For seeing whether a given statement holds true, minimizing complexity is the most important.
Precisely, and that's the main difference between computer science and the rest of mathematics.
Typically CS cares about the process to find a result, and not just its value nor the possibility or impossibility to find it.
Typically, programmers care about the process to find the result. Some programmers are computer scientists. You can not conclude that all computer scientists are programmers, so your statement is based on logical fallacy.
There are results in theoretical computer science that don't care about the efficiency in the process; the most essential are the computability theorems exploring what parts of mathematics can be computed, and what we mean by computation anyway.
But the most essential part -the halting problem- was resolved long ago, so the lion's share of applications of computing science is in finding practical ways to use computers, which again needs to take efficiency into account.
Efficiency and tractability of representation is also an issue, though, and mathematicians (and programmers) do care about that, a great deal. That's why the lambda calculus has been used as the basis for proof assistants such as Coq, whereas Turing machines have not.
Sometimes that could mean using the lambda calculus, particularly in study of language theory and type systems. Other times that could mean some sort of black box model, such as when proving lower bounds for solving problems using specific operations (see e.g. the sorting lower bound). Yet other times, like when establishing the ground-zero of some new variety of computational hardness, I can't think of many more suitable models to cut up into pieces and embed into the substrate of some other problem than those based upon Turing machines.
My original comment certainly reads that way, but my intent was really to point out that it doesn't make sense to privilege the Turing machine model in the study of computation. I wrote more about why in this comment: https://news.ycombinator.com/item?id=27334163
As I said above, it may very well be that the best usage for Turing machines is using them in mathematical proofs; where the efficiency of the computation is not a concern.
This response might come off as a little facetious, but seriously, I think the idea of "founding" industrial computing languages/platforms upon theoretical research models of computation misunderstands the relationship between theory and practice. There is a relationship for sure, the research on these models usually does want to translate into real-world implications somehow, but your functional programming language is not the literal lambda calculus.
Each time a new theoretical model is created to represent a particular programming problem, entirely new languages are created to ease the practical approaches of building systems for the underlying problem.
And it is worth keeping track of which models are good for which problems. So no, theoretical models are not good just for doing math with them, also for guiding practical usage.
That was a claim someone made, but it turned out to be a misunderstanding, and is incorrect.
I've covered this here: https://news.ycombinator.com/item?id=27338055 (see the parent comment for quotes from Godel & Church that I'm referring to.)
Computing science cares a lot about building efficient processes. Thus to create real working programs, a better basis is a combination of lambda calculus for defining mathematical structures and (Von Neumann based) agent-based models for defining stateful processes.
Modern programming languages are evolving to be capable of representing either model, to adapt themselves to the style more suited to the problem at hand.