The philosophy of mathematics, or mathematical philosophy, may seem like the same thing. But to mathematicians, mathematical philosophy means many areas of study, such as ethics, logic, or metaphysics. The philosophy of mathematics is actually a branch of philosophy that studies the philosophical assumptions, implications, and foundations of the mathematics world. This branch of philosophy gives us an idea of just how mathematics fits into our modern world.

These philosophies tell us a great deal about the state of modern mathematics and logic. Like many abstract and complex studies, philosophies come and go; some good, some seemingly on the mathematical fringe. Currently, there is no single philosophy that truly defines our mathematical and logic foundations, especially when it comes to combining both mathematical knowledge and the application of mathematics to physical reality.