The way a Pure Mathematician thinks is different from the way an Applied Mathematician thinks. A Pure Mathematician looks at life as something they want to enhance. Several will go their entire lives trying to construct an original theory, or one could consider it a work of art, to improve the mathematical foundation as a whole.
For example, Dr. John Nash wanted to come up with an original idea within mathematics. But instead he found a theory that was wrong in his opinion and improved the original theory so it will be true and won a Nobel Prize for his improvement in the subject.
An Applied Mathematician will look at life as a problem waiting to be solved. They will ask questions from an array of subjects and try to solve them using mathematics. These subjects can range from chemistry, physics, economics, and even music.
For example, people wanted to build a computer that could do a massive amount of computations in as little time as possible. This is called a Supercomputer.
They asked the question and then used Applied Mathematics to answer and solve the problem.
These two types of mathematics use different ways to solve problems. Pure Mathematics is really based off of techniques, and the way of solving a problem in Pure Mathematics is based on proofs.
Applied Mathematics, on the other hand, uses modeling and theories already proven by Pure Mathematicians to solve real world problems.
A Pure Mathematician would ask questions like: How could this theorem be related to mathematics? How could I improve this theorem? How could I prove this theory to be a contradiction?
An Applied Mathematician would ask questions like: Where could I apply this to? Could I use more theories to support my findings? Is this useful in answering the question?
Mathematics as a whole is fundamentally essential to everyday life. The history between Pure and Applied Mathematics goes hand in hand with one another.
All it took was individuals who asked questions, who went about solving them or proving a certain theory they create.
Ideally, they think the same way, but from a deeper perspective, one can see that Pure Mathematicians want to improve the understanding to further the reach of mathematics. Applied Mathematicians solve questions that are very well needed to improve life.
Pure Mathematics can be considered an art or a never ending musical symphony. It creates a beautiful masterpiece that is used by Applied Mathematicians. They feed off each other and make this world a better more understanding place.
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