That is not an easy question to answer. Maths essentially means obtaining theorems from axioms. But what that stands for? It means that Maths consists of a long list of games of the kind “And if …?” which mathematicians keep on doing as time passes by. Those games require rules (the axioms) that have to be followed and then mathematicians explore the consequences concerning the application of those rules (theorems) during the game.

For instance, we can start playing by using some of the rules:

- One point only has an application;
- Two parallel lines do not intersect;
- Two nom-parallel lines intersect with one point;

Thanks to this kind of rules did Euclides “invented” geometry. And this is what other mathematicians have done for the last centuries and thus they have invented the arithmetic, the numbers theory, the calculus and so on.

Let's imagine that I would invented a new board game like the chessboard. I would start by specifying which pieces make part of the board and which are the rules that allow them to move. Then I would let people to try the several possible combinations to win. The difference is that unlike the chess game, in Maths we cannot win. In Maths we only want to understand what can or not be done. So, a mathematician that had played this game, he would have asked the following questions:

- If I put a horse (piece with an L movement) in a certain square, it will be able to reach any board square?
- What is the minimum number of movements for a certain piece to be able to move itself from one place to another?
- What would happen if the board had a triangular shape?
- What would happen if a certain piece became visible or invisible at every 4 moves?
- What would happen if the game was played by 5 players?
- What would happen if the board was a three-dimensional one?

In other words, mathematicians are interested in finding out not only what happens if we play according to certain kind of rules but also what would happen if the rules were changed. For instance, the German and the Russian mathematicians having in mind the Euclidian’s rules, wondered about “What would happen if two parallel lines could intersect each other?”. This question gave birth to a completely new field of geometry, which enabled Einstein to discover the relativity theory later.

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