Is it morally right and pedagogically right to google answers to homework? This is a soft question that I have been struggling with lately.
My professor sets tough questions for homework (around 10 per week).
The difficulty is such that if I attempt the questions entirely on my own, I usually get stuck for over 2 hours per question, with no guarantee of succeeding.
Some of the questions are in fact theorems proved by famous mathematicians like Gauss, or results from research papers.
As much as I dislike to search for answers on the internet, I am often forced to by time constraints if I even expect to complete the homework in time for submission. (I am taking 2 other modules and writing an undergraduate thesis too).
My school does not have explicit rules against googling for homework, so I guess it is not a legal issue.
However, it often goes against my conscience, and I wonder if this practice is counterproductive for my mathematical development.
Any suggestions and experience dealing with this?

First of all, be relax and take things easier. If some problems are hard 
and you cannot solve them then I see no problem to ask for help as long as you 
want to understand and learn the tackling ways of the problems, not only to hand in a solution. The real fact is that some teachers do really poor at their classes and expect a lot from their students. I don't know how things in your
case are, but if you like mathematics you may learn a lot on your own. Moreover, if you study the problems and the solutions posted on this site you'll learn a lot!    
