Poincaré Conjecture


Poincaré Conjecture: Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere. In a 1904 paper, the French mathematician Jules Henri Poincare stated that every closed simply connected 3-manifold is homeomorphic to the 3-sphere. Dr. Grigory Perelman of the Steklov Institute of Mathematics (part of the Russian Academy of Sciences in St. Petersburg) solved the 100-year-old Poincare conjecture. The ICM awarded Perelman the Field…

Minesweeper – P vs NP


  It’s not often you can win a million dollars by analysing a computer game, but by a curious conjunction of fate, there’s a chance that you might. However, you’ll only pick up the loot if all the experts are wrong and a problem that they think is extraordinarily hard turns out to be easy.…

Milestones in Mathematics History


20,000 BC Carved notches in wood represent numbers. 3500 BC Numbers based on place value (base 60) used in Sumeria. The Sumerians had no symbol for zero. They used an empty space to represent a zero in the middle of a number but had no way to represent zero on the end of a number. Thus…

Fields Medal: Fundamental Lemma Proof – Prof. Ngo Bao Chau


Links to the original proof: – In French: Fundamental Lemma Proof – Ngo Bao Chau – In English: bodecoban-ngobaochau A talk by David Ben-Zvi on the Fundamental Lemma for a broad graduate audience at The University of Texas at Austin: The Fundamental Lemma, abstract: I will give a gentle overview of the ideas surrounding the Fundamental Lemma and…