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 "moving sofa problem" has stumped mathematicians for decades.
The "moving sofa problem" has stumped mathematicians for decades.

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:

  • There's a 50-50 chance that two people in a room of 23 will share a birthday and a 99 percent chance of such an occurrence in a room with 75 people.

  • It's a virtual certainty that the order of cards in a well-shuffled deck has never existed before.

  • The only number in the English language that is spelled with the same number of letters as its name is "four."

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