How can we imagine abstract mathematics?

Why does math exist?

Reading time: 6 min

"Why does math exist? What is math anyway? Who comes up with such an idea and brought mathematics into the world? "

The question of why mathematics exists can certainly be approached in a great many ways. Here is a free attempt:

At some point as we grow up, after a basic language has become established in us, things can be counted. "Count" means, instead of "apple" you can suddenly say "two apples" and receive twice the amount of food from your parents. So there is a clear advantage over the children who cannot count. Before counting, the child of course notices that they say “apple” and then suddenly an “apple” is placed on the table. :)

We later call this knowledge abstraction (we generalize something). Instead of seeing one apple (and only that one) in front of us and assessing the next apple as something completely different, suddenly there is the possibility of combining both objects and making "two apples" out of them.

Through the abstraction we can imagine more apples, one, two, three, four, five, .... etc. Quantities result.

Quantities can also be counted. An abstraction of an abstraction, so to speak.

Children then notice that, in addition to objects such as fruit, vegetables, fingers, stones, leaves, etc. can also be counted. And not just individually, but also together. Bananas and stones are things (objects).

Mathematics is probably the highest degree of this abstraction, because we no longer need objects, but use the numbers or numerals,, as independent objects. With these we can now play and create things and situations as we like. You can be the god of your self-created world, so to speak, you determine the elements that appear in it and you can connect them with each other, combine them and other things. And so we don't go crazy (Fun), mathematics gives us a framework, an abstract description of what may be possible. :-)

Later you come up with ideas like: If I always add something, then yes, then. And abstract that if I want to put it briefly, using not just numbers, but characters in general. For example as an assignment with.

And maybe you get frightened the moment you wonder where the end of the numbers is?

And then you realize, when you get to know the coordinate system, that and can be drawn in wonderfully as points. If you then connect them, you recognize new connections! You can draw new conclusions ... two-dimensional, with another axis also three-dimensional. You can create formulas / descriptions for circles, spheres, etc. What a world!

Mathematics also helps us to discover new things.

Well, that was a little trip. I hope a little of it helps answer the question of existence.