A hypothesis concerning the zeros of a simple function is among the oldest unsolved mathematical problems of today.
We will describe the context and give examples to illustrate how
the question is considered important both in and out of mathematics. The original conjecture has now been generalised to a large class of functions and has generated a great deal of research some of which we will mention in this talk.
The Black Hole Entropy Problem is a longstanding puzzle paving the road to the construction of a Quantum Theory of Gravity. After reviewing what the problem actually is, I will discuss approaches that have been taken in the last 20 years to tackle it. A key ingredient will be that of Asymptotic Symmetries that played a significant role in the discovery and subsequent developments of the so-called gauge/gravity (or holographic) dualities. The existence of these Asymptotic Symmetries indeed suggest a dual description of a gravitational system (including black holes) in terms of certain types of Field Theories exhibiting an infinite-dimensional symmetry. I will discuss how these observations hint at a possible resolution of the Black Hole Entropy Problem.
