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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)))
I almost fell asleep reading that summary. Is this of any practical use what so ever? What is that â" in the last sentence supposed to be?
For the simple reason a line has two ends only
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?"
Does this help register allocation? Sounds like register allocation
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.
Sorry, I mean "Aubrey de Grey"
Maths?
Maths is hard, I guess.
English, even harder.
At last!
We should compromise and call it Numbers & Stuff
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.
Perhaps this could lead to a proof for the somewhat similar four color theorem? Also deceptively simple, and maybe obvious, but unproven.
We all know when using graphs at the large scale every shit is converging towards number 6.
So basically the problem seems to come to what is the most "connection dense setup". How many connections can you give every dot. But then that is not necessarily the entire solution, as odd vs even can have an effect as a triangle with an odd number of dots in a circular connection needs more colors than a square. I can see why they limit this to 2d planes, as the answer will clearly go up with every dimension added. 1D is simple, the answer is always 2 (for dots>1). Honestly, it sounds like it should be easy to solve.
Distances will not matter, it does not matter how dence you pack the dots it is all relative. so we are only talking about shapes and angles.
So we have a triangle that takes three,
Troll is not a replacement for I disagree.
Mathematics is
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.
I'm no mathematician and haven't read the linked article, but given a random point and a random distance, there are an infinite number of points at that distance from the first point. Problem is, there is an infinity of distances, so the chances that two random points will be at the same distance to the first is ... zero. That is, for any finite number of points (in a continuous line, plane, volume, or hypervolume), there is virtually no chance that any two pair will share the same distance. That seems to me to suggest that two colors is enough. Of course, if you constrain the locations of the points to some grid/lattice, then it would seem to relate to the occurrence of primes...but who the f**k knows....
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.
What right have amateurs to meddle into things that are reserved to professionals, for good reason? People should know their place. If you have any doubt that you should not do something, then you should not do it. One can never see the full consequences. Do not complicate your life.
If we could cure people of this stupid Europhilia affectations - "maths", for Christ's sake? Yes, TOS was on The Guardian, but the summary is for a largely US audience.
I guess it makes everyone feel sophisticated, while they suck on their 2-quart bottle of Mountain Dew in their mom's basement.
You're unreasonably bothered by this. Why does it upset you so? It's not as if "maths" is incorrect; after all, it's a contraction of MATHematicS. So... what's up?
> the summary is for a largely US audience
If we could cure people of this stupid USAcentrism...
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.
Oh grow up, languages are live, they change with the times...unlike....errr...you.
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.
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.
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Americans seem to hang on to the "old way" of speaker longer than the British do.
Americans are the Englishingist speakers in the world, bigly!
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.
Ironically, Mountain Dew is sold by the liter, not by the quart.
hey msmash why dont you reach up my anus and pull out the rest of the crusty turd you keep polishing into "diamonds"..
Sounds like a mainlander Chinese. Theyre good slaves and know their place.
...with no practical utility. Think about: if humanity has been able to live for 60 years without a solution to this"problem", do we need one now? No. This is proof of the difference between mathematical intelligence and social/emotional/practical intelligence. These bright people had better used their minds to solve REAL world problems, like inventing better batteries or affordable water-making/extracting machines.
At some colleges (University of Southampton, for example) computer science is part of the Department of Electronics and Computer Science within the Faculty of Engineering, totally separate from math.
Sure, computer science requires some math knowledge. So do engineering courses, science courses and medicine, to name a few, but you don't consider any of them to be "math" courses.
Imagine the 2D solution is 5. I then likely have a graph with 5 colours where two points not adjacent must be the same colour. Take this graph, copy it and then rotate it slightly out of the plane about one of those two points until the other point is the line distance away from it. Now those points are connected and then must be of opposite colors so I have a graph that now requires 6 colors. Also this new graph likely has 2 points that must be the same color. I copy and rotate again creating something that now requires 7...
Not so impressed after reading the story and finding out that it involved a computer search.
I suppose it is a proof for some definition of proof. But it is devoid of the insight that makes human proofs beautiful and which actually advances our understanding.
False. It is sold by the Fluid Ounce. Any marking of liters is approximate, and is only an advertising promise, not a label describing what units the product is sold by. In the US, every product is clearly "sold by" some type of unit, it may be based on volume, or weight, or something else. If you don't understand that, then you're at risk of being an idiot who whines that the box for some food product isn't filled to the top, when it's actually being sold by weight instead of volume. It matters to the consumer, because the rules are very narrowly written and affect product value.
