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mathematicianQuanta Magazine
•Science
Science
75% Informative
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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