How did unsolvable math problems ‘start’? How can you have an answer but no idea how to get there in maths?
In: Mathematics
I’m going to assume you’re talking about unsolved problems, because your description sounds like it.
Thing is, most of the time they’re not like your normal school problem which is like “which number is the solution to this equation?”
More often it’s like “There is no number that has property XYZ?” People try it with very many numbers (nowadays with a computer) and if they find that the first gazillion numbers don’t have property XYZ it’s a clue that probably no number has. So we think it’s probably true (and call the statement a “conjecture”) but that’s no proof. There might still be number so large we haven’t checked it that has XYZ.
Solving the problem means proving that it’s true for all numbers that exist, which takes an abstract argument because you can’t just check infinitely many numbers.
So how does such a problem come about? By noticing a pattern. Much of mathematics is noticing patterns, then finding out what reason they have — which is sometimes very hard.
I hope that was your actual question, if not, sorry.
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