The Fundamental Group The Fundamental GroupFor most people math is a polarizing subject, you either like it or hate it, and even if you love it... you still hate it. To add to the controversy, math is used in almost all fields of study. To help understand what math is and how math has evolved over time we have the Family of Mathematics.
The real world mathematics applied mathematics is used to understand how the tools of mathematics can be applied to solved existing problems outside of mathematics. It is the social flirt of math spreading and growing family of Mathematics.
As abstract as it gets. If applied math is understanding how to use the tools of math, pure math is what builds builds them. It is math for the sake of math. Pure math abstracts the ideas of mathematics, studies the underlying structure of mathematical objects, and constructs new objects. Although pure math does not have a goal of being applied, it is believe that the concepts of pure math being studied today will be applied at some time in the future. For example cryptography is secured by many of the principles of number theory.
The difference in applied and pure math is a matter of personal philosophy, in general a way to think about it is all math is applied math, just maybe not applied yet.
Physics the first child of mathematics. A little frantic with wild hair and just on this side of sane, physics would make use of Mathematics to interpret the physical world around us. As the first child of mathematics it is hard to dispute physics as the favorite child of math (but don't tell the others). Physics would go on to have a daughter Chemistry and a grandson Biology who together would make up the family know as the Natural Sciences.
Statistics, your Grandpa's machine learning, and not everyones cup of tea. The driest of the children of mathematics, statistics is a true number cruncher, always getting bent out of shape about about "Significance" and "making sure the conditions of the model has been meet". Many believe statistics to be the biggest dork in the family of mathematics, and if we all are being honest it is probably true. Statistics, does make up for this shortcoming by being extremely useful for condensing terabytes of information in to a single number.
Engineering, the grunt of the family working to implement the ideas of the other family members. From day one you could tell Engineering was a little different. They didn't wait for rigor or formal proof. The guess and check method was Engineering's preferred method of innovation, and they had wild success at it! Engineering would become a remarkable member of the family, and probably the most well know. All that fame does tend to get to Engineering's head and it can be a bit of a narcissist, letting everyone know how good at math it is. A gentle reminder where it came from is all Engineering needs and it's another happy member of the family, continuously working to use the concepts of the other family members to address real world problems
Computer Science, the odd ball. He kind of came out of nowhere and really didn't fit in with any of the other members of the family. He was awkward and not well spoken, but he could do simple mathematical calculations faster than had ever been imagined. As people began to understand what make Computer Science tick, it became clear how useful he could be. Not only could he do computations which would change the course of humanity, if you knew how to talk to him Computer Science would provide the family with a way to create a virtual world, which is how you are reading this. Computer Science was an outlier at the beginning and many didn't think he would make much of an impact. In 2019 the doubters were proven wrong and computer science is a proud member of the family of mathematics
Economics, the bastard of mathematics. Yes it cannot be said that Math was always faithful to lady science. A love affair with the arts resulted in an invisible hand know as economics. What started off as a scandalous romance, ended with a child that could apply math to understand and model the forces in society driving the production of goods. The most politically charged of the children of Math, Economics has really come into its own and has even been able to apply the principles of mathematical proof to the economy. Economics would go on to have a large Family of it's own which includes Micro/Macro Economics, Finance, and Game Theory.