Video: Are Mathematicians Creative?

From the YouTube description of the video (below):

"Is doing research in mathematics a creative process? When mathematicians talk of their subject as beautiful, what do they mean? What are their motivations? Their dreams? Their disappointments? These themes are explored in the collection of five short films produced as part of Mathematical Ethnographies project. The focus is not on mathematics, but on the people who create and teach mathematics - on mathematicians."

Some of my favorite bits from the video:

"Like writing a sonnet, you have to conform to precise rules but having that structure there to constrain you somehow enhances the creativity."

"To be good at mathematics you have to develop a new insight."

"There are moments where things become clear, it comes out of nowhere.  I'll be in the shower, cycling, and somehow the answer comes."

"It's hard to see how asking a question no one has ever thought of before is a logical process."

"I always think it's nearer to architecture rather than to other arts; one is trying to build this formal structure up and there are supports and girders and there are connections..."

Are Mathematicians creative? If creativity is a process more than a product, I think then that the answer is yes. What do you think?