[dagw]

Very few "real world" math problems reduce to easily computable closed form expression. You're almost always dealing with numeric approximations. So even when your problem has a unique correct answer finding it is either impossible or computationally impractical. A large part of applied math is finding newer, faster and cleverer ways of approximating these solutions. Making the best choice between all the different ways to get the right answer can often be the difference between run times measured in hours vs centuries.