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George C. Williams and John Maynard Smith arrived at slightly different conclusions about the evolutionary maintenance of sexual reproduction, despite that both were staunch neo-Darwinians, simply because they approached the problem from different angles (life history vs. population genetics). This difference between their perspectives made them notice the so-called paradox of sexual reproduction for the first time. That is, Williams and Maynard Smith used their difference in perspective constructively, in order to raise a problem that had previously been overlooked by ‘monocular’ views. Evidence from before, during and after the recognition of the paradox supports this thesis of constructive difference. First, Maynard Smith had diagnosed the individual cost of sexual reproduction in full detail by 1958, but nobody raised an eyebrow for a decade. Second, both the correspondence between Williams and Maynard Smith and their publications show that they saw the same problem but against different backgrounds, because they viewed it from different perspectives. Third, further differences between Williams and Maynard Smith concerning the evolution of sex make no sense except in the light of the initial difference in their perspectives.