It's a very good question! I started to learn Russian and lo! What did I see? No articles! And you are right. They are just about as useful as hen's teeth. But, many languages have them. I think you can compare them, if your algebra is good, to the following:
1,2,3,4,... = the (definite)
a, b, c,.. x, y, z = an, a (indefinite).
Well, do we really 'know' 1,2,3,4,... we suppose so. They are pretty definite.
And do we really 'know' a, b, c, ..x, y, z.... we think not. They are more cloudy.
Anyway, learn them in English and you will have a good nose for them in German, French, Spanish, Italian...