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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.'"
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.
Obsessed, and smart.
He had a mathematician's mind, sure. Probably not much brighter than what we consider reasonably bright and particularly attuned for maths. But what he had that sets us apart, was a raging obsession. The kind of demon that consumed Newton and possessed him to calculate pages of logarithms and Tesla to study from dusk 'til dawn and further, without respite.
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
So, because he ended up losing his mind, that invalidates all his accomplishments?
Are agnostics skeptical of unicorns too?
Newton later turned to alchemy, and was obsessed with disproving the trinity.
Newton wasn't wrong. He just discovered physics, to first order.
Ramanujan is a totally different ball game. Completely self thought, from a book of identities and formulae. He found a sort of Cliff notes for the BA in Math in England. He assumed that is the way to present mathematics. Just the final result without any deriviation or proof. Did not know what was already invented and well known. He reinvented the wheel so to speak so many times. Almost all the major math break throughs of the previous century, he reinvented all over again, independently. Think about it. One century of mathematicians original work completely reinvented by this lone clerk toiling away in colonial India working as a harbor master's assistant. He presented his inventions without any proof or even a hint of how it was arrived at. Most of his first letters were rejected as some crackpot's ravings by math professors in England. Hardy was the only one who saw that among all the well known identities, that were being presented as new inventions, were real gems never seen before. He invited Ramanujan to England and the rest was history.
A special tit bit: BTW he and I both have the same ancestral temple, that of Lord Oppiliappan at Kumbakonam, Tamil Nadu, but his favorite god was not Oppiliappan, but Nama Giri Devi, the ancestral god of his mother's family. I wish we were related. His personal life was very sad. Died at age 30. His wife was left as a destitute and ended up working as house maid.
sed -e 's/Chuck Norris/Rajnikant/g' joke > fact
Quite the contrary. It hits close to home, but there is strong correlation that that creativity and mental illness are hopelessly linked. The implication is that those who can reason outside of accepted boundaries are those who create revolutionary thoughts
"When life gives you lemons, don't make lemonade. Make life take the lemons back!" -- Cave Johnson
Actually, Newton was an alchemist foremost. He only did physics and calculus to help with his alchemy.
And no, alchemy was not the crackpot gold-seeking they teach it was in history class. Promises of gold were and still are what gets you the funding. Alchemy was a larger discipline concerned with truth about the world, a kind of philosophy 2.0 that finally recognized the need for empirical data and experiment; the most advanced worldview up to that point. Later, as it progressed, physics and chemistry were branched out from it, other parts merged into medicine, philosophy and humanities.
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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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noodles?
rewriting history since 2109
Probably not much brighter than what we consider reasonably bright...
From what evidence did you draw this conclusion? I'm not personally qualified to assess Ramanujan's brilliance (and neither are you, I suspect), but G.H. Hardy, the western mathematicion who worked most closely with Ramanujan, certainly was. What did he think? "I have never met his equal, and can compare him only with Euler or Jacobi." By all accounts, Ramanujan's abilities went way, way beyond "not much brighter than what we consider reasonably bright". He possessed one of the most gifted mathematical minds in recent history.
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.
Yes, Tesla was a bit eccentric in the latter part of his life. On the other hand, his behavior is quite symptomatic of exposure to high frequency electromagnetic radiation. Just because he fried himself doesn't make his accomplishments less impressive. Madame Currie had a similar problem when radiation which nobody thought was bad for you at the time.
Newton spent most of life working on Alchemy--far more than he did on Physics or Mathematics. He didn't turn into a crackpot, he was one from the start.
So...what was your point?
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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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.
So which one was he? Fullmetal, flame, sowing life, etc?
Probably not much brighter than what we consider reasonably bright and particularly attuned for maths.
Give a reasonably bright math graduate an entire lifetime and he is unlikely to be able to reinvent all the math that Ramanujan reinvented due to not knowing it already existed, nor invent all the new math stuff that Ramanujan came up with. Ramanujan did all that in only 32 years.
The merely obsessive would get stuck in ruts or fruitless paths. Ramanujan came up with tons of stuff.
The way his mind works is pretty different:
He was sharing a room with P. C. Mahalanobis who had a problem, "Imagine that you are on a street with houses marked 1 through n. There is a house in between (x) such that the sum of the house numbers to left of it equals the sum of the house numbers to its right. If n is between 50 and 500, what are n and x?" This is a bivariate problem with multiple solutions. Ramanujan thought about it and gave the answer with a twist: He gave a continued fraction. The unusual part was that it was the solution to the whole class of problems. Mahalanobis was astounded and asked how he did it. "It is simple. The minute I heard the problem, I knew that the answer was a continued fraction. Which continued fraction, I asked myself. Then the answer came to my mind," Ramanujan replied.
This is not the "normal" savant rapid addition/multiplication sort of stuff.
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
While "tidbit" is standard American English, this word has had different spellings in previous years and in different regional standards. (The OP is from India, so some differences in his English can be expected). See e.g. Merriam-Webster for a mention of the alternative spelling "titbit".
"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
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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2 + 2 = 5, for very large values of 2
You lose, Robin.
From the original "2 + 2 = 5 for SUFFICENTLY LARGE values of 2"
Simple to prove, with a question: "how large a cup does it take to hold 2 heaping cups of flour taken twice from the barrel?"
Another way of putting it: all the stuff we remember Newton for was for him a fun hobby project. Not only was alchemy a big focus of his, he also played around with religion and magical ritual (as did several other British academics in his time).
Same story with Rene Descartes, a couple generations earlier: His focus was first and foremost on his philosophical works, the algebra work (including inventing exponents and analytic geometry) was just for fun.
It gives you an idea of how ridiculously smart these guys were. I mean, it's one thing to have a lasting impact on something you've devoted your life to, but it's even more amazing to be just saying "Hey, I think I'll do some genius level work in math today". Especially because they were living in a time when there was plenty of superstition screwing up science - for comparison's sake, Newton was about 50 years old when the Salem Witch Trials were going on.
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Her friends call her Edwina.
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
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.
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.
I have to say that some of the best moments of my life were calculating the area under the curve by tactile measurement.
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.
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.