Given that it is the spookiest time of the year, we felt that there is no topic more appropriate to talk about today than the Millennium Problems: the world's most daunting mathematics problems!
What are the Millennium Problems?
The Millennium Problems are seven mathematic and computer science problems presented by the Clay Mathematics Institute in 2000. The Institute offers a one million dollar prize to anyone who solves them. The famous seven problems are:
- Yang-Mills and Mass Gap
- Riemann Hypothesis
- P vs NP Problem
- Navier-Stokes Equation
- Hodge Conjecture
- Poincaré Conjecture
- Birch and Swinnerton-Dyer Conjecture
How many of them been solved?
So far, only one of the seven problems has been solved. In 2003, Russian mathematician Gregori Perelman solved the Poincaré Conjecture - building off of work from Richard S. Hamilton and a century of work from mathematicians trying to prove it. Perelman was offered the Fields Medal, but declined it.
How close to being solved are the unsolved problems?
Over the last nineteen years, dozens of solutions have been submitted for these problems. Many of them have not held up to peer-review, and some of them are currently being peer-reviewed. The late British mathematician Michael Atiyah submitted a solution to the Riemann Hypothesis in 2018, which was met with both excitement and skepticism.
For more information about the millennium problems, check out the CMI website!
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