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Hilbert had no patience with mathematical lectures which filled the students with facts but did not teach them how to frame a problem and solve it. He often used to tell them that "a perfect formulation of a problem is already half its solution."
That has always seemed to me an important point, and I was even more convinced of it after hearing it confirmed by Hilbert.
But how had I come to believe in this idea in the first place? A combination of my own experience and other things I'd read. None of which I could at that moment remember! And eventually I'd forget that Hilbert had confirmed it too. But my increased belief in the importance of this idea would remain something I'd learned from this book even after I'd forgotten I'd learned it.