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How does a mathematician think?

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To answer the question what is mathematics, the merriam webster dictionarydefines mathematics as “the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations”.

But what is wrong with this definition? This may sound surprising to some people but saying that “math is the study/science of numbers” or something similar is like saying “biology is the study of plants” even though biology may have some study of plants, biology is not solely confined to studying plants.

The same is so with mathematics. Mathematics does have numbers but this is just one type of area in mathematics. There are many different definitions of what mathematics and there is no simple satisfactory answer. Even though this is a very complex question to answer, the best way I can describe mathematics is mathematics is a language that expresses relationships and this language allows us to understand our universe and to solve the problems in it. Mathematics uses symbols (i.e. numbers, operations, etc.) but these collections of symbols represent more than what is on the page. These symbols help us represent and understand problems and to solve them. But the symbols are not as important as the thought process. Any two people from different parts of the earth can view a page of mathematics and if they both understand mathematics they are able to understand the implications of what is being said without saying a single word. There is no other language like this that is taught.

So why do we learn math? Mathematics is the key to all professions that require the knowledge of the exact sciences. I believe that we learn mathematics because it helps us with abstract thinking. Mathematics trains our minds to take steps towards reaching a solution to any problem or question. In other words, it promotes the habits of our thought process in order to reach to a logical conclusion. The symbols are our tools of communication and we have to master the concept rather than just knowing what the correct answer is.

Where did math come from? No one really knows exactly where math came from but it is possible that math existed prior to the first words spoken by humans.

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