How is error possible in mathematics?

Experiment is the sole source of truth. It alone can teach us something new; it alone can give us certainty.

How is error possible in mathematics?

One geometry cannot be more true than another; it can only be more convenient.

Logic sometimes makes monsters. For half a century we have seen a mass of bizarre functions which appear to be forced to resemble as little as possible honest functions which serve some purpose.

There are no solved problems; there are only problems that are more or less solved.

It is often said that experiments should be made without preconceived ideas. That is impossible. Not only would it make every experiment fruitless, but even if we wished to do so, it could not be done. Every man has his own conception of the world, and this he cannot so easily lay aside. We must, example, use language, and our language is necessarily steeped in preconceived ideas. Only they are unconscious preconceived ideas, which are a thousand times the most dangerous of all.