Two answers in the words of others are below. We also refer those interested to read the short, wonderful, provocative book A Mathematician's Lament by Paul Lockhart.
College students study the best paintings, the most glorious music, the most influential philosophy, and the greatest literature of all time. Mathematics departments can compete on that elevated playing field by offering and making accessible to all students intriguing and powerful mathematical ideas… Indeed, these courses [general education and introductory mathematics courses] should be developed and offered with the philosophy that the mathematical component of every student’s education will contain some of the most profound and useful ideas that the student learns in college. (Committee on the Uundergraduate Program in Mathematics, 2004, p. 28)
Almost everyone knows that mathematics serves the very practical purpose of dictating engineering design. Fewer people seem to be aware that mathematics carries the main burden of scientific reasoning and is the core of the major theories of physical science. It is even less widely known that mathematics has determined the direction and content of philosophical thought, has destroyed and rebuilt religious doctrine, has supplied substance to economics and political theories, has fashioned major painting, musical, architectural, and literary styles, has fathered our logic, and has furnished the best answers we have to fundamental questions about the nature of man and his universe... Finally, as an incomparably fine human achievement mathematics offers satisfactions and aesthetic values at least equal to those offered by any other branch of our culture. Despite these by no means modest contributions to our life and thought, educated people almost universally reject mathematics as an intellectual interest. (Morris Kline, from Mathematics in Western Culture, 1953)