No, not everyone does. Physicists, for example, are sometimes known to maintain that math is only human models approximating underlying physical substrates, and that pure / theoretical math is an artificial construction whose validation depends on finding physical manifestation of the theory. That would put experimental physicists to the right (above?) the mathematicians.

But even if you did believe the mathematicians claim, by the same logic you would philosophy above them.

I think it pretty amazing reading physics forums where it seems clear that a lot of the people think mathematics is almost some kind of joke until substantiated by physicists. And then there was the usually insightful Lawrence Krauss's blanket dismissal of philosophy — while philosophical musings that contradict known data are problematic, much of philosophy lies outside the domain of physics.

Anyway, in regard to the idea of science "stack", I kind of enjoyed Alan Lightman's Reunion where he poses a nineteenth century astronomer's obsession with and histrionics in response to rejection by a cute young woman in his observatory as a kind of "proof" that biology studied more powerful forces. The event simultaneously lead to the astronomer abandoning his career and inspired hers in biology.[1] Though obviously meant as joke, the author himself transitioned from a successful career as a physicist to writing and teaching literature.

[1] http://books.google.com/books?id=4nQhY2fbX2IC&lpg=PP1&pg=PA1...

Disagreeing on the configuration is different than disagreeing on the existence.

Ok, I interpreted it wrongly. But I still don't agree. I've worked in academia and a NASA research center and never did I observe a respected scientist making such an observation. I know that's anecdotal evidence, but I don't know what else to fallback on.

I always thought that the old tired line of "X is the core science!" was a trap that only mathematicians, physicists, and ignorant grad students fell into. I wasn't aware that any respected (and respectful) scientists actually took it seriously.

I think perhaps you're still thinking of a value judgement. To me, it is obvious that we have different fields of science for different scales. For example, there are many aspects of physics that a biologist takes for granted or doesn't even reason about when considering biological systems. They may need to reason about, say, chemistry from first principles. But I would be surprised for many biologists to have to apply much reasoning from quantum mechanics.

Again, this is not a value judgement. A similar thing exists with computers. People who write web applications depend on user-application infrastructure, who depend on systems applications, which depend on operating systems, which depends on computer architecture, which depends on materials engineering and so on. As a systems programmer, I regularly reason about operating systems and computer architecture. But I never reason about the properties of the materials that make the hardware. The computer architects, though, may have to reason about the materials, as it can provide constraints to their designs.

As a general principle, it is always good to have at least some knowledge of 2 levels of abstraction below (and above) where you work, because they tend to leak!

Emergence it is!