IF YOU LOVE OR USE MATH, READ THIS PLEASE:
i remember i read about Russell. About how he tried to "fix" the way people used math, to save it from incorrect proofs, to make sure math is controlled by logic and indisputable facts. I think he inspired me and should inspire you as well.
Thanks to him and other mathematicians such as godel and hilbert we know things we didn't know.
godel was the first to realize some questions will never have an answer (godels incompleteness theorems) although until that time EVERYONE (including Russell) thought every question has an answer.
Hilbert helped it in his own way, because he believed the opposite- every question must have an answer.
What im trying to say is nothing is "obvious" until you prove it.
and here comes the problem.
What is the proof our way of inferring one theorem is right because other theorems are right? What if the way we infer things is just like an exiom we can change, and get to new "types" of math just like exiom such as "parallel lines can meet" leads to no Euclidean geometry?
i also read about intuitionism that claims proofs by contradiction can't be used because we can't prove every sentence is right or wrong.
im definitely not the first one to think about this, but I can't think about math without thinking its roots are rotten.
Am i wrong? Am i right?
