An Outreach Note on the Poincare Conjecture for Non-specialists

Abstract

The Poincare Conjecture, a problem formulated by the French mathematician Henri Poincare more than a century ago, has been   one of the main challenge of modern mathematics. It  states that any three-dimensional space which is closed on itself  and without holes can be deformed into a sphere of dimension 3. Even if the conjecture was solved  at the beginning of this century, it still remains a mysterious, appealing and intriguing problem worth to be further studied in detail.  The purpose of this short popularizing note is, on the one hand, to provide a quick overview for non-experts of what we know today about the Poincare Conjecture and its related  problems in dimension 3, and,  on the other hand, to explain why it has represented  a central problem in mathematics.