one and one is two ones

I was taught in school, and it seems to be generally accepted in our civilization, that when you add one and one the answer you get is two. But if you ever ask a mathematician what ‘one’ and ‘one’ is, he or she will answer instantly, 'two ones'. I don't think it's an abbreviation thing. I think 'two ones' is the right answer. So what? ,you might ask. Indeed. I too have asked that exact same question. It bubbled around in my head for a few years. The zen simplicity of ‘who cares?’ ‘what’s the difference?’ comforted me for a time but I couldn't ignore the inconsistency once it was pointed out, and a strange unbidden sense of outrage grew. It must be like that feeling a business owner gets when he discovers a close friend and colleague has been embezzling your companies funds for the last 20 years. At first the mind refuses this information. If he was sleeping with my wife I could understand it, but this… It's that moment in a Hollywood movie when the room spins around. That sense of outrage a motor tax payer feels when he runs over a pot hole eventually gave way to wonder. The implications, of this correction (to the answer of the sum of my two ones), will be lived out ever day and written about on occasion. Everything just got a whole lot more interesting.