Also, for anti-American unit-idiots, don't make the mistake of mis-naming US Customary Units as "Imperial," because there is an actual system of measures called Imperial. In the UK a Fluid Ounce is likely to be Imperial, and have a different value than a US fluid ounce.
As an example, a bottle of Mountain Dew with the words "2 liters" on the label, it is not being sold by liters. It is merely being advertised using that word. If you look at the label, the mandatory part that tells the consumer how much of the product they are buying will say "67.3 Fluid Ounces."
Like, totally. I can't even.
While it is nice, that you seem to have time for a hobby, the rest of us would prefer that you concentrate your mental power to solve the problem of immortality.
Thanks in advance
A US fluid ounce is defined as 1/128th of a US gallon, and The US gallon is legally defined as 231 cubic inches, which is exactly 3.785411784 litres., so the 67.3 Fluid Ounces is an exact number of liters. The "2 liter" proclamation on the bottle is probably an approximation, but the actual contents are legally defined in liters.
"When you have eliminated the unacceptable, whatever is left, however improbable, must be the truthiness" - Holmes
The can of Canadian coke zero in front of me does not have any reference to fluid or ounces. Just 355ml serving size, 46mg ace-k, 34mg for caffeine and 85mg aspartame.
How does anyone know there is an answer?
Just because someone can postulate a question doesn't mean there's an answer, so has someone proved there is an answer?
so that no two connected points have the same colour
They mean directly connected, or neighboring. "Connected" in graph theory means that there is a path.
Indeed. No matter how many times I've read it said as "maths" or heard it that way it always sounds like something a mentally challenged child would say.
People should care about amateur status. It deserves to be elevated above the same achievement of a professional.
I don't agree. First off all, "amateurism" is something of an overblown myth. Just because you don't get paid to do something doesn't mean you haven't put in a huge amount of time and effort. A lot of Olympic athletes are "amateurs" because they don't get paid to play but make no mistake that they've devoted a good portion of their life to their chosen sport and are very very good at it. Second, the achievement deserves to stand on its own merits. Why should someone who devoted their life to a vocation and happens to get paid for it be more or less worthy of accolades than someone who derives their income from some other profession? That makes zero sense.
When amateurs achieve something professionals do not it becomes evidence that achievements in a field are borne out of talent rather than grinding.
There is nothing about talent that is more worthy of respect than there is about hard work. Frankly for most problems of consequence you need some measure of both. Hard work beats talent when talent doesn't work hard.
It shows that you can achieve without funding and fancy equipment.
That's sort of a man bites dog argument. The reason that "funding and fancy equipment" exists is because it generally is necessary to solve a problem. Good luck finding the Higgs boson without a large particle accelerator. The theory on the other hand required nothing of the sort. There is no such requirement for most mathematics unless you regard pen and paper as "fancy equipment". As for funding, have you forgotten that mathematics is the language of science and engineering? It's not at all rare to find an engineer or scientists who is more than fluent in rather arcane branches of mathematics.
It's relevant because someone paid to do mathematics is presumed to have the time, inclination, motivation, and ability to advance the field.
That would be a naive assumption. It's not at all unusual to find scientists and engineers who are more than fluent in some rather arcane branches of mathematics. Math is the language of science and engineering. Almost any professional physicist is going to be highly competent at mathematics. Should it really be surprising that some of them might spend a bit of time working on some random math puzzles in their spare time or that they might be pretty good at it? Where they derive their income should be at most a footnote but probably is utterly irrelevant.
An amateur is presumed to only be able to work on problems in his scant spare time, with a mind trained to handle problems in another field.
That would be an inaccurate assumption. Many Olympic athletes are technically amateurs because they don't get their income from their sport but in reality they have spend vast amounts of time and effort learning their chosen sport. The only thing amateur means is that you don't get your income from the activity. It does not and should not imply that they haven't devoted any time or effort into the activity. I coach the sport of wrestling and have for over 25 years. I'm technically an amateur because I do not derive any meaningful income from it but I'm good at it. Better in fact than I am at my paying job which I'm also pretty good at doing. There just isn't enough money in it for me to make my living doing something I happen to be very good at so I'm resigned to "amateur" status. It just means I'm not paid to do it for a living.
Not correct, of course, but it's similar to rooting for the underdog.
Maybe if one doesn't actually know anything about the background of the "underdog". Most of the best mathematicians I know do not devote their lives to working as a math professor at a college. Such an assumption that you have to follow a certain path is a failure of the person doing the assuming.