Sometimes simply asking the question in the first place is a key step, even when it takes a genius to actually solve the problem. So, even though he couldn’t calculate his way out of a paper bag, Antoine Gombaud, Chevalier de Méré , played an important role in birthing probability theory – by asking Pascal and Fermat to solve the the problem of points – how to divide the stakes of an unfinished series of games. Of course asking the right people is also part of the goodness.
Franciszek Pokorny, who headed the Polish General Staff’s Cipher bureau after World War I, was the first to realize that cryptography and cryptanalysis are essentially mathematical in nature – and that you therefore want to hire mathematicians, rather than classical scholars or members of the band of the battleship California. He recruited Marian Rejewski, Henryk Zygalski and Jerzy Różycki: they weren’t considered world-beaters by other Polish mathematicians – not like Arne Beurling – but they broke Enigma.