It could be said that mathematics is the language of physics. That is another way of better understanding what is physics. Numerical values, units of measurement, and similar concepts are all mathematical in nature, and are used to describe physical quantities in the most accurate and precise manner.
In brief: Cough headache. There are a couple of possibilities. Coughing can raise the pressure inside your head, which can cause pain sometimes. There is also a poorly-understood entity called the primary cough headache,  that is associated with coughing, straining, laughing, crying, etc.
Harmless, primary cough headaches are believed to be caused by increased pressure in the head that comes from coughing and other types of strain. This pressure increase is called the Valsalvaâs maneuver, which is sometimes done deliberately by closing the mouth, pinching the nose and breathing out.