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The premise is simple, what are some conceivable areas of science where development could happen a lot earlier. Obviously things such as quantum mechanics would have to wait for their pre-requisite knowledge and technology.
To start off I'd like to suggest genetics or at least hereditary studies; its amazing to me that no one published a systematic study of inheritance until Gregor Johann Mendel in 1866. This was something that could've easily been done within a few plant life cycles and would've had a massive impact on selective breeding in agriculture in contrast to OTL's poorly understood methods of selective breeding.
Marketing and psychology: both social sciences that in the right environment could've blossomed. I think it wouldn't be hard in any sufficiently large market with guilds/institutions that retained and taught both sciences.