People sometimes say that what really matters is the means to the end, not the end itself. They then draw a sharp contrast between engineers and academics, saying that engineers focus on the end result, while academics focus on the means, but this is not true. To be truly free of the end result, you have to work on problems simply because they are interesting, completely ignoring their importance. It also means that you completely ignore any recognition of your work. Recently, a mathematician pumped prompts into a machine over the course of a year to yield an important result: this, I think, is exactly what mathematics is not.
My long-term advisor and close friend is the person I'm most closely aligned with: we work on problems simply because they are interesting, and we are often not able to give our reviewers a satisfactory answer to the question of motivation. You would think that I'm some kind of engineer, as I work on LLVM, but there is a sharp difference between me and the others — most contributors work on problems out of necessity; it could be a bug fix or an optimization result for an important benchmark. I will admit that I don't even look at any benchmarks, and invent problems to work on simply because they're interesting. Many of them happen to have good a optimization result, but that doesn't concern me. My work on LLVM, my work in logic, my writing, and indeed, virtually everything in my life has a self-fulfilling motivation. I have never been able to motivate myself to do anything that is necessary, except by applying a sharp unpleasant force on myself.