If math is a such a definite subject with solid answers, how are there still unsolved math problems? How do people even come up with them?
In: Mathematics
You are thinking about math as the set of tools needed to solve a specific problem that has to do with numbers. That’s an accurate description of the math that people are taught in school.
However, when you are doing math in university (“real math”, if you will), you understand that the scope of the subject is very different. One thing worth noting – most mathematicians will disagree on what even is a proper definition of mathematics. For what it’s worth, I will give you my own definition: math is the process of deriving properties from axioms and definitions. In more ELI5 terms: math is about creating rules and definitions, and seeing what interesting consequences follow from those rules when applied to those definitions.
If you think about it in these terms, then you can see how open ended the subject is. You can come up with your own definitions or rules, see how they fit in the existing rules or definitions that other people agree upon, and see if using your own stuff creates any interesting results. As an example of this happening in real life – mathematicians used to think that infinity was just an absolute concept. But Cantor showed that if you looked at two different infinite sets and tried to match their items one by one, you could come up with some sets that would have infinitely many “unmatched” items left over even after you ran out of items on the other side. So he came up with a definition for two different types of infinity, based on whether you could match items of different sets with one another without running out of items on either side. So then lots of questions crop up – can you find some properties that only one type of infinite sets have, but the other one doesn’t?
I hope this gives you a sense of how and why the subject is open ended – mathematicians can come up with interesting new definitions and ideas, and then as they apply existing rules to them there is a whole host of questions that crop up about what general statements can be made.
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