“How can we quantize the exterior surfaces of geometric objects?”
It is safe to say that almost every human individual can easily relate to three-dimensional objects. However, mathematicians do not feel suffice with just simple qualitative descriptions of space, but rather they seek to go deeper, into the quantitative realm. And as such, they will take processes and patterns that we see everyday and systematize them in a rigorous manner. One of the properties that mathematicians will analyze include the surface area of a three dimensional objects. To put it in simple terms, the surface area of an object is the outer layer that envelops it (think of something like skin on a human). Measuring the surface area has many practical applications in the natural sciences. For example, in physics we can use the surface area of a Gaussian surface to measure the electric field due in a certain area with Gauss law, and in biology by using the surface area to volume ratio of a cell membrane to quantize how rapidly a substance will spread from the interior the the outer coating. All in all, surface area is a fascinating concept with numerous applications to the real world.