Well, for instance in computer science all the theorems are completely culture free, so it is not impossible. But it is indeed difficult, and to be expected for the most part.
You are making a category error here. Culture doesn't produce a theorem (or a work of art, or a [fill in the blank]), but the people that did produce it necessarily operate in a culture. Among other things this affects what work gets done supported, what people do it (and get supported), how the results are communicated (and if) etc. As a student it effects what you are taught, what you are told is important, and what areas you are pointed towards.
You can't tease this stuff apart. Part of the process of becoming a scientist is to become acculturated to that science.
Yes of course there are cultural influences. But it seems some branches of STEM are fairly immune to the opinions of the surrounding culture. E.g. what can we say is victorian about any mathematical conclusion? Yet Darwin's supposedly scientific conclusions in this work appear to be very culture bound.
i guess i'd argue that the more abstract something becomes, the more its original motivations tend to be obscured. this is the nature of abstraction, for better and worse.
i'd hesitate to say though that this means more abstract ideas are less culture-bound in the sense of being value-neutral. an abstract idea still carries at least the implicit assertion that this is an idea worth paying attention to, at the unavoidable opportunity cost paying attention to others. and ideas which seem entirely free-floating are probably worth paying special suspicion to.
Yes, the maths that underpin a nuclear power plant exist independent of any culture, but the same cannot be said of the decision to deploy that plant in a rain forest on the edge of an ocean where a village has survived for millennia.
I would agree with that. There is often a practical question motivating comp sci and mathematical discoveries. The difference from Darwin's case is the mathematical conclusions are never wrong, regardless of the underlying motivation. That is what I mean by culture free. Change in culture cannot change the validity of mathematical deductions. On the other hand, Darwin's conclusions in Descent of Man are wrong, and he appears to have drawn these conclusions due to his cultural bias.