Perhaps it is better to think of 'abstract maths' as being a language we have invented to describe what is 'out there'. Stuff exists, we we need to develop ways of describing the numerical aspects of said stuff, hence maths. Maths is something we invent in order to describe stuff that we discover.
Hi torridon,
Thanks for your post.
Some people argue as you suggest, but that would make maths subjective while facts point to it being objective.
Humans do invent the labels we use in maths - e.g. two, two squared, square root of two etc. But under each such label is an abstract reality, independent of the physical world, which is capable of defining relationships between all physical things - whether in units, distances, weights, momenta, spin, locations etc.
Firstly, humans invent words in national languages for theses realities (e.g. two, zwei, deux), then international symbols (e.g. 2), but the underlying realities must exist independently of these inventions, because they have an amazing propensity to forecst the existance of physical things of which we had no previous knowledge.
Higgs field and gravity waves are merely recent demonstration of this propensity. Quantum Mechanics itself owes much to Max Born introducing Heisenberg to mathematical matrices. These not only confirmed Heisenberg's work on hydrogen but also resolved problems with helium and heavier elements which Heisenberg had thought meaningless.
God bless