Papers of Srinivasa Ramanujan (1887-1920), mathematician
trin.cam.ac.uk
trin.cam.ac.uk
Definitely interesting for Ramanujan enthusiasts, but if you're looking for (say) his papers with Hardy about partitions, numbers of prime factors of "typical" numbers, etc., then this isn't the place to go.
https://en.wikipedia.org/wiki/1729_(number)
This is hands-down my favorite math story:
It is known as the Hardy-Ramanujan number, after an anecdote of the British mathematician G. H. Hardy when he visited Indian mathematician Srinivasa Ramanujan in hospital. He related their conversation:
I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."
It takes about 10 minutes to read one line. But its worth it cause he was able to create his own path and what he does with formal power series and summing divergent series is staggering to behold
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.
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.
If we applied the same training and familial advantage to many kids would any of them turn out like Mozart?
I'd argue they probably wouldn't because his brain was fundamentally different and that made the difference.
If he didn't have those advantages would he have been discovered as a prodigy as quickly and as early? Maybe not.
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.
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.
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.
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.
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?
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.
Sometimes this might bind you for the rest of your life to the epicycles of your era.
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.
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
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?
It seems that a lot of math geniuses died premature. Eisenstein, Abel, Galois, Riemann..
I've read some of his work.. there are formulas appearing out of nowhere, like magic. He said that he saw them in his dreams.
He had access to 1 book, basically, a collection of math theorems and that's it. Only 900 pages (IIRC) and the rest of the stuff he discovered (and re-discovered in some cases) on his own.
Unparalleled genius!
A trend on home improvement shows is to print out old patent drawings and hang them as decoration. It always seemed so off putting necause most people never bothered to choose based on work that was intesterimg or meaningful to them, or even know what the patent was about.
For me this feels the opposite, so many personal connections...The subject matter, respect for his talent and contributions, the person, and in huge part the inspiration of being to achieve in the face of long odds and adversity.
But sure, not everybody can be No. 1, it would be silly to expect millions of 'talents comparable to Mozart', there can't be countless people in the NHL etc.
So... you sound disappointed, maybe. Did you put in '10,000 hours' and it didn't work out? I don't know much about the '10,000 hours' theory, less about how you think it's overhyped. People often have an idea that it's an unpleasant ordeal, all that practice, but if it's what you love, it's a pleasure. (I enjoyed every minute) Sure, I believe people have different levels of..how far they can go, but its importance is vastly overrated. Like much more important to me seems how much you enjoy practising, whether art, music, sport, anything, whether you love doing it more than anything, and do it for decades.
I've often thought that if I'd grown up living in a town, a popular kid etc I would have turned out 'untalented' in anything, except chatting and being popular; but I grew up fairly isolated on a farm, pre-internet, and so played piano a lot, read a lot etc. And I wasn't so happy, so playing piano was a great joy. Maybe if I'd been happy already, I wouldn't have 'needed' to play piano so much. I had very low self-esteem...thanks to bullying at home and at school, so...it was wonderful to escape to the beautiful world of music. I think factors like that, that influence how much you practice, how many hours you put in (though I never thought of it like that), how much you love doing it, are much more important than differences of natural ability.
My hobby these days is playing Tekken, which I guess is similar enough to piano in that you can practice forever and you've never totally mastered it.
Did you mean to say my 'account' is one of those? Well, I didn't say either of those two things. (I think your account was overly reductive.) :-) Good luck!
We all have high potential, most of us never come closer to reaching it 100%, but to think we are all equal in our skills from birth is a bit naive and definitely not true, as experienced by probably everybody during their lifetime.
Life ain't fair since the start, we can work hard at overcoming our limits, and that's all great. But so far if 2 people put in same amount of effort, the ones with better genes always wins.