I don't see why anyone non-mathematical would want using neuronal networks in the first place. There's lots of machine learning tools that are designed to work out of the box (decision trees, SVMs) whereas neuronal networks on the other hand give you greater flexibility but make it radically easier to shoot yourself in the foot if don't understand the whole thing. And "the whole thing" involves a gobload of math - including multidimensional calculus, little bits of probability theory, and numerical optimization.
That said, it's probably ok if you just want to get your feet wet to see what it's all about. There's even (decent) libraries for Python: http://deeplearning.net/software/theano/ http://code.google.com/p/pynnet/
Matching tutorial: http://deeplearning.net/tutorial/