Nicomachus tells us that in order to study, learn, and know philosophy, we must first begin with arithmetic. Arithmetic is the study of the finite quantity - numbers, while geometry, second on Nicomachus' list, is the study of finite sizes - shapes. While most people struggle to understand the world of numbers, many intuitively understand the world of shapes. As children, we knew who received the bigger piece of pie, or which sledding hill was the steepest. The truth is that the study of numbers first started with the study of shapes. Numbers were created to communicate the truths behind the shapes and patterns that we observe. Geometry existed long before the language of arithmetic, but in order to truly communicate with geometry we must have arithmetic.
Euclid's Elements is written in full sentences and pictures. A student in a modern geometry class would be hard pressed to communicate the postulates in geometry without an algebraic sentence, yet Euclid wrote the entire book on geometry without algebra. The fact that geometry evolved in this way and that it was even possible reveals the truth that mathematics is not dependent on some man-made world, but rather on a being higher than ourselves.
This is why we can agree with Nicomachus that the study of arithmetic is first. The study of geometry however is a natural step beyond. In geometry we see the link of the natural world to the hidden world of numbers. We discover the connections of area, space, distance, and volume with ratios and dimensions. Geometry is perfectly setup to reveal the wonder of creation. By measuring shapes and studying the consistency of the postulates, axioms, and theorems in geometry we begin to understand the created world.
May we remember that our mathematical studies are always first and foremost about the pursuit of God and knowing him more through his creation.