How can one start to THINK IN NUMBERS?

[cdux]

I keep hearing even by very brilliant Engineering co-students that they require a lot of text-based theory before going into numbers. However, there is also a good deal of good Mathematicians that state they can think in numbers, requiring theory, but not strictly in a text form, or at least an extensive one.

So, how can one go about in order to start thinking in numbers, having as a base the minimal required studying of theory?

Is it only a matter of just paying more attention to it at the initial steps and not rely solely on later friction with practice, or is it a generally different state of mind?

I wait for your opinions. Even if they are not targeted and go beyond the field slightly, they're welcome.

edit: 'Numbers' is loosely used to mean also Mathematics.

 

[Simon Bridge]

I suspect your different sources are being glib - they are actually talking about the same things but not being precise in their language - possible for effect.

What's important in the math is not the numerals or values themselves but the relationships between them.

What the sources are talking about si the way that the math becomes a language that you use to describe the phenomena under investigation. You gain this awareness/facility the same way you become fluent in any language - you have to immerse yourself in it and use it all the time.