This is a question that has been winding around my head for a long time and I have not found a convincing answer. The title says everything, but I am going to enrich my question by little more explanations.

As a layman, I have started searching for expositories/more informal, rather intuitive, also original account of non-commutative geometry to get more sense of it, namely, I have looked through

The English translation of

*Review of non-commutative algebra*by Alain Connes,*Surveys in non-commutative geometry,*Clay mathematics proceedings, Volume 6,

Nevertheless, I am not satisfied with them at all. It seems to me, that even understanding a simple example, requires much more knowledge that is gained in grad school. Now for me, this field merely contains a lot of highly developed machineries which are more technical (somehow artificial) than that of other fields.

The following are my questions revolving around the significance of this field in **Mathematics**. Of course, they are absolutely related to my main question.

How can a grad student be motivated to specialize in this field? and

What is (are) the well-known

result(s), found solely by non-commutative geometric techniques that could not be proven without them?