What are the examples of some mathematicians coming very close to a very promising theory or a correct proof of a big conjecture but not making or missing the last step?



What are some examples of narrowly missed discoveries in the history of mathematics? 
Freeman Dyson discusses a few examples of this in his article [*Missed Opportunities*](http://www.ams.org/bull/1972-78-05/S0002-9904-1972-12971-9/S0002-9904-1972-12971-9.pdf). One that I thought was particularly striking was that mathematicians could have discovered special relativity decades before Einstein just by staring at Maxwell's equations hard enough, and also on the basis that the representation theory of the Poincare group is simpler than the representation theory of the Galilean group. 


