It is possible for a mathematician to be "too strong" for a given occasion. He forces through, where another might be driven to a different, and possible more fruitful, approach. (So a rock climber might force a dreadful crack, instead of finding a subtle and delicate route.)

The first test of potential in mathematics is whether you can get anything out of geometry.

A linguist would be shocked to learn that if a set is not closed this does not mean that it is open, or again that "E is dense in E" does not mean the same thing as "E is dense in itself".

Try a hard problem. You may not solve it, but you will prove something else.

The infinitely competent can be uncreative.

Mathematics is a dangerous profession; an appreciable proportion of us go mad.

A heavy warning used to be given that pictures are not rigorous; this has never had its bluff called and has permanently frightened its victims into playing for safety.