when matematicians solve some problem that has’nt ever been solved how do they know they got the right answer and they did the right steps ?
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Usually what we need are proofs.
You state something lets call it a conjecture and if mathematics is consistent that conjecture is either true ore false.
Ok but how do you prove it that is the question. It depends but there are general ways statements can be proven. In theory the easiest way to think about it is that if the statement is in fact true assuming the opposite leads to a contradiction. If you can show that, then you have proven your statement. When mathematicians do this its called an indirect proof. Its not always the best approach but thats the core idea.
But to answer your question exactly, we know we got the right answer because we knew what the answer had to be and we had started from solid proven ground, taken logical steps and got what we were looking for.
Finding the steps that lead you towards the solution is the job. You can make an incorrect step which is a mistake, your step either makes or doesn’t make sense in math thats obvious. You can make a correct but unnecessary step, you didn’t get cloaser to the solution or you did the right step.
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