His life story is incredibly interesting. I also think that it is a lesson to us all that someone doesn't have to be formally trained in a field to make major contributions to it.
It is true that he went on to do crazy mathematics without any formal education but we really don't know what he could have achieved if he were well versed in contemporary mathematics or even had access to some advance textbooks.
It is also true, per se, that you don't have to be formally trained to make major contribution but I guess this really doesn't apply to Ramanujan. Being formally trained is one thing and being completely untrained is another. He didn't even have access to decent textbooks. He was starving. He had no mentor. It was his sheer genius which played a key role. Given his circumstances, I don't think any other ordinary person could achieve that much with any amount of hard work.
Interesting viewpoint of the life of genius. I just read a book (Peak, 2016) on deliberate practice where there is compelling evidence that all works of genius stem from very hard work and lots of time.
Is it possible that Ramanujan would not have been so successful had he followed the standard learning path? Is it possible that Ramanujan's genius stems from a "genius" of what mathematical questions he chose to think about?
>Is it possible that Ramanujan would not have been so successful had he followed the standard learning path?
Sure, it's possible. But there's always a problem when you teach yourself something, no matter how good at it you are, in that you don't know what you don't know.
Even if you're a genius and an autodidact, sometimes a little direction, a little mentoring, a little collaboration goes a long way in moving your understanding down the field.
Here's the biggest problem with a lack of education as far as math goes. How much time did he spend re-inventing the wheel because he didn't know which wheels had been invented? And he always did it better and faster than anyone else would have, or did? Probably not. His genius may have minimized the handicap of a lack of education. I somehow doubt that lack of an education was a benefit to him. Once he got into academia though through his recognized genius he probably learned a lot of things from a lot of people to try and fill in whatever gaps in his understanding he may have had. I very much doubt he lamented how learning things from experienced peers crippled his own genius...
No one is such a genius that they're an island unto themselves and no one and nothing any other human being has done matters. That type of genius is fantasy for Hollywood, not reality.
No matter who we are, or the level of our genius. We all stand on the shoulders of giants who came before.
> Even if you're a genius and an autodidact, sometimes a little direction, a little mentoring, a little collaboration goes a long way in moving your understanding down the field.
Sometimes this might bind you for the rest of your life to the epicycles of your era.
I think it’s definitely possible, maybe even likely.
Maybe it relates a little to that concept of “we were able to do it because we didn’t know it was impossible”?
Another aphorism that might somehow relate is, mistakes are considered an important part of creativity, in both art and science.
It’s hard me for me to escape the conclusion that there were likely some benefits related to stuff like this, that can force a person down paths less travelled.
As the same time, I bet there’s probably some way to build an entire house with a screwdriver. Would you want a great architect to work under those constraints?
Tangential, someone won a nobel prize for physics. There’s a case that we was greatly impacted by autism but functional, and speculation some of those personality traits helped him get there. If that were true, should we wish he never had it?
It seems clear that ironically, ignornace is sometimes an asset, but it’s almost impossible to untangle what and how much benefit was had in a particular case.
I’m sure I would have loved to had been his friend, know what he was like in real life. Even though I believe it’s plausible there were some insights related to his disadvantages, not sure anyone who could go back in time would not want to lay the world’s knowledge at his feet, and stand back and see what happened.
From what I've read about him, he didn't even derive his solutions. They "came to him" (he thought from the divine) and he had to be taught how to go backwards from the solution to formal proofs.
Based on that it sounds like he was a savant, rather than having taught himself a unique solving technique or depending on the questions he thought of. Personally, I think he'd have excelled equally well in a standard learning path. There are definitely other cases of people going the "standard" route and still possessing this sort of savant-like ability. E.g. https://en.wikipedia.org/wiki/Erik_Demaine
Could it be that kids who only can multiply with a calculator are worse off than kids who don't have access to a calculator? I'm thinking him not having the text-books.
Either way I think it's interesting to consider what intellectual tools like computers are doing to our ability to think. A similar thing I read somewhere how kids no longer are able to use keyboards since they only use their phones.
And what about asking Alexa or Siri for the answer to everything? Not learning languages because everything can be machine-translated. Do such tools in fact make us dumber?
His genius stems from mathematical intuition. Even without formal education, he implicitly understood certain topics and was deriving proofs based on that intuition. Not everyone has that innately, but I see no reason why it couldn’t be learned.
