The people who use python for numerical analysis use solutions like numpy, with which their programs spend most of their time executing optimised numeric routines.
The sad fact is you can't always do this. Then you are forced to drop down to C/C++/Fortran.
It would be great if you didn't always have to do this.
https://www.wakari.io/nb/travis/Using_Numba https://www.wakari.io/nb/travis/numba
And the slides from PyCon Talk: https://speakerdeck.com/pyconslides/numba-a-dynamic-python-c...
For example, consider the problem here:
http://arxiv.org/abs/0903.1817
Ultimately I needed to run a math formula on some surfels and connect an edge in a graph if the formula came out True. Following that I had to prune a bunch of edges in the graph. In 2009 (when I did it), I had to drop down to c++. (Admittedly, this was also partly due to a lack of a good python graph lib.)
I'd be very surprised if Numba is helpful with something like that - the branching and complex data structures don't seem like a great fit for it.