I know that all the representation,the symbols,equations all this is a sort of expressing some universal fact mathematically. Understanding the universe doesnt mean learing those symbols and representations ,right?.There are many who understand math,but dont know the symbols,forms that mathematicians represent.For example some one might know about knot theory but when represented in math form and asked about what is it,he dont understand.Does that mean he doesnot knot theory.What I mean to ask is that "Is learning all those representations,symbols,etc necessary to think mathematically?"Dont mind about tag pls.
closed as unclear what you're asking by Lord Shark the Unknown, Peter, John Omielan, Somos, Yanior Weg Jun 22 at 8:43
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I don't think this is the best platform to ask this question. Towards a partial answer to your question I can say that In real life what you call a 'Mathematical Thinking' is basically thinking logically, and yes you don't need to learn mathematics for that. If you want to contribute something in the field of mathematics, then obviously you need to learn the basics. Knowing the destination is not enough, you need to find out a path too. The technical details are the paths for your destination.
In order to talk about your life, you need to be able to speak a language, let's say, English. But you don't need to talk English to understand your life. But if you want to express how your life is and impart understanding to other people, you need to talk to them. But again, this does not need to be in English. You can equally well choose Farsi, or maybe Swahili. It doesn't matter what language you choose, as long as you can express everything you want to say.
Math is similar. You don't need to speak its language (aka symbol system) to understand it. But if you want to talk with others about it, it is necessary to have a common language. Similarly, there is a choice in languages/symbols that work equally well for this task. And actually, math is not a singular set of unique symbols, but is a collection of languages that are similar but vary depending on the field and, more importantly, whom you speak to. The very same concepts can be expressed in multiple ways and regularly are expressed in multiple ways. A prominent example of this are the calculus systems developed by Leibniz and Newton. Though equivalent, they differ greatly in how they express things.
I'd say learning those symbols, representations, etc., is only half the task, if by 'learning' you mean 'understanding'. A good mathematician also applies concepts learned to tackle new problems. In the context of an ordinary person, thinking mathematically means reasoning through logic.