I often wonder about stories of relatively short-lived geniuses such as Ramanujan. Is there a timeline where he recovered and continued making discoveries for decades? Is there some correlation between extreme genius in one area and suboptimal physical health? What if he had existed in modern times instead?
Modern world, not just India, is way worse at talent discovery. It's impossible to even publish a physics paper and get a DOI. There were some new research ideas coming in chinese and hindi during early bitcoin days, all of which were lost to a vocal english population, and some the ideas are only resurfacing now again after 15 years of noise. I know of Shannon-Satoshi level bitcoiner theorist who died in poverty as a janitor in Canada. I know of many ideas that were never discussed, so am sure many such people exit in other fields. Only cause Ramanujan's equations are from a different time and so weird have they survived plagiarism otherwise IP is completely insecure now & intelligent non-smart people are in poor health.
I mean we have one extreme genius who showed promise early and remained exceptionally productive in mathematics for a long career: Leonhard Euler.
"Euler's work averages 800 pages a year from 1725 to 1783. He also wrote over 4500 letters and hundreds of manuscripts. It has been estimated that Leonhard Euler was the author of a quarter of the combined output in mathematics, physics, mechanics, astronomy, and navigation in the 18th century, while other researchers credit Euler for a third of the output in mathematics in that century"
But of course everyone is interested in the "what if" question of what might have happened had a particular person not died young:
- What if Galois hadn't died in a duel?
- What if Niels Henrik Abel hadn't died of tuberculosis?[1]
- What if Emmy Noether hadn't died of cancer so soon after she started teaching at Bryn Mawr and Princeton?
[1] This one is one of the saddest stories in maths to my view. Abel died in his 20s basically because of extreme poverty and 2 days after he died a letter arrived from one of his friends who had got him a teaching position that would have made him financially secure. Hermite said of Abel "Abel has left mathematicians enough to keep them busy for five hundred years."
> long tradition of naming theorems after the second person after Euler to discover them.
Some of my favourite examples of this are:
- The "Lambert W" function, discovered by Euler to solve a problem Lambert couldn't solve
- "Feynman's trick" of differentiating under the integral[1]. Invented by Euler. Done by Feynman because he says in his autobiography he learned it from "Advanced Calculus" by Cook. So now it's called "Feynman's trick". Like dude it had been around for 250 years before Feynman did it.
- "Lagrange's notation" for derivatives. Yup. Euler.
- The "Riemann Zeta function". Of course discovered and first studied by Euler. Riemann extended it to complex numbers though.
Another example is William Kingdon Clifford, who also died too young, while having excellent chances of advancing mathematics.
James Clerk Maxwell died simultaneously with Clifford. Maxwell was not so young, but his death was also very premature.
Had not both Clifford and Maxwell died too soon, there would have been very good chances for the mathematical bases of the theory of physical quantities to be improved many decades earlier, possibly skipping over the incomplete vector theories of Gibbs and Heaviside, which while very useful in the short term for engineering, in the long term were an impediment in the development of physics.
He lived in India. In the early 1900s. The average lifespan in India in 1920 when he died was 21 to 25 years old. He was 32 when he died, so better than the average. The math checks out.
Very low historical life expectancies are driven by childhood illness and maternal mortality. If you made it to 15 your life expectancy might be somewhere in your late 50s.
There isn’t data for life expectancy at 15 before 1950 for India here (when it was 60) but you can see the it for Sweden back to 1751.
Well, these numbers are averages between people living until old age (65+ years) and high infant mortality. I don't think most people keeled over when they reach 25 years...
This is a good example why "mean" and "median" have very different meanings. You can't use an average of life expectancy in an era where a huge percentage of people died before age 5. It's not a useful statistic to the make the point you suggest, and in fact is misleading.
The average life expectancy in the 1920s, even in India, was most definitely not 21-25 years. Various sources show the expectancy age as 51-57. This is because there wasn't enough data for this.
