Mathematician's Three-dimensional Pencil Solution

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Science

Kakeya’s problem: How does it affect the volume of space that a pencil moves through?

Summary

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Three -dimensional Kakeya conjecture shows limit to how small a pattern of movements can be.

Problem has eluded some of the greatest living mathematicians for five decades .

Hong Wang of New York University’s Courant Institute and Joshua Zahl of the University of British Columbia proved the conjecture.

Kakeya conjecture says no three -dimensional sets have a Hausdorff or Minkowski dimension below 2.5 .

But a special property called graininess allowed mathematicians to prove it.

They used a special machine to walk the bound up to three dimensions, starting from the lower bound.

“I really think there’s a critical mass of ideas to really revolutionize the whole field coming from here,” Hickman said. “It’s a very, very exciting time.”.

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