Why $\textstyle l_2$ norm?

Recent progress in signal processing theory has generated a renewed interest in the effectiveness of using the $\textstyle l_1$ norm. It is interesting to note that, for example, in sparse signal recovery one can do a more accurate signal reconstruction minimizing the $\textstyle l_1$ norm.

The reason I have been thinking about $\textstyle l_1$ norm is because it apparently looks more useful for a portion of my current research. Maybe over a hundred years ago, or so, whenever mathematicians started thinking about norms $\textstyle l_2$ won, but current research trends show that $\textstyle l_1$ norm is very handy for a number of practical purposes.