In a scientific context, a hypothesis is a guess, based on current knowledge, including existing laws and theories. It explicitly leaves room to be wrong, and is intended to be tested to determine correctness (to be a valid hypothesis, it must be testable). The results of testing the hypothesis (i.e. running an experiment) may support or disprove existing laws/theories.
A theorem is something that is/can be proven from axioms (accepted/known truths). These are pretty well relegated to math and similar disciplines (e.g. computer science), that aren’t dealing with “reality,” so much as “ideas.” In the real world, a perfect right triangle can’t exist, so there’s no way to look at the representation of a triangle and prove anything about the lengths of its sides and their relations to each other, and certainly no way to extract truth that applies to all other right triangles. But in the conceptual world of math, it’s trivial to describe a perfect right triangle, and prove from simple axioms that the length of the hypotenuse is equal to the square root of the sum of the squares of the remaining two sides (the Pythagorean Theorem).
Note that while theorems are generally accepted as truth, they are still sometimes disproved - errors in proofs are possible, and even axioms can be found to be false, shaking up any theorems that were built from them.
I was referring to the difference between a theory and a hypothesis.
Theorem would also be interesting to add to the mix.
In a scientific context, a hypothesis is a guess, based on current knowledge, including existing laws and theories. It explicitly leaves room to be wrong, and is intended to be tested to determine correctness (to be a valid hypothesis, it must be testable). The results of testing the hypothesis (i.e. running an experiment) may support or disprove existing laws/theories.
A theorem is something that is/can be proven from axioms (accepted/known truths). These are pretty well relegated to math and similar disciplines (e.g. computer science), that aren’t dealing with “reality,” so much as “ideas.” In the real world, a perfect right triangle can’t exist, so there’s no way to look at the representation of a triangle and prove anything about the lengths of its sides and their relations to each other, and certainly no way to extract truth that applies to all other right triangles. But in the conceptual world of math, it’s trivial to describe a perfect right triangle, and prove from simple axioms that the length of the hypotenuse is equal to the square root of the sum of the squares of the remaining two sides (the Pythagorean Theorem).
Note that while theorems are generally accepted as truth, they are still sometimes disproved - errors in proofs are possible, and even axioms can be found to be false, shaking up any theorems that were built from them.
4 months later, sorry for the late reply. Thank you for this explanation! 😁🙏