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Sure, that speaks to the usefulness of mathematics and the way it's constructed: perhaps the API analogy is the way to go about explaining it to others. Howeve

Sure, that speaks to the usefulness of mathematics and the way it's constructed: perhaps the API analogy is the way to go about explaining it to others. However, I am mostly talking about people (mathematicians even) who do not understand that something as basic as 2+2=4 relies on our faith that: 1. there exists "one", and 2. there exists a successor to "one" (simplified, for interested readers, look for Peano axioms). The beauty of mathematics and the human mind are in that everything else flows from there! Most of them would claim that this is universally true, whereas as a mathematician, one needs to understand the difference, and be open to, as you put it, playing with assumptions!

eru 5y ago
> However, I am mostly talking about people (mathematicians even) who do not understand that something as basic as 2+2=4 relies on our faith that: 1. there exists "one", and 2. there exists a successor to "one" (simplified, for interested readers, look for Peano axioms). The beauty of mathematics and the human mind are in that everything else flows from there! I don't see any faith in here: Math just says 'if something like 1 were to exist, and if successors were to exists (etc), then after a long chain of reasoning you could conclude that 2+2=4'. The 'faith' perhaps comes in when you go from '2+2=4' to eg two hens in my coop and two more hens in my coop means that I have four hens in my coop. (And that's not trivial! Not all things in the real world or even in math behave like that. For some not even as an approximation.)
- necovek 5y ago
  You are getting caught up in what mathematics does say: and you are right about that. I am contrasting that with what people think it says (i.e. 2+2 is 4), without understanding that there's an "if" in there. They take it for granted as indisputable truth, meaning that they have faith in those "ifs" being fulfilled.

eru 5y ago

> However, I am mostly talking about people (mathematicians even) who do not understand that something as basic as 2+2=4 relies on our faith that: 1. there exists "one", and 2. there exists a successor to "one" (simplified, for interested readers, look for Peano axioms). The beauty of mathematics and the human mind are in that everything else flows from there! I don't see any faith in here: Math just says 'if something like 1 were to exist, and if successors were to exists (etc), then after a long chain of reasoning you could conclude that 2+2=4'. The 'faith' perhaps comes in when you go from '2+2=4' to eg two hens in my coop and two more hens in my coop means that I have four hens in my coop. (And that's not trivial! Not all things in the real world or even in math behave like that. For some not even as an approximation.)

necovek 5y ago
You are getting caught up in what mathematics does say: and you are right about that. I am contrasting that with what people think it says (i.e. 2+2 is 4), without understanding that there's an "if" in there. They take it for granted as indisputable truth, meaning that they have faith in those "ifs" being fulfilled.