The statement has a ring of truth to it, but it seems to fall apart upon deeper examination. For example, how do you define innovation and when wars really begin and end? Certainly we can use dates for declarations of war and peace treaties, but other conflicts like the Cold War, seen as a source of great invention and innovation, make things difficult. Other versions of the quote like "War is the mother of invention" are even more problematic because many inventions that are perceived as coming from war actually existed prior to the war that made them famous. Napalm and Agent Orange were around during the Second World War, for example. One concession might be that states of war create new economic circumstances where a previously unprofitable innovation or invention suddenly becomes economical; however, these kinds of circumstances are not unique to wars. Steam powered machines were around for hundreds of years before political and economic changes in the world economy made them profitable to use.

More accurate might be to simply say that necessity sometimes leads to innovation; however, but I have to admit that isn't quite as catchy.

I thought that this saying was from Heraclitus, in Fragments 53:

"Πόλεμος πάντων μέν πατήρ ἐστι, πάντων δέ βασιλεύς, καί τούς μέν θεούς ἔδειξε τούς δέ ἀνθρώπους, τούς μέν δούλους ἐποίησε, τούς δέ ἐλευθέρους."