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A pendulum in motion can either swing from side to side or turn in a continuous circle. The point at which it goes from one type of motion to the other is called the separatrix, and this can be calculated in most simple situations. When the pendulum is prodded at an almost constant rate though, the mathematics falls apart. Is there an equation that can describe that kind of separatrix?

Read more: https://www.newscientist.com/article/2193080-5-of-the-worlds-toughest-unsolved-maths-problems/#ixzz7Uvhz8qFz

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The Navier-Stokes equations, developed in 1822, are used to describe the motion of viscous fluid. Things like air passing over an aircraft wing or water flowing out of a tap. But there are certain situations in which it is unclear whether the equations fail or give no answer at all. Many mathematicians have tried – and failed – to resolve the matter, including Mukhtarbay Otelbaev of the Eurasian National University in Astana, Kazakhstan. In 2014, he claimed a solution, but later retracted it. This is one problem that is worth more than just prestige. It is also one of the Millennium Prize Problems, which means anyone who solves it can claim $1 million in prize money.

Read more: https://www.newscientist.com/article/2193080-5-of-the-worlds-toughest-unsolved-maths-problems/#ixzz7Uvj2ozGz

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