# Definition:Millennium Problems

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## Contents

## Definition

The **Millennium problems** are a collection of seven mathematical problems stated by the Clay Mathematics Institute on $24$ May $2000$.

Each carries a prize of $\$1 \, 000 \, 000$ (US dollars).

Six of them remain unsolved.

They are as follows:

- P versus NP
- The Hodge Conjecture
- The PoincarĂ© Conjecture (the only one of the seven to be solved)
- The Riemann Hypothesis
- Yang-Mills Existence and Mass Gap
- Navier-Stokes Existence and Smoothness
- The Birch and Swinnerton-Dyer Conjecture

## Also known as

Can also be referred to as the **Millennium Prize problems**.

## Also see

- Results about
**the Millennium Problems**can be found here.

## Sources

- 2002: Keith Devlin:
*The Millennium Problems* - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**Millennium Prize problems** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**Millennium Prize problems**