Mathematics gives people a way to examine, understand, and prove the physical world around us. It is the abstract study of many topics including algebra, trigonometry, calculus, and geometry, just to name a few. Mathematics is figuring out patterns to hypothesize conjectures about abstract ideas to explain and understand our physical world; mathematics also gives people a way to prove or disprove those hypothesized conjectures.
To me, mathematics is the most important subject we learn in school because it is not only a way to exercise our brain but it allows people to improve and/or develop their problem solving skills. Mathematics shows people how to reach a wanted result by following a succession of steps in a specific order without error. This process is used in the real world by everyone and can teach people how to optimize their daily lives. Mathematics is useful in every field from art to business.
I believe the top 5 biggest moments/discoveries in the history of mathematics are:
1.) Numbers. Being able to quantify things is essential for doing any form of mathematics. Without numbers there would be no calculus, algebra, statistics, or any other subcategory of mathematics.
2.) Pi. Pi is important because it allows us to use a symbol as the representation for the ratio of a circle's circumference to its diameter. This makes for easier calculations especially in long or difficult problems.
3.) Calculus. Calculus is the mathematical study of change which allows us to have a better understanding of the nature of space, time, and motion. We use calculus to study and understand the world we live in.
4.) Pythagorean Theorem. The Pythagorean theorem allows people to find the third side of a right triangle when the other two sides are given which is useful in a lot of areas of mathematics. This theorem was developed around 2000 and 1786 BC which is such an advanced concept for that time.
5.) Quadratic formula. The quadratic formula is the most useful and important method for solving a quadratic equation, which is done in almost every area of mathematics. The best thing about the quadratic formula is that it works with all equations whether our answer turns out to be real or complex.