Euclid's Elements is less pervasive on the Internet then content produced for Liberal Arts math courses. As those courses tend to emphasize critical thinking and problem-solving math over pure theory and advanced concepts, they tend to be far more common and tend to win compared to more domain specific meanings.
Problems with polysemy across divergent, more advanced theories has been one of my biggest challenges in probing some of my areas of intrest.
Funny enough, one of my pet areas of obscure interest, riddled basins, is constantly muddied not by math, but LSAT questions, specifically non-math content directed at a reading comprehension test: "September 2006 LSAT Section 1 Question 26"
IMHO a lot of the prompt engineering you have to do with these highly domain specific problems is avoiding the most common responses in the corpus.
LLM responses will tend to reflect common usage, not academic terminology unless someone cares enough to change that for a specific case.
Examples:
https://en.wiktionary.org/wiki/Euclidean_geometry
https://www.cerritos.edu/dford/SitePages/Math_70_F13/Postula...
Problems with polysemy across divergent, more advanced theories has been one of my biggest challenges in probing some of my areas of intrest.
Funny enough, one of my pet areas of obscure interest, riddled basins, is constantly muddied not by math, but LSAT questions, specifically non-math content directed at a reading comprehension test: "September 2006 LSAT Section 1 Question 26"
IMHO a lot of the prompt engineering you have to do with these highly domain specific problems is avoiding the most common responses in the corpus.
LLM responses will tend to reflect common usage, not academic terminology unless someone cares enough to change that for a specific case.