Famous Problems the Experts Could not Solve After Yitang Zhang stunned the mathematics world by establishing the first finite bound on gaps between prime numbers, it got me thinking about the following question:
$\underline{\text{Question}}:$ What are other examples of proofs provided by younger, less accomplished mathematicians that the experts of the time could not solve or did not attempt to solve? 
For example, in 1979 the American mathematician Thomas Wolff created a new proof of the Corona problem whilst still a graduate student at Berkeley. He solved the equations in a nonanalytic way and then modified the solution to make it analytic bounded (which leads to the equation $\overline{\partial}u=f$). 

Kurt Heegner showed the Stark-Heegner theorem. At that time, he wasn't connected to any university, in fact, no one looked to his proof until Stark showed the same result. He wasn't young, but Yitang Zhang wasn't either. 
