The Poincaré Conjecture (Rabbits are Spheres)

In 2003, a reclusive, Russian mathematician named Grigory Perelman announced that he had solved the famous, intractable Poincaré Conjecture, which concerns the nature of space. Depending on who is talking, Poincaré’s conjecture can sound either daunting or deceptively simple. It asserts that if any loop in a certain kind of three-dimensional space can be shrunk to a point without ripping or tearing either the loop or the space, the space is equivalent to a sphere. Essentially, any object without a hole, according to Perelman's proof, is a sphere. So, human beings, animals, even the most intricately shaped objects that don't have holes are, in fact, spheres.

The conjecture is fundamental to topology, the branch of math that deals with shapes, sometimes described as geometry without the details. To a topologist, a sphere, a cigar and a rabbit’s head are all the same because they can be deformed into one another. Likewise, a coffee mug and a doughnut are also the same because each has one hole, but they are not equivalent to a sphere.

Mathematicians have been waiting for this result for more than 100 years, ever since the French polymath Henri Poincaré posed the problem in 1904. And they acknowledge that it may be another 100 years before its full implications for math and physics are understood. For now, they say, it is just beautiful, like art or a challenging new opera. Personally, I am excited for our world's top minds to realize the potential of such a breakthrough; the possibilities seem to be endless.

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