... unfortunately, there is a flaw in the reasoning. ... [T]o say that each of two numbers cannot be bigger than the other is to repeat the statement that is to be proved. It is not correct in logic to prove something by saying it over again; that only works in politics, and even there it is usually considered desirable to repeat the proposition hundreds of times before considering it as definitely established.
— Carl E. Linderholm, "Mathematics Made Difficult"
(There are many more good quotes to be found in this book.)
Every month on the month, Less Wrong has a thread where we post Deep Wisdom from the Masters. I saw that nobody did this yet for December for some reason, so I figured I could do it myself.
* Please post all quotes separately, so that they can be voted up/down separately. (If they are strongly related, reply to your own comments. If strongly ordered, then go ahead and post them together.)
* "Do not quote yourself." --Tiiba
* Do not quote comments/posts on LW/OB. That's like shooting fish in a barrel. :)
* No more than 5 quotes per person per monthly thread, please.