it's more like philosophy is the dumping ground for stuff that we don't understand well enough to formalize and place in its own little box. that means that it changes with time.
so there was a point when foundational issues in maths and logic were philosophy. the importance of frege, and then later peano, russel, etc, is that they were the ones that found a way to attack that set of problems, letting us isolate a chunk of knowledge as logic, set theory, etc.
a similar process is probably happening now with consciousness - we're starting to develop the tools to answer questions that are currently "philosophical".
Exactly. Claiming that Philosophy never answers anything makes one hell of a selection bias. When Philosophy answers something, it ceases to be Philosophy.
"Without mathematics we cannot penetrate deeply into philosophy.
Without philosophy we cannot penetrate deeply into mathematics.
Without both we cannot penetrate deeply into anything." _ Leibniz
There is mathematics in it, but it's not just mathematics; it was originated, and is still used in areas like AI, as an attempt to formalize thought, i.e. a kind of formal philosophy. A good portion of the foundational work was done by philosophers (e.g. Frege, Russell), and a lot of current work (especially in modal logic) is done by philosophers as well.
Usually logic is considered part of mathematics. However, in an important sense, logic precedes mathematics. You can't do mathematics without using logic.
Many have, take the sort of mathematics done in order to understand physics. Logic is the study of formal reasoning. Mathematics is the study of form and structure. It took R&W's Principia Mathematica to attempt to show that the entirety of mathematics was rested on a logical foundation. That's pretty recent on the scene if you think about the history of mathematics! To me, the idea you expressed, seems like a very 20th century thing.
Unless you are a true original in every sphere, then we can make a reasonable guess that the majority of what you believe lies within the known sets of human beliefs. Then from observing your actions and reactions to stimuli, (ie, your interaction on this board), we could extrapolate from there and make a reasonable guess on your beliefs on a wide variety of subjects. It won't be absolutely correct, obviously, but it won't be a complete shot in the dark either.
That's math, though, not philosophy.
The difference: Math is a symbol game that occasionally produces useful tools for other fields, whereas philosophy is a discussion of human problems.