The question revolves around a disease that begins as a single cell and grows into a merciless disease claiming millions of lives each year, with scientists continually unlocking its mysteries. The appropriate answer would be a disease that fits this description.

Option 1: Cancer - is in point of fact a group of many related diseases that begin as a single mutated cell which grows out of control. This fits with the description given, which makes it the correct answer.

Option 2: AIDS - is caused by the human immunodeficiency virus (HIV) which attacks the immune system, making the body more susceptible to infections and diseases. It does not start as a single cell but as a virus infestation and therefore doesn`t match the description provided.

Option 3: Tuberculosis - is an infectious disease that primarily affects the lungs. It is caused by the bacterium Mycobacterium tuberculosis and not by a single cell that grows out of control.

Option 4: Alzheimer’s disease - is a progressive brain disorder that affects memory, thinking skills, and the ability to carry out simple tasks. It is not a single-cell mutation, rather, it is typically characterized by the buildup of proteins in the brain over time.

Therefore, the correct answer is cancer.