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Problem 1115

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Geometry Difficulty 5.0 Find the answer Tenth Philippine Mathematical Olympiad · Philippines

Graph theory's Four-Color Theorem says that four colors are enough to color the regions in a plane so that no two adjacent regions receive the same color. The theorem was proved in 1976 by Kenneth Appel and Wolfgang Haken, 124 years after the Four-Color Problem was posed.

Fermat's Last Theorem in Number Theory was proved by Andrew Wiles in 1995, after 358 years of attempts by generations of mathematicians.

In 2003, Grigori Perelman completed the proof of a conjecture in topology. Considered as one of the seven millennium prize problems, the conjecture says that the sphere is the only type of bounded three-dimensional surface that contains no holes. Mathematicians worked on this conjecture for almost a century. What is the name of this conjecture that earned Perelman the Fields Medal which he refused to accept in 2006?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

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Official solution

Solution:

Poincaré Conjecture

Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.