He most likely did not and thought that his work in low dimensions would easily scale up to higher dimensions, unaware of the monsters that lurk there. He had

He most likely did not and thought that his work in low dimensions would easily scale up to higher dimensions, unaware of the monsters that lurk there. He had the proof for the power of 2, and when he wrote his line he might have had the proof for powers of 3 in mind (which he didnt write down) and thought that that one would generalize for all n. Which turned out to be true, but for completely different reasons. https://math.stackexchange.com/a/324764/243949 https://math.stackexchange.com/a/324764/243949