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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There are a lot of mathematical (and scientific) questions that can be solved in different ways.
The most easy to understand is that sometimes we know the question and we know the answer, but we don’t know how to work it out. A method to calculate the answer is a “solution”, and we can check that against lots of different scenarios to see if it holds up.
Think about the moon’s position in the sky. The question is “what will the moon’s position be at 1am?”, And we can find the answer by looking up at the sky. If someone came up with an equation to calculate it we could easily check against the correct answer by just looking at the sky. Then we can redo it for 2am to double check.
These things are useful because we can then use it to estimate the answer for times when we can’t see the moon, maybe midday when the sky is too bright and the sun is up.
(I pulled the moon example out of the air. Don’t take it literally)
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