Central Problems

Abstract

This chapter gives a brief qualitative presentation of some of the most important astrophysical and mathematical problems in gravitational lensing (Section 2.1). To put these problems in perspective, we also present several quotes highlighting some of the differences in the viewpoints of mathematicians and physicists (Section 2.2).

When the problems in physics become difficult we may often look to the mathematician, who may already have studied such things and have prepared a line of reasoning for us to follow. On the other hand they may not have, in which case we have to invent our own line of reasoning, which we then pass back to the mathematician. Richard Feynman

The combinations that can be formed with numbers and symbols are an infinite multitude. In this thicket how shall we [mathematicians] choose those that are worthy of our attention? Shall we be guided only by whimsy? … [This] would undoubtedly carry us far from each other, and we would rapidly cease to understand each other. But that is only the minor side of the problem. Not only will physics perhaps prevent us from getting lost, but it will also protect us from a more fearsome danger … turning around in circles. History [shows that] physics has not only forced us to choose [from the multitude of problems which arise], but it has also imposed on us directions that would never have been dreamed of otherwise …. What could be more useful! Henri Poincaré