Emerton: Mathematicians argue by passing to an extreme case at the beginning. Non-mathematicians object to this as invalid or irrelevant.
James D. Taylor: Going to extremes sets the parameters of a discussion.
Gil Kalai: Outside mathematics, passing to extreme cases first and considering unrealistic situations is a damaging habit of thought.
Michael Thaddeus: Be self-critical.
Yemon Choi: Self-criticism is not particular to mathematicians.
David White: Reduce clutter in discussions. Break hard problems down to easier pieces.





