Thinking about Proofs

When I think about when I first truly learnt about what a proof is, I actually think it was relatively recent. A little over two years ago I took Math 220, the course on proofs at UBC. However, even after completing this course, I'm not sure if I could really call myself a proof expert. By taking four upper-year level proof related courses after Math 220, I feel like I know what a proof is more. Before taking this proof course, I had seen proofs, but I never really did them personally and I seemed to take the stance of "it just works, because it works" and trust in the mathematical authorities. I think what got me to my definition of a proof today, is by actually doing rigorous proofs, including proving well-known ideas, such as proving numbers to be irrational, etc. 

In retrospect, I wish I did learn about these logic system much earlier. John Mason talk about how young children are able to provide counterexamples and similar reasoning that is used in math. I found that once I learnt about symbolic logic, I found it easier to question the way things were. In some proofs, you really look for the counterexample, and after taking this course I think my precision of language did improve. 

When I look back on the "geogebra reasoning", I think that exploring with these tools is convincing and more explorative, but are not quite as rigorous as a proof. The step that I think geogebra is missing is some sort of accurate/reliable algorithm to confirm each case and the boundaries. I also think some sort of word or explanation of exactly what is being proven is important. I think these things would make me 100% something is proven true.