When Isaac Newton was developing different formulas for orbits of planets and deriving calculus as a result, he ended up creating entirely new fields of study, and along with that created a huge number of solved problems. The scientific community during Newton’s time and immediately following for the next century or two had massive discoveries, deriving countless equations in physics. They found out how to solve problems in Electromagnetism. They solved classical beam theory. They solved fluid flow problems. The solved all kinds of differential equations like some of the problems arising from the Helmholtz equations.
Solving many different closed form problems, the ones where there is a clear answer, is the work that naturally happens as an industry starts to flourish, but it’s not the real work. The real work lies beyond the closed form solutions. The problems where the constraints impact the work more than the problem formulation itself. This is where marketing lives. This is where architecture lives. This is where product design lives. This is where customer service lives. This is where sales lives. This is where construction lives. This is where humanitarianism lives. This is where politics lives. This is where endless work and effort awaits in working towards a better future.
The closed form solutions always come early on. They may tell us how to make a simple beam with the smallest possible cross-section. It won’t tell us how to make the most economical possible building system when usefulness of the space or feeling often supersedes that anyway (to the delight of architects and the chagrin of structural engineers).
Your job isn’t to find the closed form solutions of the world, that’s a happy side effect. Instead, it’s to pick an area of the world where you can immerse yourself, learning the tradeoffs and to “see” the compromises. The work is to become someone who can lead others in this area of your expertise. There is a huge amount of work to be done on open-ended problems, everyone is looking for people who operate there.