Math is an exploration, a way to search for truth.

In general,  

You start with an idea.

Then you try to modify that idea in two ways (two directions, you might say) - or maybe 3:

1. You try to make that idea more precise, and

2. You try to make that idea more general.

(3.) You see what follows from the ideas that are produced by 1 and 2. 

More specifically, it can work like this:

You start with a truth.

1. Then you try to make that truth more precise, and

2. More general. 

3. Then you see what follows from the truths that follow from 1 and 2.

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