[seanhunter]

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."

[Balinares]

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.

[seanhunter]

> 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-...

[adrian_b]

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.