Were the world’s most “difficult” math problems constructed to be unsolvable?
In: Mathematics
It’s not hard to construct a math problem that’s unsolvable. For example, 3x + 5 = 3x + 4 has no solution. There’s no value of x where that will make that equation valid. In a way “there’s no solution” is a solution because that’s the point when a mathematician will stop thinking about a problem
For an example of difficult unsolved problem, take the collatz conjecture. Let’s say you have some positive number. If it’s even, divide it by 2, and if it’s odd, multiply it by 3 and add 1. If you repeat these steps over and over again, most numbers will eventually turn into a 1. In fact, we have not found a number that does not eventually lead to 1. The question is, is this the case for all positive numbers? We don’t know. To solve this, we would either need to find a number that does not eventually reach 1(kind of like finding a value for X), or show that no such number could exist(showing that no value of x could possibly exist). Either answer would be good enough to solve the problem, but we don’t have either.
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