brain of the man very likely was different than 99% of the rest of humans.
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Law and medicine are the prestigious subjects in India, those who aren't good enough for that study computer science.