An Outreach Note on the Poincar\'e Conjecture for Non-specialists

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.