We will never know, but I think his lacking formal training helped him as it didn't confine him in a boundary and allowed him to choose his own path. Its often said he rediscovered many things already known, there by casting a bit of uselessness to his works. Be that as it may, I think, more than having access to established and formalized knowledge, he should have just lived longer. He would have been like the mathematicians in renaissance Europe who tackled and pursued whatever interested them and produced great stuff. Eventually, he would have done something remarkable. Of course, he could have ended up being utterly mediocre once his "beginners luck" faded, but it is more likely that he would have succeeded.
> I also think that it is a lesson to us all that someone doesn't have to be formally trained in a field to make major contributions to it.
I don't think it serves that lesson at all but rather an extraordinary minority of very talented indidvuals can bypass such training/education in extremely rare circumstances. He's a Mozart and education and training is still necessary for the vast majority of people.
Nope -- he was a prodigy from the earliest age. He was composing music at the age of 5.
Thats kindergarten. You might be thinking of other composers who are regarded as his equals -- Mozarts brain was just tuned for music in a way ours are not.
I would have been composing at 5 had my father been a musician/composer/teacher! (I did start piano at 4, in a not-particularly-musical household) As it was, I remember hearing that when I was about 9, and thought "Oh well, it's too late for me" - which is a shame! But his first compositions weren't great. You write that like it's some super-human feat or something.
"he was a prodigy from the earliest age. ... Mozarts brain was just tuned for music in a way ours are not." I don't know why people talk like that. Maybe as an excuse for not achieving great things themselves, or even having to try.
There was a Hungarian guy who decided to train his 3 daughters to be chess players, to see just how good they could be given a proper training. The 2nd strongest sister became world champion. The strongest one never played in women-only events, she was too strong, and turned out to be the strongest woman chess player of all time, by a long way. (i.e. Susan and Judit Polgar) I don't think it was because their brains were 'tuned for it'. They just had the perfect environment.
Another example, this[1] music producer's kid developed perfect pitch despite the lack of any training. He was exposed to a rich variety of complex music right from the start. When the dad discovered his son's ability, he found out that the kid had his own names for the notes. IIRC, based on which song begins with that note. I think it's quite likely that if the dad had spent all his days composing music, the son would have been doing that from an early age as well.
Your proposal can't actually test the hypothesis because it can't (reasonably) be done. We don't know how many children were similarly situated and did not turn out like Mozart.
It could be that many musicians with a similar background were/are similarly as good as Mozart, and Mozart's music is especially famous for its cultural appeal and his father's aggressive "marketing" to royalty. There are many reasons one particular musician's musicical legacy can succeed aside from raw skill and creativity, much like the success of a company has a nontrivial luck component.
It could also be that he really was extraordinary above and beyond his family's musical background. Like most discussions about the nature versus nurture of genius, we can't really assert one thing or another.
Is music composition difficult? Are most five-year-olds asked or encouraged to write music? Is this something that most adults have attempted and failed to do? Do you think that you could write a piece of music if you had time and inclination?
I'm asking honestly, because I'm pretty sure that I'm not having a typical life experience. Personally, I don't really bother to listen to music, because music is never further away than wanting to hear a melody. It's something to do on the bus, or when my mind is otherwise unoccupied. One starts with a note or a scale, finds a 'lick' in it, develops it into a theme or refrain, introduces a counterpoint or noodles around through the keys a bit, and eventually we work around to a restatement or finale (or get bored or forgetful in the middle). I suspect that this is easier for me than others, but I don't think that I'm any kind of musical genius. I'm at least hoping that creating music is more of a normal part of the human condition than not, at any rate.
I agree that education/training is required for most everyone. But there are times that these minorities could contribute a lot but how certain industries/fields are structured they are shut out.
What strange ideas people have about Mozart and genius. Everyone is bad when they start doing anything. They gradually get better by putting in countless hours. I'm not a Mozart expert, but I know his father and sister were musicians, so his education and training would have started extremely young. You'll find a similar thing with most prodigies.
Reading https://en.wikipedia.org/wiki/Srinivasa_Ramanujan , it sounds like he was obsessed with maths from the age of 10 or so. He learned from books. Sounds like by the time he got to college, what he was interested in wasn't taught there anyway; he was already too advanced/specialized.
His story seems to me a sad one, so often sick, dying only 6 years after arriving in England, at 32, etc.
https://en.wikipedia.org/wiki/Srinivasa_Ramanujan