> 1729 is known as Ramanujan number or Hardy–Ramanujan number, named after an anecdote of the British mathematician G. H. Hardy when he visited Indian mathematician Srinivasa Ramanujan who was ill in hospital. In their conversation, Hardy stated that the number 1729 from a taxicab he rode was a "dull" number and "hopefully it is not unfavourable omen", but Ramanujan remarked that "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways". This conversation led to the definition of the taxicab number as the smallest integer that can be expressed as a sum of two positive cubes in a given number of distinct ways. 1729 is the second taxicab number, expressed as 1³+12³=9³+10³.
When I explain this to people, I say: given Rubik's cubes of size 1x1x1, 2x2x2, 3x3x3,..., 15x15x15, and a scale. Make the scale in balance with something on it.
The solution is to put 1x1x1 and 12x12x12 on one side and 9x9x9 and 10x10x10 on the other.
Particularly see the presentations on Ramanujan by Prof. Ken Ono and the various documentaries on him linked to in my comment chain here - https://news.ycombinator.com/item?id=41910851
K. Srinivasa Rao has said, "As for his place in the world of Mathematics, we quote Bruce C. Berndt: 'Paul Erdős has passed on to us Hardy's personal ratings of mathematicians. Suppose that we rate mathematicians on the basis of pure talent on a scale from 0 to 100. Hardy gave himself a score of 25, J. E. Littlewood 30, David Hilbert 80 and Ramanujan 100.'"
I often wonder about stories of relatively short-lived geniuses such as Ramanujan. Is there a timeline where he recovered and continued making discoveries for decades? Is there some correlation between extreme genius in one area and suboptimal physical health? What if he had existed in modern times instead?
Modern world, not just India, is way worse at talent discovery. It's impossible to even publish a physics paper and get a DOI. There were some new research ideas coming in chinese and hindi during early bitcoin days, all of which were lost to a vocal english population, and some the ideas are only resurfacing now again after 15 years of noise. I know of Shannon-Satoshi level bitcoiner theorist who died in poverty as a janitor in Canada. I know of many ideas that were never discussed, so am sure many such people exit in other fields. Only cause Ramanujan's equations are from a different time and so weird have they survived plagiarism otherwise IP is completely insecure now & intelligent non-smart people are in poor health.
> intelligent non-smart people
I always knew I was som thing but just didn't know what it was called
Awful. There’s a lot in there I had not thought to consider.
I mean we have one extreme genius who showed promise early and remained exceptionally productive in mathematics for a long career: Leonhard Euler.
"Euler's work averages 800 pages a year from 1725 to 1783. He also wrote over 4500 letters and hundreds of manuscripts. It has been estimated that Leonhard Euler was the author of a quarter of the combined output in mathematics, physics, mechanics, astronomy, and navigation in the 18th century, while other researchers credit Euler for a third of the output in mathematics in that century"
https://en.wikipedia.org/wiki/Leonhard_Euler#Contributions_t...
But of course everyone is interested in the "what if" question of what might have happened had a particular person not died young:
- What if Galois hadn't died in a duel?
- What if Niels Henrik Abel hadn't died of tuberculosis?[1]
- What if Emmy Noether hadn't died of cancer so soon after she started teaching at Bryn Mawr and Princeton?
[1] This one is one of the saddest stories in maths to my view. Abel died in his 20s basically because of extreme poverty and 2 days after he died a letter arrived from one of his friends who had got him a teaching position that would have made him financially secure. Hermite said of Abel "Abel has left mathematicians enough to keep them busy for five hundred years."
It's well known that mathematicians have a long tradition of naming theorems after the second person after Euler to discover them.
Jokes aside, I wonder even more how many there are who died in a sweatshop or a cotton field, and whose names we'll never know.
> long tradition of naming theorems after the second person after Euler to discover them.
Some of my favourite examples of this are:
- The "Lambert W" function, discovered by Euler to solve a problem Lambert couldn't solve
- "Feynman's trick" of differentiating under the integral[1]. Invented by Euler. Done by Feynman because he says in his autobiography he learned it from "Advanced Calculus" by Cook. So now it's called "Feynman's trick". Like dude it had been around for 250 years before Feynman did it.
- "Lagrange's notation" for derivatives. Yup. Euler.
- The "Riemann Zeta function". Of course discovered and first studied by Euler. Riemann extended it to complex numbers though.
