What is the most fundamental thing about a mathematician?

What is the most fundamental thing about a mathematician?
Yet another nonsensical question from parag
Dywyddyr: Surely there is a better explanation than this(oxygen..... etc). Not every Tom Dick and Harry can be a mathematician? Surely there must be more to it than meets the eye.
An engineer thinks that his equations are an approximation to reality. A physicist thinks reality is an approximation to his equations. A mathematician doesn't care
A mathematician is a blind man in a dark room looking for a black cat which isn't there.
Algebraic symbols are used when you do not know what you are talking about.
A team of engineers were required to measure the height of a flag pole. They only had a measuring tape, and were getting quite frustrated trying to keep the tape along the pole. It kept falling down, etc. A mathematician comes along, finds out their problem, and proceeds to remove the pole from the ground and measure it easily. When he leaves, one engineer says to the other: "Just like a mathematician! We need to know the height, and he gives us the length!"
Well I pursued it out of curiosity.I didn't do it after I was 16 but a long while later I studied it for a few years in my own time up to Calculus .At that point I realised that it developed into areas that required a lot more than I was able to bring.
At least though I felt I had learned enough to be impressed by people who did do maths well I mean those people who carved out new areas.
It seemed to me that that required great imagination even if they did have to start from positions established by people who had gone before them.
In the time of the ancient Greeks I think there was a view of the world that held that numbers were the building blocks of reality (it may have been related to the school of Idealism I never learned much about all that though.Perhaps they got numbers from the vibration of a string when it makes a note but like I said I only know fragments of information about that)
Most fundamental thing about mathematicians? No idea really. I like the fact though that (as with science in general) it cuts across political and cultural borders.
Mathematics uses numbers and symbols; therefore, a mathematician must have a strong ability to work with abstractions (that is, the formation of ideas, as of the qualities or properties of a thing, by mental separation from particular instances or material objects) and to work with operations upon those abstractions (that is, processes, such as addition, division, etc, involving a change or transformation in a quantity).
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