The antithesis between death and life is not so stark for the Christian as it is for the atheist. Life is a process of becoming, and the moment of death is the transition from one life to another. Thus it is possible for a Christian to succumb to his own kind of death-wish, to seek that extreme of other-worldliness to which the faith has always been liable, especially in periods of stress and uncertainty. There may appear a marked preoccupation with death and a rejection of all temporal things. To say that this world is in a fallen state and that not too much value must be set upon it, is very far from the Manichaean error of supposing it to be evil throughout. The Christian hope finds ambivalence in death: that which destroys, also redeems.
By and large, I seem to have made more mistakes than any others of whom I know, but have learned thereby to make ever swifter acknowledgment of the errors and thereafter immediately set about to deal more effectively with the truths disclosed by the acknowledgment of erroneous assumptions.
Research teaches a man to admit he is wrong and to be proud of the fact that he does so, rather than try with all his energy to defend an unsound plan because he is afraid that admission of error is a confession of weakness when rather it is a sign of strength.
Mathematics is not a deductive science -- that's a cliche. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork.
Paul R. Halmos
Source: I Want to be a Mathematician, Washington: MAA Spectrum, 1985.