Dear Hasmukh,
You're absolutely right, focusing on the etymology and deeper interpretation of concepts in physics and mathematics. Mathematics and physics - two fundamental sign systems that are experiencing a crisis of interpretation and representation. It is necessary to understand more deeply the origins of mathematics, as indicated by Edmund Husserl in "Origin of Geometry".
The second important issue on which you do focus - understanding of space in physics and mathematics. It is necessary to re-interpret the ontology space. That is the task set by Husserl:"Only to the extent, to which in case of idealization, the general content of spatio-temporal sphere is apodictically taken into account, which is invariant in all imaginable variations, ideal formation may arise, that will be clear in any future for all generations and in such form will be transferable by the tradition and reproducible in identical intersubjective sense."
Fundamental knowledge, mathematics and physics, requires a deep ontological justification (basification). In fundamental physics is necessary to introduce an ontological standard justification (basification) along with the empirical standard.
Rabindranath Tagore gave a good hint mathematicians and physicists:
I ask my destiny - what power is this That cruelly drives me onward without rest?
My destiny says, "Look round!"
I turn back and see It is I myself that is ever pushing me from behind.
I invite you to see and appreciate my analysis of the philosophical foundations of mathematics and physics, the method of ontological constructing a new basis of unified knowledge - the primordial generating structure, "La Structure mère" as the ontological framework, carcass and foundation of knowledge, the core of which - the ontological (structural, cosmic) memory. I believe that the scientific picture of the world should be the same rich senses of the "LifeWorld» (E.Husserl), as a picture of the world lyricists , poets and philosophers.
Kind regards,
Vladimir