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2This remind me of what Rota said of Church: It may be asked why anyone would bother to sit in a lecture which was the literal repetition of an available text. Such a question would betray an oversimplified view of what goes on in a classroom. What one really learns in class is what one does not know at the time one is learning. The person lecturing to us was logic incarnate. His pauses, hesitations, emphases, his betrayals of emotion (however rare) and sundry other nonverbal phenomena taught us a lot more logic than any written text could.– KimballCommented Sep 4, 2015 at 15:18
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2(cont'd) We learned to think in unison with him as he spoke, as if following the demonstration of a calisthenics instructor. Church's course permanently improved the rigor of our reasoning.– KimballCommented Sep 4, 2015 at 15:19
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1tl;dr: Good lectures are better than bad textbooks.– JeffECommented Sep 30, 2015 at 10:54
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1@Chan-HoSuh But almost all of the specific criticisms compare good lectures to bad textbooks. Good textbooks help the reader speed past the easy parts. Good textbook authors are forced to concentrate on the essentials. Good textbooks present mathematics as a growing thing and not a timeless snapshot. Good textbooks show how mathematicians do mathematics. The only thing a good textbook can't do—at least, not yet—is realize when the reader is confused and adapt.– JeffECommented Sep 30, 2015 at 13:41
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3I don't see a contradiction in the views of Serre's books here. Exemplary mathematical writing is not the same as exemplary mathematical textbook writing.– Mark MeckesCommented Sep 30, 2015 at 17:29
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