Surely that is an assumption based on your own bias, I have found that mathematicians can be quite aloof about their own discipline tbh....I live with a couple of them.
Yet that again is simply an assumption, you are basically dismissing any kind of explanation in favour of..."don worry your pretty little head about it, you wouldn't understand anyway"....
Surely the idea would be to explain why, in laymans terms or even pointing someone in the direction of a source than if you are unable.
Well, school is about preparing students for the world, a world where the vast majority of them will only use mathematics as a functional tool and will never question why something must work that way......and if the only answers they get when they do ask are "you wouldn't understand anyway" no wonder they are put off.
I'm not assuming anything, someone who thinks 1 orange + 1 orange = 2 oranges is a proof of 1+1=2 does not know what they're talking about. I don't know about other mathematicians, but I've tried explaining mathematics to friends, family and my partner - no-one gets it, so we give up. Plus we live in a world where people think it's "cool" to be bad at maths, chat **** about the subject while going around taking full advantage of things created thanks to mathematics (such as the internet, mobile phones, cars etc.)
I'm not dismissing explaining something, but trying to explain why 1 orange + 1 orange = 2 oranges isn't a proof is very difficult because it's such an absurd thing to say to start with. Explaining why 1+1=2 isn't straight-forward, and requires years of knowledge from undergrad mathematics, probably why you find a lot of mathematicians not as forthcoming when it comes to explaining. Very few things can be explained explicitly without needing to then explain something else, then something else. Many proofs are essentially a proof, within a proof, within a proof. So sometimes trying to explain something, to someone who doesn't know about mathematical rigour, which appears simple to them like 1+1=2 actually requires a hell of a lot of mathematics.
Also, school isn't really about preparing students for the world, look at physics, chemistry and biology - the vast majority of it isn't relevant to real life at all. The real reason they teach functional mathematics in schools in the UK is because it's too difficult to do otherwise. If you look at how other countries teach it (even in the EU) it's done much more rigorously, and even hints upon analytical mathematics, which is something you'd need to know a lot about to discuss proofs.
Seems like we've got a pure mathematician in the house
Ignorant engineer inbound . . .
I believe that maths has to be taught as a functional tool at the younger ages; you're not going to be able to teach (most!) <16 year old kids to appreciate the full sphere of mathematical reasoning and logic. My first encounters with the more abstract concepts (complex numbers, group theory etc) came when I was 17 and doing IB maths - I'd chosen higher level maths at this time as I had a genuine interest in the subject, rather than doing it out of necessity.
Haha, I only sound like a pure mathematician because what's being discussed is very pure (and I have to do it in my degree - so I don't have a choice in the matter). I actually much prefer applied maths (I was going to do aerospace engineering, before I was stupid and accepted an offer to do straight maths)
I do agree that most people won't be able to appreciate "proper" mathematics, but other countries teach mathematics to young people very differently with very basic analysis - to get people to appreciate the rigor you need in mathematics, which would probably greatly help people understand the subject better.
