Top Ten Mathematical Tools Ever Invented

I'm not including algebra here, because it is elementary and almost all the mathematical tools listed here use algebra in some way or the other.
The Top Ten
1 Calculus

Functions are useful. Calculus offers real-world solutions to problems dealing with charts, mapping drawings, and solving the behaviors noticed in life with something simpler while getting the general idea of what the image in question is closely related to with some sort of equation function. There are many other uses, such as finding the differences and changes to a degree. In the highest applications of Calculus, these might be done to perfection.

If Newton had not discovered calculus (and also one more mathematician whose name I'm currently having difficulty remembering), then physics wouldn't have much scope at all, and we would all be living in the 17th century even now. Although calculus is difficult to explain in common language terms, it will be a very interesting field for you if you get to know about it.

2 Coordinate Geometry

Well, who can beat this beast! Descartes gave us this wonderful mathematical tool that could solve any geometry problem with ease. Physics would be very incomplete without this. It helped us use algebra in solving geometry problems.

This mathematical tool is simple in its making, but brilliant and ingenious in application.

3 Trigonometry

Who thought that ratios of the lengths of sides of a right-angled triangle would create miracles in the field of science! Although this field of mathematics is very easy to learn, its applications in physical sciences are so crucial that all the mathematical theorems of advanced mathematics and physics would collapse if trigonometry were not applied to them.

4 Vector Algebra

Vector Algebra is very necessary for the fields of both physics and three-dimensional geometry. It is an algebra concerning directed line segments. All Newtonian Mechanics would collapse if the human race somehow forgot this one.

5 Determinants

Determinants are the most beautiful mathematical device to look at! They just look so pretty. You just have to draw two vertical lines with sufficient space between them and write numbers in imaginary rows and columns to create one.

However, there are special rules for solving a determinant, and its algebra is somewhat complicated too. So, why was the determinant ever invented? It was invented to make solving systems of linear equations a little easier. It saves time. And as I have said, because determinants are beautiful to look at, equations and mathematical formulas that involve them are easier to remember.

6 Matrices

It just looks very similar to a determinant but is very different from it, both in terms of its applications and its way of solving.

7 Set Theory

Set theory gave birth to both relation and function fields of mathematics. Although set theory has very limited applications, it is very useful in solving permutations and combinations problems, probability problems, and others.

8 Binomial Theorem

This is yet another masterpiece.

9 Progressions and Series

Like arithmetic progression, geometric progressions, and harmonic progressions.

10 Probability

This is the only field of mathematics that was not invented because science needed it, but because the game of gambling needed it. Probability has many applications, like in weather forecasting, and of course in quantum mechanics. Probability is what gives us a realistic picture for different wave functions in quantum mechanics.

The Contenders
11 Unit Circle

It makes Trigonometry so easy!

12 Base e

Used in biology, chemistry, finance, everything! It is used in the ever-useful natural log for calculus. It is so beautiful what natural growth can give.

13 Factorization

It is crazy that I learned this in high school and still have to use it today.

14 Prime Sieves
15 Binary Mathematics
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