If you have a solution to a problem, and have strong intuition that it will work, it seems wasteful to spend a lot of time proving the obvious. But it's in good taste to remember that you need proof of what you think is correct. Intuition and insight is great, but you need supporting evidence to back up every solution.
Essentially, the issue is that after you've spent several minutes, hours or days solving a problem sometimes you say to yourself "oh, how obvious". What many people seem to forget, though, is that it's not so obvious to others who aren't you and don't have your background. You need to clearly explain your ideas and you have to have empirical or other strong testimonial evidence to support your solution. Otherwise, you might as well have waved your hand and said "Here's how to make a square wheeled vehicle--it will work, go ahead and try it yourself". You may be certain you can do it, but what's the use if you can't show such a thing?
Some claim the unbelievable and ask others accept it or to prove it for us. We all know this is poor behavior. But when these propositions actually do appear obvious and believable on the surface, the behavior somehow seems acceptable. The problem with this is that the "how obvious" mentality creates scientific dogma that in the past has lasted for over a millennium (for example, Aristotle's assertion regarding the four elements in On Generation and Corruption). This may be avoided today due to the huge number literate and educated people, but it still is a problem.
In essence, it's good to remember that individuals who have a solution to a problem should put as much effort as is reasonable into proof of it. This helps us all reach the truth.
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