There is an anecdote about a very well-known professor of mathematics which, if it is not true, deserves to be. It relates that while addressing a learned audience, he wrote a mathematical statement on the board, saying ‘This, of course, is obvious.’ Growing more doubtful, he said ‘Excuse me,’ and taking pencil and paper, was absent from the room for about twenty minutes. He returned beaming, and said triumphantly ‘yes, gentlemen, it is obvious.’
Psychologically, the charm of this story is that there is no inconsistency between the first confident statement, and the relatively lengthy period of deliberation needed, once doubt had arisen, before this confidence could be regained. By the first statement, the speaker meant ‘We can accept intuitively the truth of this statement.’ By the second statement, he mean that, having acceptance was justified. Being sure of something is one thing; knowing why one is sure is another.
Richard R. Skemp, The Psychology of Learning Mathematics Pg. 54