You should not put too much trust in any unproved conjecture, even if it has been propounded by a great authority, even if it has been propounded by yourself. You should try to prove it or disprove it.
A mathematics teacher is a midwife to ideas.
The open secret of real success is to throw your whole personality into your problem.
Beauty in mathematics is seeing the truth without effort.
It may be more important in the mathematics class how you teach than what you teach.
If the proof starts from axioms, distinguishes several cases, and takes thirteen lines in the text book ... it may give the youngsters the impression that mathematics consists in proving the most obvious things in the least obvious way.