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"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."
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.
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-...
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.
I always knew I was som thing but just didn't know what it was called
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...
Show you workings then
> 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.