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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.
it does not mean you're any good at what you do.
"Have you ever thought about just turning off the TV, sitting down with your kids, and hitting them?"
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 could, the geometric shape can be abstracted into other things. Such as time, and process, I could see this being used to help optimize a parallel programming process where a particular code takes so long to run, but to avoid collisions the different elements in time, will need to hit different process points at different time, then you need to span it up, so how many unique process points will you need. Say with a massively parallel system, such as an advanced quantum computer.
If something is so important that you feel the need to post it on the internet... It probably isn't that important.
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.
Big Science and maverick outsiders can actually greatly benefit from each others' existences, for the mavericks are free to ask questions which might be out-of-bounds in academic circles -- and so, they are much better positioned to start new groundbreaking lines of investigation. We can solve the publish-or-perish problem with this exact approach, but it will require us to care more about long-term innovations than our short-sighted desires to confirm our pre-existing worldviews.
The top-down philosophical approach of specialist science has left us with a sort of vacuum of tools to support the outsider maverick thinkers. To the extent that it is acknowledged that outsiders can contribute in important ways, we will inch closer to creating these tools.
It was well known that one never needs more than 7 colors- this comes from a little work where one can tile the plane with hexagons and then pick 7 distinct colors cleverly. It was also known that you needed at least 4 colors, since one can construct configurations which require 4 colors. Both of these parts are simple enough that working out the details are fun exercises. What Aubrey de Grey did is use a careful construction involving certain specific subconfigurations to aid a computer search to construct a very big configuration which was highly likely to need 5 colors; he then verified using a computer system that this configuration did require 5 colors. But note that while this is progress this isn't a full solution; this shows that the number of colors needed is at least 5, but whether it is 5,6 or 7 is unclear. My own guess based on his work is tentatively towards 6 because it looks like there's a lot of room in his configuration that might allow one to bump it up to 6 with a few more ideas and the argument for why one needs at most 7 is so simple that it seems like something should be able to reduce that even if no one has figured it out yet.
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.
Perhaps this could lead to a proof for the somewhat similar four color theorem?
No need.
"The four color theorem was proved in 1976 by Kenneth Appel and Wolfgang Haken... To dispel remaining doubt about the Appel–Haken proof, a simpler proof using the same ideas and still relying on computers was published in 1997 by Robertson, Sanders, Seymour, and Thomas. Additionally, in 2005, the theorem was proved by Georges Gonthier with general-purpose theorem-proving software."
https://en.wikipedia.org/wiki/...
We all know when using graphs at the large scale every shit is converging towards number 6.
As proven by the "Kevin Bacon Six Degrees of Separation" theory.
His ignorance covered the whole earth like a blanket, and there was hardly a hole in it anywhere. - Mark Twain
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.
As long as we can agree that the British don't belong in the American internet I think we're all on the same page.
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.
Hmmm...lemme guess, when Evariste Galois was inventing group theory, you'd be in the peanut gallery claiming you couldn't see any use for it (hint, he did it in the early 1800s). And when those wild and crazy guys were screwing up developing the math for quantum mechanics, you'd be asking them for a practical use (hint, they did it in the early 1900s).
In short, if someone cannot point to a use of something, it shouldn't be done. How enlightened of you? Have you explained your theory to scientists? I'm sure they'd listen to you.
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.
The British often linguistically treat "mathematics" as though were the plural of some noun "mathematic". But the -s is the nominative -s.
Yes, as you say mathematics, like pyrotechnics, the s is an integral part of the noun, and not a plural. It comes from Greek -ikos.
Exceptions exist, like "music" which perhaps should have been musics (from mousikos), given that the (once synonymous) technikos became technics.
On the other hand there is "chiropractic", where the name is as made up as the practice, and it doesn't have an s at the end.
No matter how much sense a definition makes in your own head, that's not how language works.
Socialism: a lie told by totalitarians and believed by fools.
Only in the same way that math is a subfield of biology, since it's done by humans.
He's not paid to publish math papers, is the point.
Socialism: a lie told by totalitarians and believed by fools.
That would be Hilbert space filling curves. Those are used to optimize parallel processing. Also used in a way to arrange the folding of the brain so that every region is a minimum distance from the spinal cord and optic nerves.
Vintage computer adverts: http://www.vintageadbrowser.com/computers-and-software-ads
Exactly, but don't we have a countable number of rotations, therefore necessitating a countable solution?
But I am starting to see why this problem is so hard. If i understand it correctly, dots can be any distance apart, it is just that the ones equal distance apart have lines.
So the solution is probably not a pretty looking pattern, where all neighbor dots are equal distance but instead a bloody mess of thousands of patterns overlapping each other and all you can see is chaos.
Troll is not a replacement for I disagree.
In 3D the number most likely jumps to infinity. This is like the how many colours does it take to colour a map so that no adjacent countries have the same colour. 1D is trivally 2, 2D is four but the proof sucks, 3D is clearly infinity.
Although it might be tempting to "analogize" the problem the 4 color map problem, in fact the problems are not at all similar and have a different answer.
Even, the wikipedia entry on this problem has an answer to this particular generalization to 3D...
The problem can easily be extended to higher dimensions. In particular, finding the chromatic number of space usually refers to the 3-dimensional version. As with the version on the plane, the answer is not known, but has been shown to be at least 6 and at most 15.
This is a pointer to paper the illustrates the upper bound for R^3 in case you are interested.