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.
1 It tends to occur at the same times every day.  Sinus headache causes pain in the front of the head and face. It is due to swelling in the sinus passages behind the cheeks, nose, and eyes. The pain is worse when you bend forward and when you first wake up in the morning.