Duality

@CypherHoof

Actually, cribbing was a lot of how maths was transmitted in ancient times. Almost every Greek treatise we have only made it down through the millennia because people made translations and copies and even nicked large chunks outright to bolster their own expositions. 

@Stone Cold Steve Tuna

That comment on why 1 + 1 = 2 actually prompted me to research the proof of that equation; I've never thought of looking it up before. 

It's a pretty short proof (and relatively easy to understand) if you work using the Peano axioms, which are elementary enough that the system of mathematics that is constructible from them can't prove a lot of what conventional maths can. They centre around a primitive mathematical concept called the 'successor function', S(n), which outputs the natural (counting) number that comes immediately after the natural number n that you input. To put it in more familiar language, S(n) = n + 1, but the concepts of both '1' and '+' are defined by S(n) and the concept of 'n' is defined by the Peano axioms, so the chain of definition is formally the other way around.

Proof spoilered in case you're interested in the full step-by-stepping:

Ach, you're not alone when it comes to long division. I consider it one of my greatest mathematical achievements that I still remember how to use it. I hardly use it much nowadays, but I spent hours and hours as a kid trying to comprehend the method behind it before it finally clicked in my head and stuck.

Finding formulas from other formulas is an important skill. This ability is much to your credit. 

That cantaloupe comment is discriminatory against people who want to make a fruit salad in their bathtub. For shame.

My favourite season has got to be autumn. Balanced between freezing cold and burning hot, and without the abrupt deluges that come with spring. How about yourself?

Whenever I think of explaining why 1+1=2, I think of that scene in 1984 where they’re trying to explain why 2+2=5.

Hah, thanks! Guess I have a few good traits, though even a broken clock is right twice a day.

 I am okay with autumn. I prefer spring a bit more personally. Leaves aren’t falling. I used to love summer because then I got to swim a lot, but nobody I know enjoys swimming, so I don’t get to anymore. Were you ever big on swimming? Water sports?

Always hated that proof though.

It comes down to "define the '+' operator in an arbitrary system such that for some m and n, m=n+n ; define m as 2 and n as 1; assert that this is a proof that 2=1+1 in a completely different, arbitrary system"