Mathematics is full of signs which are often used as metaphors by non-mathematicians.My husband, for example, used to say: The distance from zero to one is bigger than that from one to two.I fully agreed with him, realising what he meant.However, I refrained from saying that was why he could not learn maths at school.But it would be a good thing if maths teachers realised that some children live in rich worlds and find it hard to strip down to the bareness of mathematical signs and equations.
A student once told me she saw Zero with a lot of tiny numbers floating around it like butterflies which showed possibly great insight into infinitesimals but which would not aid her in learning Econometrics or any other such nonsensical stuff hich was her chosen destiny.
And the precision and clarity [up to a point] of mathematics does not do well when applied to broader issues as a “friend” kindly pointed out to me before being very rudeNow we mathematicians criticise each other’s methods but we are rarely rude as it does not aid the mind.And it’s in the mind we live.Which is not a good idea but maybe we went there as a safe place when life was too much to bear.
For life is much harder than Mathematics,as King Lear might have said.
How my heart sings 
Well,that would keep me busy for a few months.:)
That’s a challenge I’d like to take up but where to put it on the ‘to do’ list? The interplay between maths and reality fascinates me. But, I gather that Hilbert said “Physics is too hard for physicists”, implying that the necessary mathematics was generally beyond them.
When maths confines itself to three dimensions then it can ‘follow’ reality but, when someone says “why stop at three'”, he has to determine new rules that will still work in a coherent and consistent way. Then it turned out that maths was ‘leading’ reality, when it later turned out that these new ‘rules’ work in the real world of quantum mechanics.
Yes, it is intriguing.Maybe maths is not as abstract as we imagine.It must come somehow from the sensual /imaginative world.I tried studying this once but didn’t get far.Concentration of a high order is needed.I am almost saying, if we can conceive of it, it must exist in some world [ perhaps of our invention…. or is it a discovery?]
I’m sure several of us would welcome more of your expert thoughts on this fascinating subject.
I recall reading this article in a journal in the Institute and liked it very much.Yes, the people you mention are giving a meaning to one thing that looks like another… there must be a name for that…
It’s such a pity that articles lapse into impenetrable jargon, which often introduces difficulties that are unnecessary to the arguments being made. I stalled at “The states are vectors in Hilbert space, the observables self-adjoint operators on these vectors” followed by “Let us not forget that the Hilbert space of quantum mechanics is the complex Hilbert space, with a Hermitean scalar product” I’m sure that David Hilbert and Charles Hermite would be delighted that their names are remembered in this way but it doesn’t shed any illumination!
Let us not forget that many people would like to read this if the authors understood how to make it more accessible.Of course this language is designed to keep people out.They would not admit it but it is for an elite.
Do you remember those full-page ads that some Eastern mystical sect used to place in newspapers? I recall that one suggested that the ancients knew about Einstein’s theory of general relativity because they wrote symbols that ‘look like’ Einstein’s equations.
I was an experimental physicist but knew that I had to turn to the mathematicians for a model to help me to understand my observations and to make useful predictions from them. Why is that so? It seems that mathematics and the ‘real world’ both follow the same consistent logical rules. Fortunately, a rather different logic from that mentioned in my first paragraph.
Eugene Wigner wrote an article about “”The Unreasonable Effectiveness of Mathematics in the Natural Sciences” – see http://www.maths.ed.ac.uk/~aar/papers/wigner.pdf
Brilliant post!!! First – I have the utmost respect for those who know math so well and then for those who can also teach! I have some absorption and endured thru upper stats classes with a satisfying A! And just to add to your thoughts on the value and overall applicability of maths – I know beyond a doubt that taking trig in high school helped me become a better problem solver and see other fruits!
Well said here
Thank you and I’m glad you found learning trigonometry helped you
Yes – and of course I am sure it helped my brain in ways I will never see or be able to measure !
Yes,it would do.
😊
It’s another language,you see.:)