My answer to question on Quora: What do you think about opinion that Mathematics is mother of all sciences?
I doubt that mathematics is mother of psychology. Or of astronomy; I share a view of those historians of mathematics who suggested that it was astronomy that was the mother of mathematics. Or of physics.
I am prepared to treat with respect — even if I disagree — rather extreme views on the place of mathematics in human civilisation. I quote, for example, from Vladimir_Arnold’s paper On teaching mathematics:
Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.
The Jacobi identity (which forces the heights of a triangle to cross at one point) is an experimental fact in the same way as that the Earth is round (that is, homeomorphic to a ball). But it can be discovered with less expense.
Indeed let us turn to astronomy and make a thought experiment. Imagine that in the last ten thousand years the climate on the Earth was slightly different: with the same temperature an precipitation, but with a mist in atmosphere which did not decreased the luminosity of sunlight (so that agriculture is not affected), but scattered light, turning Sun and Moon into diffused light blobs and completely hiding the stars. Would mathematics have a chance to develop? For millennia, the starry sky was the only source and standard of precision — and, until relatively recent times when more precise periodic processes were discovered (thanks to physics) — absolute precision). Would mathematics develop beyond basic arithmetic and primitive geometry for agricultural use? Would the concept of mathematical rigour emerge?
In my opinion, very complex interactions between sciences do not fit into a crude “mother-daughter” simile.