What is mathematics? A fair question, though one I haven’t considered too much, even though I’m a student whose done math for quite some time (15 years and counting). I would say that mathematics is a language used to study and discuss patterns found in nature. The fact that math is a language makes it a very important tool in many sciences. It has allowed humans to communicate in order to understand the way the world and universe around us works. In math, as in any language, the more one knows about the language and the structure, the more adept one becomes at being able to convey and understand complex thoughts and ideas.
As one might guess, there are numerous (perhaps countably infinite?) milestones in the history of mathematics. I’ve never been too good with history, so I’m not at all sure about order, and I’ll just start with my favorite, which is Isaac Newton’s discovery of calculus. I am still astonished to this day, when I imagine someone my age coming up with a completely new type of mathematics in order to solve a problem they were working on. Another one of my favorites is the acceptance of zero as a number, an idea I’ve been raised to accept, but which took mathematicians years of debate to conclude. A milestone that I can personally relate to is the acceptance of i as a numberl. My older brother taunted me for a couple weeks when I was in 4th grade with the simple question: “What is the square root of -16?” (of which my answers were -4!… no 4! … no…). Also high up on my list of favorite math milestones would have to be the acceptance of irrationals as numbers. I feel like my list would not be complete without the two completely different milestones that I will lump into one underrated milestone: the discovery of e and pi. What kind of a subject would math be without the most beautiful expression, e^(i(pi))+1=0?