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Apr 17, 2011 at 22:12 comment added ProbLe Bill, it is very kind of you to give me your invaluable comments above, which enlighten me a lot on how to learn mathematics! I am so excited to practice your method just from today! "I gain something by trying to rethink and express it, trying not to resort too much to citing authorities or my intangible belief system of what is well-known." --That's it!
Apr 17, 2011 at 20:00 comment added drbobmeister Couldn't have said it better myself!
Apr 17, 2011 at 17:44 comment added Bill Thurston @ProbLe---glad to do it. Knowledge is organic. I enjoy trying to rethink basic facts that I learned some time ago, and attempting to express them in clear terms. Typically when I learned things like this from textbooks and classes, they seemed technical and complicated. Unless I go over and rethink them, my memory gradually decays, making unjustified simplifications and unfeasible shortcuts. I gain something by trying to rethink and express it, trying not to resort too much to citing authorities or my intangible belief system of what is well-known.
Apr 17, 2011 at 16:38 comment added ProbLe Bill, thank you very much for your detailed answer and for reminding me these basic facts about cut locus and conjugate locus.
Apr 17, 2011 at 16:26 vote accept ProbLe
Apr 17, 2011 at 16:56
Apr 17, 2011 at 16:26 vote accept ProbLe
Apr 17, 2011 at 16:26
Apr 17, 2011 at 16:26 vote accept ProbLe
Apr 17, 2011 at 16:26
Apr 17, 2011 at 13:24 history edited Bill Thurston CC BY-SA 3.0
Unrolled overlong sentence, put in more background, clarified
Apr 17, 2011 at 13:15 history answered Bill Thurston CC BY-SA 3.0