Wednesday, April 14, 2021

Q: Is This an Easy Problem or a Hard Problem? A: Yes

I'm not 100% sure of the solution to a famous mathematical conjecture proposed by Paul Erdős some 50 years ago -- by which I mean I'm not sure I understand it. Even this relatively simple explanation at Quanta magazine quickly gets esoteric for one whose math skills drop off once we travel beyond arithmetic.

The thing I thought most interesting about the story was that Erdős and a couple of friends -- Vance Faber and Lászlo Lovász -- dreamed up this problem as intentionally one of the simplest they could think of during a tea party. They dallied with it a little at the party and set it aside to finish the next day. "The next day" turned out to be January 2021, as five mathematicians from the University of Birmingham -- Abishek Methuku, Dong-yeap Kang, Tom Kelly, Daniela Kühn and Deryk Osthus -- finally figured out a way to prove their answer to the Erdős -Faber-Lovász Conjecture.

Although Erdős died in 1996, both Faber and Lovász are still living and congratulated the Birmingham team, which is technically known as the Combinatorics, Algorithms and Probability Team at the university.

The thing that struck me was how the problem was intentionally created to be simple and initially thought to be so by the conjecturing trio, only to turn into a mathematical hairball that took 50 years to figure out. Math, much like life, often winds up with intended simplicity giving way to unintended complexity.

Now as to whether or not I'll ever be able to figure out what any of the 8 mathematicians listed were talking about? I think that problem has a simple answer: Highly unlikely.

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