A common misunderstanding about "proving theorems"
I want to share an experience which occurred me a three years ago.
I was chatting with a colleague of mine, a more-than-talented engineer (actually a genius), about relating with professional people in meetings.
Just pardon us - this is the kind of subjects you deal with somewhat before the first coffee break, when blood level of sugar is very low (at least it was, in my specific case).
And maybe was just this lack of brain food which induced us on the verge of a quite philosophical side.
During the chat, my friend said:
"Oh, that's so! You mathematicians always prove all." (he was very generous, pretending I was a mathematician thank to a degree I've got an eon or two ago) "That's unfair!"
I was stunned. And my surprise grew as he clarified the concept: according to him, relating to other people meant more or less taking a stand on something, waiting others to take their counter-stands, then confronting head-to-head until one prevailed over the others. (As he said, the fight often went on for excruciating hours, until all left the meeting room each stick on their position).
In his view, packaging some argument as a "proven theorem" made it unassailable, leaving no space to the ensuing contest: a way to "always win".
But, it isn't! That exchange made me reflect for some days, until I realized how far our starting points were. Funny!
My friend joke connected with many other things I had heard in the past.
It reminded me of a past geological era when a professor resented terribly I had used the word "theorem" for a micro-result I placed in my thesis.
Of others, who said the class how giving your name to some important theorem might change your life.
Stating and proving "theorems" seemed imbued of status-seeking, a dimension I was entirely blind to, until the puzzle composed.
Then I turn to reality, and see an entirely different thing:
We all (mathematicians and not) "prove" "theorems" continuously.
They may not always be of mathematical nature (although sometimes are). Most often have to do very much with day-to-day applications of commonsense and logics.
Building "theorems", and proving them, may well be a way of communicating, and often a collaborative task. The need to "prove" logically a statement is of immense importance, if the statement resulted from some intuitive process. Results from intuition are almost invariably so personal and complicated, that just explaining them demands a lot of unraveling. And once you have sorted your "discovery" enough, then it is safe to validate it. Helping to unravel and validate are two important uses of proofs.
Is this important?
I imagine so. Assuming mathematical results as something definitive, stated as an absolute truth, contributes a lot to the image of the inaccessible, self-centered mathematical nerd many girls and boys desperately try escaping from.
Sure, we will make a good service if we spoil logics of its weapon-like image. Some people may love it, and that's OK. But I think it's superfluous.