When most people think about math problems, we think back to algebra class, geometry, or for the real showoffs, trigonometry.
For true mathematicians, however, things get much more complicated. Rather than taking 5-10 minutes to figure out a problem that already has a known answer, these people work for a lifetime on problems that they know may never be solved.
In August of 1900, David Hilbert presented 10 of the 23 problems that had yet to be solved by the mathematical community to the Second International Congress of Mathematicians in Paris. The hope was that over the next century, the top math minds in the world would be able to solve them.
Throughout the 1900’s, all but five of them have been solved. So, in the year 2000, a community of mathematicians presented new problems that could serve as the focus for the next century.
The presentation took place at the College de France and the Clay Institute in Paris. This was a nonprofit foundation that is entirely dedicated to helping to discover and disseminate mathematical knowledge throughout the world.
It was decided that the group would present 50 as yet unsolved problems, and offer a monetary reward to anyone who could solve them. Creating the list of which problems would be included in the “millennium prize” as it was called, was a difficult process as mathematicians from around the world were able to submit and discuss potential options for inclusion.
In the end, they presented the problems, including their top seven list, each of which would come with a $1 million prize for solving it. One of those seven is known as the Poincare Conjecture, which states:
“Every three-dimensional topological manifold which is closed, connected, and has trivial fundamental group is homeomorphic to the three-dimensional sphere.”
Simple enough, right?
Well, in November of 2002 a paper was submitted to ArXiv preprint server, which discussed something called the Ricci flow. Then, in March and July of 2003, two more papers were submitted.
All of these papers were sent in by Grigori Perelman, who is a well-known Russian mathematician. In the papers, he skipped over the standard process of providing opening statements and explaining his processes. Instead, he got right to the point. The point was, it seems, to solve the Poincare Conjecture.
Oddly, however, he didn’t come right out and say that this is what his papers actually did. Instead, another mathematician, Vitali Kapovich, had to email him to clarify. In the email, he said:
“Hi Grisha. Sorry to bother you but a lot of people are asking me about your preprint ‘The entropy formula for the Ricci…’ Do I understand it correctly that while you cannot yet do all the steps in the Hamilton program you can do enough so that using some collapsing results you can prove geometrization? Vitali.”
For those who aren’t world-class mathematicians, that was basically asking Perelman if he had just solved one of the most difficult problems in the world, the Poincare Conjecture.
Perelman replied simply:
“That’s correct. Grisha.”
Not surprisingly, this created quite a stir throughout the mathematical world. Perelman was immediately thrust to the top of the list for the most prestigious awards including the Fields Medal Medal, and of course, the first of the $1 million Millennium prizes.
In 2006, he turned down the Fields Medal, and when he was awarded the $1 million Millennium Prize, he declined that as well.
He is known to be very reclusive and does not want any of the attention that would come with these types of things. In fact, he seems to have become disillusioned with mathematics and hasn’t been submitting any papers or interacting with the larger mathematical community in years.
While it is not known for certain what he is doing, or what he might be working on in private, most people believe he is likely still living in a small St. Petersburg apartment. The same one he shared with his mother when he solved one of the most difficult problems math has ever known.
What a legend.
There are still six of the Millennial Prize problems to be solved, if anyone is interested.
If you thought that was interesting, you might like to read about why we should be worried about the leak in the bottom of the ocean.
