Why does algebra even exist?

The whole field is such fucking useless autism. Analysis, numerical math, probability theory - at least they all come from real world applications. But algebra is just playing with definitions as a goal in itself to satisfy the autism of its creators. Except for very basic terminology of group theory (which you can already cover as a side note in linear algebra) none of it is ever needed nor has applications. Ring theory and Galois theory are fucking useless crap obviously made up by people who are more philosophers than mathematicians.