With regard to the "pride in uselessness" thing, I caution you against generalizing here. Different people get into math for different reasons, but I would say that all the pure mathematicians I know of are motivated principally by interest in the problems they care about, and don't think too much about questions of purity.
There's a nice quote from Courant in his "Introduction to Calculus & Analysis" where he warns against "smug purism", exhorting students to draw inspiration and insight from other fields because it will make them better mathematicians. I think this is the attitude that I encounter most frequently among mature, pure mathematicians.
Chebyshev in particular was known not only for working on problems that had engineering applications, but for using methods and techniques from engineering to inform his approach to pure math problems. As the founder of the St. Petersburg school of mathematics, this approach had broad impacts on (later) Soviet mathematics and global mathematics as students brought up in this tradition went on to train later generations of mathematicians around the world.
There's a nice quote from Courant in his "Introduction to Calculus & Analysis" where he warns against "smug purism", exhorting students to draw inspiration and insight from other fields because it will make them better mathematicians. I think this is the attitude that I encounter most frequently among mature, pure mathematicians.
Chebyshev in particular was known not only for working on problems that had engineering applications, but for using methods and techniques from engineering to inform his approach to pure math problems. As the founder of the St. Petersburg school of mathematics, this approach had broad impacts on (later) Soviet mathematics and global mathematics as students brought up in this tradition went on to train later generations of mathematicians around the world.