Another popular type of proof is a proof by contradiction. This is also known as an indirect proof. Search the internet for explanations and examples of this type of proof. How might this approach be valuable in proving someone is innocent of a crime?
Search the internet for Euclid’s Elements and read about the parallel postulate and the controversy surrounding it’s improveability.
Read about the millennium problems, and the mathematicians who have won a million dollars. Andrew Wiles proved Fermat’s last theorem several years ago. Read about his struggle with this difficult problem. Could you have gone through that?
Research Godel’s incompleteness theorem. It basically states that we can NEVER prove EVERYTHING… He proved it!
Scott Kennedy’s Classroom http://www.mrkennedymath.doodlekit.com
Scott Kennedy’s Youtube channel http://www.youtube.com/user/scottjkennedy28
Introduction to geometric proofs http://www.sophia.org/introduction-to-geometric-proof-tutorial
The Millennium Problems http://www.claymath.org/millennium/
Euclid’s Elements http://www.claymath.org/library/historical/euclid/