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What Makes the Hardest Equations in Physics So Difficult?

Reprinted with permission from Quanta Magazine‘s Abstractions blog.

Familiarity hasn’t bred knowledge: Turbulence is one of the least understood parts of the physical world.Photograph by Mike / Flickr

Physics contains equations that describe everything from the stretching of space-time to the flitter of photons. Yet only one set of equations is considered so mathematically challenging that it’s been chosen as one of seven “Millennium Prize Problems” endowed by the Clay Mathematics Institute with a $1 million reward: the Navier-Stokes equations, which describe how fluids flow.

Last month I wrote a story about an important  related to

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