How is error possible in mathematics?

But for harmony beautiful to contemplate, science would not be worth following.

Point set topology is a disease from which the human race will soon recover.

We also know how cruel the truth often is, and we wonder whether delusion is not more consoling.

If we wish to foresee the future of mathematics, our proper course is to study the history and present condition of the science.

All that we can hope from these inspirations, which are the fruits of unconscious work, is to obtain points of departure for such calculations. As for the calculations themselves, they must be made in the second period of conscious work which follows the inspiration, and in which the results of the inspiration are verified and the consequences deduced.‎

It is far better to foresee even without certainty than not to foresee at all.