Wondering why this is voted down. He is quite right. Several math professors at my school who teach applied math do not know even the utmost basics...say things like computing kernel of a quotient group. Am sure they must have known it at some point during their student years, or maybe during the 60s-70s, you could get away without knowing these things, I dunno. otoh, my abstract algebra professor was able to learn and then teach me Ito's lemma all the way up to semimartingales, topics he had never set eyes upon in his entire life! So I'd say the abstract stuff makes you much more stronger - gives you tools to understand from scratch material you've never seen before. The applied people generally glaze over when you mention math topics out of their competence zone, especially topics that are "useless" for some definition of "use".