How are there unsolved math problems?
In: 9
Many unsolved maths problems are general-type statements of the form:
“For all known integers, this rule/scenario applies….”
“For all known examples of [scenario] there is/is not a solution that fits this pattern….”
“There is no integer solution to [extremely complex and detailed equation]..”
etc
These are things that can be very difficult to prove, because the set of numbers is infinite. If we haven’t found an solution to a scenario with all the numbers we’ve tried, that doesn’t necessarily mean there’s no solution, it’s just that it hasn’t been found yet. It’s entirely possible some enormous or specific number will indeed fit the solution. Similarly, just because every integer we’ve tested satisfies a pattern/rule/scenario, doesn’t necessarily mean that every single possible integer in existence will as well.
So it’s not like people can just brute force or trial-and-error a solution (x + 1 = 3….does it work if x=1? No. Does it work if x=2? Aha!) To solve these problems, they would somehow need to construct a general rule, and prove that it can work for all numbers or all scenarios outlined in the problem.
Latest Answers