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.
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."
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.
> 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.
28 comments
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.'"
> intelligent non-smart people
I always knew I was som thing but just didn't know what it was called
"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."
> 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.