Did You Know it was Impossible?

I did not know this:
And Moran says even the story of the Opera House is of operatic proportion, beginning with the competition to design the building in 1955. The Chief Judge was none other than Finnish-American architect Eero Saarinen. He didn't like the final entries, and demanded to look at the reject pile.
"And he pulled out entry number 218, which was by a 38-year-old Danish architect called Jorn Uton," Moran says. "And Eero Saarinen said, 'Ladies and Gentleman, this is your winner.'"
But there was a problem: the technology to build the design - finding a way to support the sail-like roofs - did not exist.
"The engineer looked at all these different methods to build what Jorn Utzon wanted to do and in the end he said, 'This cannot be done. It's impossible,'" says Moran.
They could have built anything, but they built it the way they did despite the fact that it was impossible. How many other buildings can you say that about?