>what stops an LLM from applying similar lines of thought* in a manner that results in a novel conjecture?

One thing is that an LLM can never assume, or find out, an inconsistency in its training data. Novel ideas often require correction of existing assumptions. As far as I understand, it is impossible, by design, for LLMs to contradict what is in its training data.

For example, an LLM trained on the data from an internet comprised of people who believe in the earth centric hypothesis can never say "Hey, that cannot be correct", or come up with the heliocentric alternative

But maybe it is not applicable to pure Math...