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60-Year-Old Maths Problem Partly Solved By Amateur (theguardian.com)
An amateur mathematician has made the first breakthrough in more than 60 years towards solving a well-known maths problem. From a report: Aubrey de Grey, who is more widely known as a maverick biologist intent on extending the human lifespan, has taken the academic world by surprise after announcing a new solution to the so-called Hadwiger-Nelson problem. The problem sounds deceptively simple, but despite some professionals spending years trying to crack it, progress has stalled since shortly after the puzzle was first posed in 1950. "Literally, this is the first progress in more than 60 years," said Gil Kalai, a mathematician at Hebrew University of Jerusalem.
The problem is as follows. Imagine a collection of dots connected by lines. The dots can be arranged any way at all, the only rule is that all the connecting lines must be of equal length. For instance, in a square the diagonal would not be joined up, but the outer edges would be. Now, colour in all the dots so that no two connected points have the same colour. How many colours are required. For a square, the answer would be two. But the Hadwiger-Nelson problem asks what the minimum would be for any configuration -- even one that extends across a plane of infinite size.
The problem is as follows. Imagine a collection of dots connected by lines. The dots can be arranged any way at all, the only rule is that all the connecting lines must be of equal length. For instance, in a square the diagonal would not be joined up, but the outer edges would be. Now, colour in all the dots so that no two connected points have the same colour. How many colours are required. For a square, the answer would be two. But the Hadwiger-Nelson problem asks what the minimum would be for any configuration -- even one that extends across a plane of infinite size.
https://en.wikipedia.org/wiki/...
(((dB)))
If you read the articles, he pushed the instance of contradictory evidence from N=4 to N=5, but has no proof that N=6 isn't a instance.
Thus, it is a new piece of evidence that N>=5, but not that it is solved.
Aubrey De gray's finding has the attention of the Polymath Project, "a collaboration among mathematicians to solve important and difficult mathematical problems by coordinating many mathematicians to communicate with each other on finding the best route to the solution."
You can follow their current conversation here.
It's the British English spelling, which makes sense given the story is from the Guardian. I guess we could squabble about whether maths or math is more appropriate, but they're both contractions of mathematics.
https://www.quantamagazine.org...
Is the article article about what was done, not the cut down version from a gossip rag sheet which is given in the summary.
So looking at his Wikipedia page, he doesn't sound like an amateur mathematician if he has a degree in computer science. Interestingly, he seems like an amateur biologist in the sense that he was self-taught and awarded a PhD based on a book he wrote based on that self-teaching.
An amateur mathematician has made the first breakthrough in more than 60 years towards solving a well-known maths problem.
Why is it relevant whether he gets paid to solve mathematical problems or not? Amateur just means that someone doesn't derive any income from the task. It has nothing to do with competence or the lack thereof. Plenty of people are very talented at things they don't get paid for.
Essentially, it has been known for a while that the answer is either 4 or 5 or 6 or 7.
This paper identifies a graph that cannot be colored with just 4 colors, so it establishes 5 as the new lower bound.
There's no reason to argue... it's actually pretty easy to explain how the (modern) English are wrong:
Separated by a Common Language: Math(s)
The British often linguistically treat "mathematics" as though were the plural of some noun "mathematic". But the -s is the nominative -s.
How do we know that these are really different affixes, and not just the same affix doing a range of jobs? Partly we know from history. The plural -s comes from an Old English case suffix (-es or -as). The verb one has derived from the suffix -eth (or -ath) in earlier Englishes. The adverbial one is related to the possessive 's. And our friend the nominali{s/z}ing (=noun-making) suffix generally affixes to roots from classical Greek.
It's easy to find other uses of the nominative -s -- for example, almost any high-level subject of study such as mechanics, physics, economics, linguistics -- but now many are long and common enough to be frequently abbreviated by common people. For example, few people talk about "economics" often enough to shorten it to "econ" or "econs" (though when they do, it's usually "econ").
This also is one of the cases that led me to rule of thumb "(modern) English people can't speak English". Americans seem to hang on to the "old way" of speaker longer than the British do.