Why is Training Neural Nets a Non-Convex Optimization Problem?

Question

I keep hearing that neural net training is non-convex. The objective function is non-convex.

My question is:

1. What is the proof that the learning process is non-convex? How can you prove it is non-convex for say max likelihood training?

2. Is training wrt all objective functions non convex?

I am unable to find answers to these questions as most online resources never care to explain the non-convexity and take it for granted.

Thanks.