‘Once in a Century’ Proof Settles Math’s Kakeya Conjecture
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Summary
For over 50 years, mathematicians have been attempting to solve the three-dimensional Kakeya problem, involving a hypothetical pencil that moves through minimal space to point in every possible direction.
Now, mathematicians Hong Wang and Joshua Zahl have proven the three-dimensional Kakeya conjecture, showing that there is an absolute limit to the minimum amount of space that the pencil must move through.
Wang and Zahl were able to show that the problem could be simplified by looking at the grains or sections that have a high level of overlap, rather than the whole, and that each point couldn’t have too many grains intersecting it.
The resolution of this problem could lead to a better understanding of the Fourier transform, and opens the door for the solving of other problems in this field.
The four-dimensional version of the problem remains open.
