Science can sometimes seem like a pretty cut and dry concept, but the things people can categorize as 'science' and 'not science' differ by place and time. Science has have specific associations with political authority and elements of culture. To some, science might be seen as a progressive force, and to others it could be corrupting and destabilizing. Science is also related to modes of authority; who does and doesn't get to call themselves a scientist can often determine who is in a position to labeling things as true or false.
I don't know much about the history of the Soviet Union, but even a brief glance at the writings of people like Lenin, Trotsky and Stalin shows they placed a heavy importance on describing socialism as a science. I understand this has a history behind it, related to Marx and Engels' view of knowledge as the empirical observation of a materialist world. However, this understanding of Marxism as a science would have traveled a far distance in time and space to reach Lenin, and I'm wondering how Lenin (or other Bolsheviks) would have regarded 'science.'
From what I understand, Lenin was himself a rather skilled university student, and his tenure as a professor was a key part of his political development. His relationship with intellectualism also seems to be important in conceptualization of a 'revolutionary vanguard.' How would he have understood 'science,' given both his background and Russian culture's relation to science at the time?
Great question!
The idea that Marxism is a "science" was practically tautological among Marxist thinkers in the 19th century, and core to Leninist dogma as well. It is meant to elevate it beyond a theory or practice of government, and make it into a truth-generating system. It is worth noting that if you want to say, "but it's not falsifiable, that means it's not really a science" — that is literally exactly what Karl Popper would say, and "is Marxism a science" was literally one of his canonical examples for creating the falsification criteria.
Leninist philosophy of knowledge and science centered around a few central ideas. One is the aforementioned one that Marxism was a science, that it was a system of analysis of the world that told you hard truths about it — such as what kinds of power relations you'd expect to come out of a given historical situation, and how to essentially predict the future of societies. It's a sort of economics-political-sociological hybrid in this model. This is how it would have been ideally understood, but in practice this was also a way of asserting that Marxism took priority over all other competing forms of knowledge about the same thing (like, say, sociology).
The full articulation of Leninist (and later Stalinist) philosophy of science is what was known as dialectical materialism. It's a kind of rough combination of Hegelian philosophy (a teleological notion of historical change as being thesis plus antithesis equalling synthesis) and hardcore materialism (all in the world is matter and energy, nothing else). What it meant in practice though often came down to one main principle: All forms of inquiry exist in separate spheres. Physics does not reduce to chemistry which does not reduce to biology: they are all different ways to look at the world. Insight from biology cannot tell you about sociology or politics. This is a way of insulating Marxist theory from any possible attack by competing forms of knowledge. This is known as a form of anti-reductionism. It also ends up meaning that on any matters with social consequences, you had to harmonize your work with Marxist theory first (and if your work contradicted Marxist theory... watch out!).
This started as kind of a loose ideal under Lenin and became a form of (deadly) dogma under Stalin. Stalin himself, after he took power, formulated these into "dialectical principles" that had to somehow be wound into any major theorizing: "Law of the Transformation of Quantity into Quality," "Law of the Unity and Struggle of Opposites," and "Law of the Negation of the Negation." Yeah, I don't know what those mean either — I don't think anybody really did, which is why either the approach people took was to just say, ad nauseum, that of course their work showed all of these things to be true, or they avoided theoretical investigations at all (e.g., they focused entirely on improving practical matters, which was "safer"). Fields that failed to adapt had problems (Cf. Lysenkoism, cybernetics, even some theoretical physics in the USSR).
A separate question you ask is how Lenin regarded science and scientists. It's a tricky thing. One the one hand, like many "modern" materialists of the late-19th century and early-20th he held up the triumphs of science (and technology) as being absolutely central towards making a society and world that avoided the retrogressive ideas he attributed to monarchism, religion, and other "backwards" forces. On the other hand, Lenin had a hard time brooking any kind of contradiction to power, and science can end up doing that very easily.
There is an article I like very much about Lenin's idealized view of science written by the historian of physics Alexei Kojevnikov, and he puts it this way:
"In the center of their ideal world was an imagined agency, called Party. This imagined Party should not be confused with the real one… The ideal Party was supposed to command single-handedly the knowledge of true politics, and therefore justifiably monopolized political power. …
"The same Party was also the bearer of another kind of higher knowledge, the knowledge of true values and higher meanings of the world, society, and history… this kind of higher knowledge went by the name Ideology and was thought to be contained in the specific body of classic text by Marx, Engels, and Lenin. Although in practice and the dominant meanings extracted from those texts fluctuated drastically and often unpredictably over the years, this inconsistency, like the difference between the ideal Party and the real party, could not be explicitly acknowledged in public discourse.
"Even in the world of communist dreams, however, the ideal Party was not expected to command the third kind of higher knowledge, the knowledge of the natural world. For this, Bolsheviks imagined a separate ideal agency which they called Science. … Science as an ideal agency enjoyed a very high status in the Bolshevik world, compared to that of Party and People (or Proliteriat). Bolsheviks knew that Party could not rule without relying on Science, in order works, that Power depended on Knowledge. On the other hand, they insisted that Science could not be separated from politics and ideology, in other words, that Knowledge could not be independent of Power. … The relationship between them could be nothing short of preexisting harmony..."
This is a sort of metaphysical rendering of an underlying model, not some specific Leninist writing. But I think it paints a compelling picture: ideally, the Party would be guided by Ideology that would work in harmony with Science. And if that harmony wasn't happening.. it's probably not Ideology's fault, it's something wrong with the scientists. (Cf. the problems under Stalin.)
There is more that can be said but I hope this paints something of the picture.
On Russian and Soviet philosophy of science, see Loren R. Graham, Science in Russia and the Soviet Union: A Short History (New York: Cambridge University Press, 1993). The Kojevnikov quote comes from Alexei Kojevnikov, "Dialogues about knowledge and power in totalitarian political culture," Historical Studies of the Physical and Biological Sciences 30, vol. 1 (1999): 227-247, on 231-232.