Recently I was learning the maths of basic orbital mechanics, a topic of which some variations are not extensively covered online. Something that came up often

Recently I was learning the maths of basic orbital mechanics, a topic of which some variations are not extensively covered online. Something that came up often in my application was wanting to express some orbital elements as vectors rather than scalars, to be able to do some things more concisely (and avoiding having slow trigonometric functions strewn all over my code) For trying to figure these out, generally GPT-4 performance was poor on accuracy and I was using it just as a tool to look up terms I would plug into google to find a better source that won't confidently lie to me. However sometimes it was doing an admirable job of transforming mathematical terms. This often can be done with just knowledge (like knowing sqrt(2)^2 = 2) and applying transformations on tokens - which is very much in the scope of these AIs. Technically that isn't much logical deduction yet, but there was a few cases where it impressed by stating things like "Since we know vectors K and V are perpendicular, we can ...". Certainly looked like the beginnings of some basic logical deduction sometimes - even if getting halfway correct answers required me to restart prompts a dozen times each.