This question seems so simple at first, but when you think of all the possibilities of responses from all of the many different types of people, it’s truly amazing how people portray it. When I think of this I immediately think of the common things that non-mathematicians might say. Personally, I know math is much more than the K-12 definitions that would normally be given. The world of math is so abstract and intriguing to think about. To me, math is a way of thinking about patterns throughout the universe. Math is interpreting and studying these patterns to find more patterns. What a concept.
Basic discoveries in math seem to be some of the most monumental for the simple fact that we had to start somewhere. I think that the concept of distance and space is one of the most important because without being able to measure or understand the world in that way, many math concepts would have not been found. This leads to geometry in general being a huge discovery, along with euclidean geometry. In order to perform any operations in math, addition/subtraction and multiplication/division are extremely important. With this, the discovery of infinity opens all sorts of new worlds in math that have become important when studying many topics. These concepts build on each other, creating new ones and without one, it’s difficult to understand another. The greatest discovery in mathematics in my opinion is the power of communication through symbols. In math there are so many symbols it seems crazy, but without them it would be difficult to communicate these concepts to one another.