Is science based on philosophy?

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>Could science exist without philosophy?
No, you can't prove science with science itself, you need some epistemological basis for it. For example, you can't solve the problem of induction without involving some metaphysics.
>Could philosophy exist without science?
Well, it did for centuries.

>>3200723
>Is philosophy the root of science?
sort of
>Are all science and scientifical progresses inherently tied to philosphy?
depends on the angle you're trying to push here
>Could science exist without philosophy?
no
>Could philosophy exist without science?
it did

Science and philosophy used to be the same thing.

Kind of. What we today call the natural sciences used to be considered no more or less legitimate than what we'd call the occult, metaphysics and theology. A learned person would have been expected to have knowledge of all of them.

philosophy was supposed to be a bridge between science and religion but then philosophers started masturbating in public

Is math related to science ?

>>3200766
Science can exist without philosophy, if you are talking about modetn academic philosophy.

>>3200723
>Is philosophy the root of science?

Yes. Read Husserl on a philosophical science.