A.I think that going about a problem with the right strategy will be very important. A lot of time could be wasted if not done right and it takes you down a long dead end road. Some of the examples were really simple to see but to explain it gets complicated. It trying to come up with what you can visually see and put it into convincing logical statements.
B. The conjectures that stood for so long before becoming a theorem were interesting. I remember in high school talking about Fermat and Euler. I know that there are a lot of things that I think about and draw my own conclusions about but it sometimes remains at that. For one reason or another those ideas don't turn into reality. In reading about these conjectures I pictured these great mathematicians thinking about great number theory and having big ideas but they couldn't make the next step to becoming theorems for certain hold backs. Then years later some other mathematician picks up the idea and finishes what was previously started. How cool and makes me wonder what other interesting conjectures are still out there waiting to be proven or disproven.
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