Are There Any Unsolved Problems in Mathematics?

Anyone who's ever moved furniture knows how frustrating it can be to get big items around tight corners, but surely you haven't been struggling with a sofa for more than 50 years. Mathematicians have, though.

The so-called "moving sofa problem" has been causing plenty of mathematical headaches since it was formally published by Leo Moser in 1966. It sounds simple enough: What's the largest sofa that will fit around a corner? To be more specific, "largest" means the greatest seating area, the hallway is a meter (3.3 feet) wide, the corner is 90 degrees, and the sofa must be pulled, not inclined or turned upright.

Although some promising solutions have been proposed over the years -- Joseph Gerver's 1992 answer is the current favorite -- to actually solve the problem, you have to demonstrate with an irrefutable mathematical proof that a particular sofa is the largest possible. And no one has done that ... yet.

Of course, mathematicians refuse to let the sofa problem lie and have even come up with variants to make matters more complicated. One such variant asks for the optimal shape of a sofa that must fit through a hallway with two right angles: one on the right and one on the left.

One suggestion: If you choose to tackle any of the sofa problems, take a nice nap first.

The magic of math: