Poincaré's Conjecture


All French media have been talking mathematics last week, after 2006 Fields Medals — usually defined as the 'Nobel Prize of Mathematics' — were awarded by the International Mathematical Union.

First, because among the four awarded mathematicians, there was a French specialist of probabilities named Wendelin Werner, who is not only a high-level scientist, but a violinist, and once was a child actor. Second, because another awarded mathematician, Russian Gregori Perelman, got the medal because of his work on Poincaré conjecture... and refused it.

You know, Frenchmen as a rule are crazy about mathematics. Of course, many were not that good in maths at school, most of them barely understand anything in maths... but they do love maths anyway. Mathematics... this is so rational, so smart, so logical a matter, how could French people dislike maths?

In 1904, French mathematician Henri Poincaré forthrightly asked his colleagues:
Hey dudes! I have a funny question: consider a compact 3-dimensional manifold V without boundary. Is it possible that the fundamental group of V could be trivial, even though V is not homeomorphic to the 3-dimensional sphere?
Ha-ha, Good question indeed, Henri, other mathematician answered... for one century, until Gregori Perelman found the solution.

As for me, I don't even understand what the question means... Do you?

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