Mathematicians Edge Closer to Solving a ‘Million Dollar’ Math Problem

Did a team of mathematicians just take a big step toward answering a 160-year-old, million-dollar question in mathematics? Maybe. The crew did solve a number of other, smaller questions in a field called number theory. And in doing so, they have reopened an old avenue that might eventually lead to an answer to the old question: Is the Riemann hypothesis correct? The Reimann hypothesis is a fundamental mathematical conjecture that has huge implications for the rest of math. It forms the foundation for many other mathematical ideas — but no one knows if it’s true. Its validity has become one of the most famous open questions in mathematics. It’s one of seven “Millennium Problems” laid out in 2000, with the promise that whoever solves them will win $1 million. (Only one of the problems has since been solved.) Back in 1859, a German mathematician named Bernhard Riemann proposed an answer to a particularly thorny math equation. His hypothesis goes like this: The real part of every non-trivial zero of the Riemann zeta function is 1/2. That’s a pretty abstract mathematical statement, having to do with what numbers you can put into a particular mathematical function to make that function equal zero. But it turns out to matter a great deal, most importantly regarding questions of how often you’ll encounter prime numbers as you count up toward infinity. We’ll come back to the details of the hypothesis later. But the important thing to know now is that if the Riemann hypothesis is true, it answers a lot of questions in mathematics. “So often in number theory, what ends up happening is if you assume the Riemann hypothesis [is true], you’re then able to prove all kinds of other results,” Lola Thompson, a number theorist at Oberlin College in Ohio, who wasn’t involved in this latest research, said. Often, she told Live Science, number theorists will first prove that something is true if the Riemann hypothesis is true. Then they’ll use that proof as a sort of stepping stone toward a more intricate proof, which shows that their original conclusion is true whether or not the Riemann hypothesis is true. The fact that this trick works, she said, convinces many mathematicians that the Riemann hypothesis must be true. But the truth is that nobody knows for sure. So how did this small team of mathematicians seem to bring us closer toward a solution? Click here to see the answer to that question, and read the rest of the article.

Fascinating!    🙂

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