Interesting Math Stuff #5: Mathematics and Logic

Mathematics and Logic. Why do these two words always come together? Mathematics on its basic level might be logical, but as we delve into the higher mathematics such as algebra, geometry, trig, and even (shudder) calculus, where does this logic go? Mathematics seems to be governed less by clear and logical common sense and more by a long list of meticulous steps, identities and rules to be memorized that only make logical sense to the select and brilliant few while the rest of us mechanically follow the steps Outlined for us with no real understanding of how or why we get the answer we do. -A question to ponder: do mathematics and logic really go hand in hand for the common person? 

A few somewhat humorous examples of when logic and mathematics produce some truly tragic results.