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Decades-Old Graph Problem Yields to Amateur Mathematician
- simulate 9y agoThe discovery was made by Aubrey de Grey, the same person who believes that humans will eventually live past 1,000. Weird! > [de Grey] found his way to the chromatic number of the plane problem through a board game. Decades ago, de Grey was a competitive Othello player, and he fell in with some mathematicians who were also enthusiasts of the game. They introduced him to graph theory, and he comes back to it now and then. “Occasionally, when I need a rest from my real job, I’ll think about math,” he said. Over Christmas last year, he had a chance to do that.
- 0003 9y agoYeah I did a spit-take when I read this. I remember him doing a TED talk ages ago...
- zitterbewegung 9y agoRecreational math / CS is so much fun . I usually try thinking of knot theory. Haven’t really discovered anything yet but it’s still fun. So far the best question I have asked is https://cstheory.stackexchange.com/questions/32292/knot-recognition-as-a-proof-of-work-system https://cstheory.stackexchange.com/questions/32292/knot-reco... .
- georgewsinger 9y agoThis guy has a background in computer science, but taught himself biology to spearhead the regenerative medicine movement. If I'm not mistaken, he published a book in biology with no formal credentials (16 years after receiving his BA in computer science), after which Cambridge honored him with a PhD in the subject. He's also Thiel backed.
- brightball 9y agoI find that I’m much more open to teaching myself just about anything now. Years of learning every new thing under the sun in the software world will do that. Doesn’t surprise me at all to hear this.
- brmgb 9y ago> honored him with a PhD in the subject Just to precise if you were confused like me, Cambridge gave him an actual PhD in Biology based on the book - meaning the book satisfied all the prerequisites of a PhD at Cambridge and he had to do a viva - not just an honorary degree. That's quite an impressive fellow.
- jey 9y ago> viva I wasn't familiar with this term; apparently it refers to the "oral defense" of a PhD thesis.
- schoen 9y agoFrom Latin "viva voce", literally 'with a live voice' and roughly meaning 'aloud'. https://en.wiktionary.org/wiki/viva_voce#English https://en.wiktionary.org/wiki/viva_voce#English
- ramesh92 9y agoedwsgfsd
- kenver 9y agoOne of the toughest experiences of my work life was my viva. The examiner picks at every hole in your work and you need to have an answer. Even if the answer is acknowledging it and proposing future work. It's a very useful experience, and when combined with the rest of a PhD, teaches you to be humble and accept that criticism of work is not an attack on the author. I still have nightmares about mine!
- Angostura 9y agoAt my university you also got a 'viva voce' as an undergraduate if your BSc is borderline between two grades. I received one and yes, I got the lower grade.
- stordoff 9y agoIt's not strictly limited to just PhDs - at my university, I was required to take one for a year-end undergraduate project.
- HiroshiSan 9y agoGotta downplay his achievements to fit the narrative of the 'prodigy'.
- 8bitsrule 9y agoAnother such word: 'fringe'
- ramesh92 9y agoscadfdgf
- sd90909 9y agoWhat do you mean? How is it downplaying?
- HiroshiSan 9y agoDownplaying in the sense that it's god given and not sweat equity.
- dabockster 9y ago> He's also Thiel backed. Is having Thiel's association a positive thing still? Serious question.
- glibgil 9y agoGiven Thiel's interest in longevity, yes
- grkvlt 9y agoOh great; an immortal Peter Thiel, just what the world needs...!
- bhasi 9y agoOh, I thought the implication was the other way around, something to do with Thiel's political leanings. My bad.
- nontechdude1 9y agofrom a political perspective, no. if you care about actual technological accomplishments, as a technologist, peter thiel's endorsement should matter a lot.
- jimmy1 9y agoAbsolutely, especially depending on our audience. To your typical SJW crowd, probably not. To everyone else, yes.
- toren 9y agoI would assume so. I couldn't care less about his political affiliations
- billhendricksjr 9y agoHis political affiliations are in conflict with his desire for long life, given who has the nuclear football. I don’t care, I’m an atheist with no kids who’d be bored out of my mind before I hit 300 years old, much less 1,000.
- wwwtyro 9y agoIf you haven't watched an Aubrey de Grey talk, you owe it to yourself to give the man a listen. Beyond the admittedly interesting topic, he's genuinely entertaining.
- ndr 9y agoAubrey de Grey is much more than just an Amateur Mathematician, I highly recommend Rob Reid's podcast episode with him: https://after-on.com/episodes/020 https://after-on.com/episodes/020
- spuz 9y agoThis was great, thanks.
