As mathematicians continue to study mathematics, often times they run into a problem which takes a considerable amount of effort to solve. For instance, trying to factor polynomials has lead to a large portion of group theory and Galois theory especially. Another example, which I have heard reference from one of my professors, is that the study of elliptic functions has lead to a large amount of Algebraic Geometry. The original goal being how to integrate elliptic curves turned into quite an interesting field over the years.
My question, although "broad", is this:
What are some mathematical problems that have been forgotten?
In the process of trying to solve one question, often times many more questions are discovered. I find it hard to believe that no question has been forgotten. As in, sometimes the cutting-edge work of mathematics has trumped the questions that seemed of lesser importance at the time of research, and after a while most everyone has forgotten about them. Surely some of us must remember! Or, are there any stories of such problems like this that have sparked new mathematical research over the years?
Best Answer
The n-body problem dates back to the ancient Greeks and was once considered the key to understanding the movement of the planets, and, by extension, the very nature of the Universe.
A "geometrical" (i.e. exact) solution was always hoped for and expected, but the desire to compute orbital motions in practice led to the development of numerical methods; in the meanwhile, it was discovered that the case $n>2$ is chaotic (an early motivation for chaos theory).
Both numerical analysis and chaos theory have since dwarfed the original problem in terms of the amount of research effort dedicated to them, and while it's difficult to say that the n-body problem is "forgotten" (if it were, we couldn't be discussing it) I'm not aware of any substantial theoretical work (let alone progress) done on it for several decades now beyond what is already covered by the more general field of numerical methods.
Add to this the fact that the relativistic version of the n-body problem is fundamentally different from the classical formulation, leading to a solution for the classical problem being of much lesser interest in today's context of large-scale celestial mechanics than it would have been two centuries ago, and you have this once monumental problem being now reduced almost to its historical importance alone.