Reasoning, understanding, explaining, and counting are all words that come to mind when I think of math. Math is not simply computing numbers to receive an answer or inputting numbers into an equation to generate another number. Math is using numbers to receive a better concept of the world around you. Math is involved in everything we use, even if you don't think it is, there is a way math is involved. I think one of the greatest things is that math is universal. While each country has different was of teaching math, the concepts are all the same.
As far as milestones or Top 5, there are so many. There's famous people, theorems, inventions, fields, concepts, etc. For sure I would say that Euclid is important. He built the foundation for modern mathematics by introducing a set of axioms; I mean there's an entire class at Grand Valley dedicated to him, must be pretty important.
Along with Euclid, you have Pythagoras and Fibonacci; there's Euler and Newton, each contributing their own piece to the world of mathematics.
Then there are calculators. Huge milestone in the world of mathematics. Calculators allowed for quicker computation and a simple way to check answers. Calculators themselves have progressed so much that no one could have imagined the effectiveness of them when they were first created.
Math is also several different fields. We have algebra (my favorite), calculus, geometry, non-Euclidean geometry, differential equations, and the list goes on. What's interesting though is that each field builds upon and integrates different fields.
Math is patterns, logical reasoning, relationships, explanations, and application. Math is far more than numbers and computation.