- IB885588 9y agoAubrey de Grey is chief science officer and co-founder at the SENS Research Foundation, which is the only charity that I personally support because I think it has small resources compared to the potential good it could do to increase healthy life and reduce human suffering. http://www.SENS.org http://www.SENS.org
- dabockster 9y agoI have to admit, I love how that site incorporates HTML5 without shoving a bunch of animations in my face. Great design!
- deleted 9y ago[deleted]
- iak8god 9y agoHere's some info pulled right from https://www.againstmalaria.com/ https://www.againstmalaria.com/: * Half a million people die each year and 400 million fall ill [with malaria] * 70% of them are children under 5 * #1 killer of pregnant women * Malaria is preventable Malaria nets cost $2. Antimalarial drugs are dirt cheap in the developing world. If you want to impact human suffering and increase human health, this is a good place to start. Not with trying to extend the long and already pleasant lives of rich people in the West.
- Mediterraneo10 9y agoThere are a lot of charities handing out mosquito nets in a driveby fashion. There are not many charities working closely enough with local communities to ensure that those mosquito nets will actually be used, and they won’t be turned into fishing nets instead. If you donate to malaria prevention, make sure it’s a truly hands-on charity.
- iak8god 9y agoThank you for the information. I have no connection to the charity I linked (except I think I may have given them $50 once), and I don't know which charities, if any, are effective at preventing malaria. Maybe they should be giving out fishing nets as well. It's telling that for the communities receiving these nets, they see starvation as a more immediate threat. Anyway, my point is just that if you're looking to make optimal use of money to save or improve human lives, there are many things that should be higher priorities than stopping people dying "of old age" in the West.
- vladislav 9y agoIn my experience, being an amateur mathematician is more fun that doing it professionally, and potentially just as productive. You don't get nearly as much time for math, so you make the most of it and work only on the most interesting problems as opposed to just writing another paper. There's no time for beating your head against the wall, so you just do it when you're inspired, which is how problems get solved anyway.
- hermitdev 9y agoI think for a large number of people, myself included, the "Eureka!" moment often occurs when you're least focused on the problem at hand. I remember in college, studying EE, I was struggling to make sense of how a flip-flop worked (the basis of a register). My ah-ha moment was literally in the shower.
- senatorobama 9y agoWhat was it?
- toomanybeersies 9y agoIf I've been working on a problem at work for too long, I'll often stop working on it and just work on something else, because I know that tomorrow when I take a shower or when I'm walking to work the next day I'll figure it out in my head.
- 8bitsrule 9y agoFor more on this subject, see the 1945 essay by French mathematician Jacques Hadamard, An Essay on the Psychology of Invention in the Mathematical Field. https://archive.org/details/eassayonthepsych006281mbp https://archive.org/details/eassayonthepsych006281mbp
- ctchocula 9y agoThank you for sharing. One thing that impressed me about Hamming's essay on how to produce world-class research [1] is that it suggests a necessary, but not sufficient prerequisite is to spend your waking life thinking hard about some problem. This is necessary in order to provoke the unconscious mind into doing the heavy-lifting required for a "Eureka!" moment, so I was pleasantly surprised when Hadamard's book has a chapter titled "The Unconscious and Discovery". It amazed me that even in the modern world we do not understand the processes that led to these breakthroughs, so we can only leave them in the realm of the otherworldly and the mystical. [1] http://www.cs.virginia.edu/~robins/YouAndYourResearch.html http://www.cs.virginia.edu/~robins/YouAndYourResearch.html
- hermitdev 9y agoThe 4-color map theory is bunk. It is very easy to create an artificial map that would require more than 4 colors to color the map without any adjacent "countries" having the same color. This is easier to draw than to explain, but I'll try. Imagine N-countries shaped generally as concentric rings. The outer-most ring, however, has an isthmus into the very center, forming both "ring" 0 and "ring" N with ring 0 being the center, and N being the outer most. Let's state this isthmus occurs at the bottom of the ring for convenience. Now, if ring 1 has a parallel isthmus that runs along the left of N's and parallel to that of of N's until it reaches N, and ring 2 has its own that runs in the same manner until it hits ring N-2, etc. Then, consider if on the right side, you do the opposite: N-1 extends until it hits ring 1, N-2 until it hits ring 2. It's a rather easy formula to produce a "map" that requires N colors if no two colors are to touch.
