system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: With "unsolvable" math problems, how do people come up with the problem and why do they think the problem is worth solving?
gpt
I am assuming you are referring to math problems which have not been solved, but may be solved in the future like the and Riemann Hypothesis. These problems are usually conjectures (sort of like a hypothesis in science) meaning that they appear to be true for every number, but we have not been able to prove it. Testing every number is impossible since there are infinitely many numbers so mathematicians use mathematical rules to try to come up with a proof and show that the conjecture is true for for all numbers. An example of this is the famous Fermant's Last Theorem that no three positive integers a, b, and c satisfy the equation a^n + b^n = c^n for any integer value of n greater than two. While it appeared to be true for all numbers it took mathematicians 400 years to prove that it is using some very complex mathematics.. These problems often do not have obvious real world applications, however the our understanding of the physical world tends to play catch up with mathematics meaning that they may very well be discovered to have physical meanings in the future. That being said there are math problems like the Continuum Hypothesis which appear to be truly unsolvable and they arise from the axioms of mathematics.