I'm looking for examples where, after a long time with little progress, a simultaneous mathematical discovery, solution, or breakthrough was made independently by at least two different people/groups. Two examples come to mind:

- Prime Number Theorem. This was proved by Jacques Hadamard and Charles Jean de la Vallée Poussin in 1896.
- Sum of three fourth powers equals a fourth power. In 1986, Noam Elkies proved that there are infinitely many integer solutions to $a^4 + b^4 + c^4 = d^4$. His smallest example was $2682440^4 + 15365639^4 + 18796760^4 = 20615673^4$. Don Zagier reported that he found a solution independently just weeks later.

Can you give other instances?

whythere are simultaneous independent discoveries at math.stackexchange.com/questions/709969/… $\endgroup$ – Gerry Myerson Jul 30 at 4:21