You might have heard of Grigori Perelman. This brilliant mathematician solved the "Poincaré conjecture" stated by Henri Poincaré as a question in his 1904 paper. The conjecture has been open for about a century before Perelman solved it through a series of arXiv
e-prints in which the first one appeared in 2002. It is one of the Millennium Prize Problems in which you will be awarded $1,000,000 for solving one of them. However, the prize is clearly not the main motivation behind the attempt of solving one of these problems as a mathematician, a scientist, or any researcher for that matter. With Perelman rejecting the prize after it was awarded to him in 2010, simply shows profound appreciation of the essence and relevance of the Poincaré conjecture in my opinion. As Perelman put it in an interview:
"Why did we have to struggle with the Poincare conjecture for so many years? To put it in a nutshell, the essence of it is the following. If a three-dimensional surface is reminiscent of a sphere, then it can be spread into a sphere. It is known as the Formula of the Universe because it is highly important in researching complicated physical processes in the theory of creation. The Poincare conjecture also gives an answer to the question about the shape of the Universe.",
one can see the philosophical importance of the problem. When asked why he declined the prize, his answer was:
"... I know how to control the Universe. Why would I run after a million, tell me?"
This seems controversial, but he is clear about how valuable his discoveries were. As for the phrase "control the Universe", one can see that this is more on the power of abstract thinking that through the solution of the Poincaré conjecture, one can fold the universe in a reversible process like crumpling a piece of paper
into the smallest sphere possible and then unfold it back again. Speaking of crumpling a piece of paper in the area of Physics, this process has mesmerized researchers
in a sense that a process considered simple can be overwhelmingly more complicated than one would have thought. To give you an idea,
it is a very intricate process that requires massive force just like detonating an atomic bomb. Just like the research on atomic bomb, a researcher should answer the "why" question first and consider its impact to humanity.
Nature can be that fascinating; kudos to the Creator of nature for that matter.
