# Poincaré Conjecture (The Proof is in the Method)

(Image by crdotx)

Though I’m a little bit late on this, Science Magazine recently published a great article on the scientific breakthroughs of 2006. Topping the list was the proof of the Poincaré Conjecture, which I’ve posted about several times on this blog. You can read their synopsis of the breakthrough proof here. It turns out that from the media’s perspective the drama behind the proof is almost greater than the mathematical result. Basically there was a lot of name calling among some members of the mathematical community concerning who made certain contributions toward the eventual proof. Sad. Apart from the soap opera, the author explains the Poincaré Conjecture in a very accessible way, which should be understandable by anyone who’s interested in reading it. This proof will be a huge deal for mathematics over the coming decades, and should help mathematicians better understand topics such as the “Navier-Stokes equation [of fluid dynamics] and the Einstein equation [of general relativity].”

Perhaps the most interesting thing to note is that the article focuses
not only on the **result** of the problem (the proof itself), but also
the **methods** used to solve the problem. This is an hugely understated
part of the mathematical process. I’m of the opinion that when the
general populace thinks about math that they are fixated on two things:
the problem and the answer. What people tend to overlook is the
**process** of problem solving. In math, there are not always clear-cut
methods that explain how to get from point A to point B. A lot of
thought is sometimes necessary to figure out how to traverse the path.
The Poincaré Conjecture is a monumental achievement not only because of
the end result, but also because of the original steps the solvers of
the problem (especially Grigori Perelman) took to get there. These steps
will be used in other problems; they are not exclusively tied to this
one specific problem. Once again, congratulations to Perelman and the
other mathematicians who had a hand in making this historic achievement!