How did unsolvable math problems ‘start’? How can you have an answer but no idea how to get there in maths?
In: Mathematics
If, by unsolvable math problems you mean problems that haven’t yet been solved then these often come from mathematicians playing around with some mathematical concept, noticing something that seems to be true but not being able to actually prove that it’s true yet.
As an example, one of the biggest open problems in maths is the Riemann hypothesis. For an eli5 explanation of what this is, we have a function, called the Riemann zeta function that takes two numbers, does some maths and gives you two numbers back (technically it takes a complex number as an input and an output, but you can just think of those as being made of two real numbers). Mathematicians have noticed that the only way they can make this function give you (0,0) as an output is either to give it (-2, 0), (-4,0), (-6,0) and so on or to give it a half as the first number (to clarify, it’s not (0,0) for any pair of numbers where the first one’s a half, just some pairs). As they experimented with this function, they couldn’t find any other way to make it give you (0,0), so some mathematicians started to suspect these were the only ways to make it give you a zero. But they haven’t worked out exactly why these are the only ways yet and they can’t say for sure that there aren’t other ways that they haven’t thought of yet.
Latest Answers