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Kepler Conjecture

No packing of congruent spheres in three dimensions has density greater than $\frac{\pi}{\sqrt{18}} \approx 0.74048$....

The Banach-Tarski Paradox Question

What is the minimum number of pieces needed to perform a Banach-Tarski decomposition of the ball?...

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A curated repository of open mathematics problems from elementary to Millennium Prize level.

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