What remarkable advance could not have been made without belief in evolution?
"But science is only a method of describing the physical universe, which simply cannot be used to examine non-physical topics."
Evolution is just such a non-physical topic. It is a philosophical belief, unobservable and untestable. Evolutionary 'theories' such as punctuated equilibrium actually predict that evidence to support them cannot be found.
This is clearly philosophical no matter how many times you claim that it is not.
PubMed is the largest and most widely used medical/biological research database in existence. It also contains a wide variety of articles from other disciplines.
A search with the keyword "evolution" returns 311,652 hits. Keeping in mind that "evolution" has other meanings unrelated to the theory, I read the titles of the articles on the first two pages of hits. Out of those, 26/40, or 65% were studies directly examining evolutionary principles. Of the remaining, the relation of 6 (15%) to evolutionary principles was unclear, and another 7 (17.5%)were clearly not related to the theory of evolution. The remaining article was, in fact, a letter to the editor about one of the evolutionary articles, so I did not categorize it.
Since discussion of the theory of evolution involves a fairly specialized vocabulary, I also did a search of "phylogeny", a method of examining evolutionary relationships. This resulted in 106,145 hits, all of which discuss evolutionary research, since phylogeny has no alternate meanings.
This is by no means an exhaustive listing of research related to evolution: many people base their research in evolutionary principles without ever using the terminology. Any time animals are used in a study as proxies for human disease, evolutionary principles are being applied. The testing of prototype drugs starts on simple organisms, and works its way up through organisms that are more and more closely related to humans, until the last stage before human testing is in non-human primates--this whole testing scheme becomes totally meaningless if one tries to pretend that nothing has an evolutionary relationship to anything else.
The field of microbiology uses the theory of evolution extensively. Microorganisms evolve constantly, which puts selective pressure on us to evolve, which puts pressure on them, etc., in a kind of biological arms-race.
Whether you choose to accept the scientific evidence, or you continue to deny its existence because you feel that acknowledging it is equivalent to admitting that there is no basis for religious faith is up to you. As long as people with your attitude don't have the ability to direct that religion be taught in science classes, or to withhold research funding for evolutionary research, I really don't care. Personally, I have not bought into this ridiculous belief that God can't possibly exist if the Genesis creation story isn't literal.