Math can be an end unto itself. This can come as a bit of a surprise in our prevailing culture, which needs to justify the usefulness of everything. Also, it's

Math can be an end unto itself. This can come as a bit of a surprise in our prevailing culture, which needs to justify the usefulness of everything. Also, it's possible for someone to study math as a liberal art, and develop the ability to do useful things with it on their own. My observation is that the people who grudgingly learned math as a means to an end, tend to forget most of it soon after graduating. This explains the widespread but paradoxical aversion to math among engineers.