A mathematical law is very different from a theorem. A law is something that is fundamentally accepted to be true but it cannot be proven. A theorem can be proven to be true (or false) using the laws of mathematics.
this post was submitted on 05 Aug 2024
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English being weird strikes again. You’d think they’d be swapped but no.
English was not engineered from the ground up to be sensible and consistent. Instead it evolved slowly over time, as new things got tacked on year after year, and other things died out or drifted in pronunciation.
Here's what Middle English sounded like:
"Whan that Aprille with his shoures soote, The droghte of March hath perced to the roote, And bathed every veyne in swich licóur Of which vertú engendred is the flour."
-Chaucer's Canterbury Tales
I wonder how that is pronounced vs today. I imagine the spoken version drifts, but the sounds are more similar than the writing.
We can't know for certain, since no audio recordings exist for obvious reasons, and we'd need a time machine to find a fluent, native speaker we can be confident is using period-correct pronunciations.
We can make educated guesses though, by deconstructing existing descendent languages and tracing back commonalities.
Here's what we've got so far:
Also worthy of note that this sort of writing would've been distinct from daily commoner chit-chat, which would probably be more recognizable to us. Not sure how much of that got recorded and survived through the years though.
I think this is straight forward. In our everyday life laws aren't derived from something else either. They just are. And OP seemed to have a hierarchical view of them as well. They were just under the assumption that a theorem could be "promoted".
I guess a real-life analogy would be a judge making a ruling under some laws. That would make a precedent in many countries but not a law. If then a new law were passed it could invalidate that precedent similar to someone disproving a theorem.
A law is something that is fundamentally accepted to be true but it cannot be proven.
Counterexamples: The law of sines and law of cosines in trigonometry.
Math laws are basically axioms, which means Assumptions we hold to be true.... meaning they are unprovable, if you could prove them from other axioms, then they would be theories and you wouldn't have to make a new assumption.
Everything else is built up on the assumptions and are called theories, assuming the axioms are correct.