Need help with well partitioned tables

[Felix Boes]

First of all: sorry for my bad english.
I hope you can help me with the following problem.

I want to save a hierarchy of categories. For example:

n) = ID of the Categorie

1) All Categories
2) 1) -> Science
3) 1) -> 2) -> Maths
4) 1) -> 2) -> Physics
5) 1) -> 2) -> 4) -> Classical Physics
6) 1) -> Religion
7) 1) -> 6) Asian Religion
8) 1) -> 6) -> 7) Bhuddism
...

I dont know yet how much subcategories I will create. I want to search for a categorie and want to find all of its subcategories.
I already have a solution, but want to know if someone knows a smarter way to solve the problem.
My solution:
Create table (
id int,
name varchar(n)
finder text
)

the finder string looks like that: _["id of catogorie above"_["id of categorie above"_[...]]id_
That make a simple search possible:
SELECT id, name FROM table WHERE finder like %_"seach id"_%;