I think we need to get clearer on what “why,” “something” and “exists” mean.
For example, if you assume that numbers “exist”, that is, you are willing to attach the descriptor “exist” to numbers, then you already have your answer: “Because numbers exist necessarily!”
Voila! End of story! Move over, folks, nothing(...) to see here.
Still, if you think that numbers are “something” and that they “exist,” then it still doesn’t answer why THE PHYSICAL world exists, or consciousness. I guess that now you can follow Tegmark’s footsteps and say that everything is mathematics, and that’s it. (But maybe there is a separate answer?)
So now (for Platonists) the “why” question is not why something exists, it is how to prove physical existence from the necessary existence of numbers or mathematical structures.
So like I said, before one tries to answer this question one first has to give some working definition as to what “why,” “something” and “exists” mean.
So when you ask, “Why did Sherlock Holmes tell Watson that...?”
You assume that Holmes exists?
Also, when you ask why some complicated theorem in number theory is true, you are basically asking for a proof from first principles (say Peano Arithmetic), you don’t need to assume that numbers exist (which would make you a Platonist).