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| How do mathematical sunflowers emerge from random data? Photo: HelloRF Zcool |
Posed by the mathematicians Paul Erdős and Richard Rado in 1960, the problem concerns how often you would expect to find patterns resembling sunflowers in large collections of objects, such as a large scattering of points in the plane. While the new result doesn’t fully solve Erdős and Rado’s sunflower conjecture, it advances the mathematical understanding of how surprisingly intricate structures emerge out of randomness. To do so, it reimagined the problem in terms of a computer function — taking advantage of the increasingly rich interplay between theoretical computer science and pure mathematics.
“The paper is a new manifestation of a mathematical idea that’s going to be a central idea of our time. The result itself is spectacular,” said Gil Kalai of the Hebrew University of Jerusalem...
Erdős and Rado conjectured that as you draw more loops, a sunflower inevitably emerges, either as disjoint sets or as sets that overlap in just the right way. Their sunflower conjecture is part of a broader area of mathematics called Ramsey theory, which studies how order begins to appear as random systems grow larger.
“If you have a large enough mathematical object of some nature, there has to be some hidden structure inside it,” said Shachar Lovett of the University of California, San Diego, a co-author of the new work along with Ryan Alweiss of Princeton University, Kewen Wu of Peking University, and Jiapeng Zhang of Harvard University.
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Source: Quanta Magazine
