[Math Lair] Famous Math Problems

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Here is a list, in no particular order, of some famous math problems, puzzles, and questions:

Konigsberg Bridges
Zeno's paradox
Fermat's Last Theorem
Three Construction Problems of Antiquity
Euclid's Parallel Postulate
See Euclidean and Non-Euclidean Geometry for more information.
Riemann Hypothesis
Four Colour Theorem
Travelling Salesman problem