[1] https://math.stackexchange.com/questions/390850/integrating-...
Another example is William Kingdon Clifford, who also died too young, while having excellent chances of advancing mathematics.
James Clerk Maxwell died simultaneously with Clifford. Maxwell was not so young, but his death was also very premature.
Had not both Clifford and Maxwell died too soon, there would have been very good chances for the mathematical bases of the theory of physical quantities to be improved many decades earlier, possibly skipping over the incomplete vector theories of Gibbs and Heaviside, which while very useful in the short term for engineering, in the long term were an impediment in the development of physics.
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And: How do we treat them?
He lived in India. In the early 1900s. The average lifespan in India in 1920 when he died was 21 to 25 years old. He was 32 when he died, so better than the average. The math checks out.
Very low historical life expectancies are driven by childhood illness and maternal mortality. If you made it to 15 your life expectancy might be somewhere in your late 50s.
There isn’t data for life expectancy at 15 before 1950 for India here (when it was 60) but you can see the it for Sweden back to 1751.
https://ourworldindata.org/grapher/life-expectancy-at-age-15...
Well, these numbers are averages between people living until old age (65+ years) and high infant mortality. I don't think most people keeled over when they reach 25 years...
But it does also show lack of accessible medical care in early years, that could have influenced his health overall.
Not so much medical care but proper nutrition and general hygiene.
This is a good example why "mean" and "median" have very different meanings. You can't use an average of life expectancy in an era where a huge percentage of people died before age 5. It's not a useful statistic to the make the point you suggest, and in fact is misleading.
The average life expectancy in the 1920s, even in India, was most definitely not 21-25 years. Various sources show the expectancy age as 51-57. This is because there wasn't enough data for this.
Once in a while I see a stat for "life expectancy at age 5". It should be some kind of normative usage.
He got ill and died after he'd come to England though.
He died in India.
right now its about in the 70s (source I read this somewhere i while ago but dont take my word for it)
> The math checks out.
Show you workings then
He had already moved to UK when he died and died from a lung problem if I recall it correctly.
He moved back to India as his health was miserable in the UK. He died in India.
I didn't know. Thanks.
Obligatory, from Wikipedia.
> 1729 is known as Ramanujan number or Hardy–Ramanujan number, named after an anecdote of the British mathematician G. H. Hardy when he visited Indian mathematician Srinivasa Ramanujan who was ill in hospital. In their conversation, Hardy stated that the number 1729 from a taxicab he rode was a "dull" number and "hopefully it is not unfavourable omen", but Ramanujan remarked that "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways". This conversation led to the definition of the taxicab number as the smallest integer that can be expressed as a sum of two positive cubes in a given number of distinct ways. 1729 is the second taxicab number, expressed as 1³+12³=9³+10³.
When I explain this to people, I say: given Rubik's cubes of size 1x1x1, 2x2x2, 3x3x3,..., 15x15x15, and a scale. Make the scale in balance with something on it.
The solution is to put 1x1x1 and 12x12x12 on one side and 9x9x9 and 10x10x10 on the other.
I've never seen a 1x1x1 Rubik's cube, but I bet I could solve it!
Previously discussed in 2024 - https://news.ycombinator.com/item?id=41909564
Particularly see the presentations on Ramanujan by Prof. Ken Ono and the various documentaries on him linked to in my comment chain here - https://news.ycombinator.com/item?id=41910851
Ramanujan's published papers and unpublished notebooks available online - https://ramanujan.sirinudi.org/
From Mathematicians' views of Ramanujan - https://en.wikipedia.org/wiki/Srinivasa_Ramanujan#Mathematic...
K. Srinivasa Rao has said, "As for his place in the world of Mathematics, we quote Bruce C. Berndt: 'Paul Erdős has passed on to us Hardy's personal ratings of mathematicians. Suppose that we rate mathematicians on the basis of pure talent on a scale from 0 to 100. Hardy gave himself a score of 25, J. E. Littlewood 30, David Hilbert 80 and Ramanujan 100.'"
When we get to human cloning this is probably the only person worth trying to clone.
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