Gauss QQC

Quote: "I mean the word proof not in the sense of lawyers, who set two half proofs equal to a whole one, but int the sense of the mathematician where 1/2 proof=0 and it is demanded for proof that every doubt becomes impossible."

Question: Is it possible to have that much proof for math? Where's the line between 'proof' and 'what just makes sense' in math?

Comment: Because proof, to me, can even be a picture drawn on a white board. It's not necessarily proof, but it certainly makes sense when it's explained. But even if I understand something, there's almost always going to be questions that come up at one point or another. Would that be considered a doubt? Or would that just mean the problem needs to be better explained for me to understand? It's just hard for me to imagine coming up with proof for certain math techniques unless you can physically prove it in the real world (which I know they have done already). All in all, I think this Gauss fellow is pretty witty, and I'm glad he was a critical thinker who thought that proof was just as important as the theory/technique. One thing I've come to realize is that in order for me to truly understand something-- especially in math-- I need to know why we do these steps, how this process applies to what we're solving, and why this makes sense in the first place. It's quite hard for me to find these answers on my own because sadly, I'm not quite creative enough to make sense of many mathematical processes--at least for now.