- IshKebab 9y ago"This mathematical theory that has been proven is bunk" Right... Either you're misunderstanding what the theory says or your crazy concentric countries idea doesn't work (hard to tell from your description).
- hermitdev 9y agoLike I said, describing it is hard, but showing it is not See this: https://imgur.com/iU7oc8d https://imgur.com/iU7oc8d There's no way to color that with 4 colors without a color hitting itself. Yes, it's contrived, but so are borders. Also, the 4-color theorem didn't limit itself to established borders, it claims to be for an arbitrary map. This image, is well, arbitrary and drawn up in paint in a few minutes, but it shows the point.
- moomin 9y agoGraph Theory, unlike number theory, is a strangely shallow subject. By this I mean that a lot of the results don’t require a large number of previous results (there’s definitely some). Compare this to number theory, where every interesting extant problem appears to require ten years study. (I realise people may infer a value judgement from shallow/deep, but none is intended.)
- deleted 9y ago[deleted]
- vinchuco 9y agoUltimately, naming is pointing at clouds, but number theory IS older: https://books.google.com/ngrams/graph?content=graph+theory%2Cnumber+theory%2Clinear+algebra&year_start=1800&year_end=2008&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Cgraph%20theory%3B%2Cc0%3B.t1%3B%2Cnumber%20theory%3B%2Cc0%3B.t1%3B%2Clinear%20algebra%3B%2Cc0 https://books.google.com/ngrams/graph?content=graph+theory%2... Afterthought: I wonder what caused the decline in the 80's (also true for other branches of math)
- Cyph0n 9y agoThat's around the time public-key crypto was invented. Coincidence?
- daniel-levin 9y ago>> Compare this to number theory, where every interesting extant problem appears to require ten years study. I don't often come here to comment but as someone in progress on an original research masters in number theory I can say this is utter bullshit. I assume your 'interesting' qualification (somehow) excludes obvious candidates like Landau's problems [0]. Some examples. I was taught about the ABC conjecture as an undergrad. You can easily teach the Brun sieve [1] method of working out that the sum of the reciprocal of the twin primes converges. Novel solutions to Diophantine problems are sometimes accessible to undergrads. Richard K. Guy wrote a whole book on unsolved problems in NT, some of which have been solved using undergraduate number theory and someone's upper bound you can just use (as easy as apt-get installing this_dope_bound). You can start reading papers without a PhD, never mind ten years of study. I think it's possible to get an utterly unrepresentative sample of either field by only sticking to "elementary" results. There are some extraordinarily subtle results in graph theory! Conversely, you can find NT problems amenable to elementary techniques [2]. [0] https://en.wikipedia.org/wiki/Landau%27s_problems https://en.wikipedia.org/wiki/Landau%27s_problems [1] https://en.wikipedia.org/wiki/Brun%27s_theorem https://en.wikipedia.org/wiki/Brun%27s_theorem [2] https://en.wikipedia.org/wiki/Quadratic_reciprocity https://en.wikipedia.org/wiki/Quadratic_reciprocity
- gowld 9y ago[Edit: because the drawing has unit edges. My mistake] Why is the Moser Spindle drawn to make it look non-planar, when it obviously is planar? The drawing obscures the point of the Moser Spindle, which is how to construct a 4-color graph from 2 simple 3-color graphs. It's also confusingly colored to make it not clear why it requires 4 colors https://d2r55xnwy6nx47.cloudfront.net/uploads/2018/04/ChromaticNumber_560Inline.jpg https://d2r55xnwy6nx47.cloudfront.net/uploads/2018/04/Chroma... Better: https://en.wikipedia.org/wiki/Moser_spindle#Application_to_the_Hadwiger%E2%80%93Nelson_problem https://en.wikipedia.org/wiki/Moser_spindle#Application_to_t...
- topynate 9y agoYou can embed the graph of the Moser spindle into the Euclidean plane without its edges crossing, but not in such a way that each edge is straight and of unit length.
- gowld 9y agoThe paper has beautiful illustrations. https://arxiv.org/pdf/1804.02385.pdf https://arxiv.org/pdf/1804.02385.pdf Animations showing how the larger graphs are built from smaller graphs would be amazing and illustrative for mortal non-mathematical-geniuses.
- 21 9y agoIs anyone else disturbed by the fact that the header image is incorrect? In that the distances between vertices are not all equal. See for example the blue node just beneath the outermost red node on the left side.
- bdcs 9y agoThe length between any two vertices which share an edge is 1 https://en.wikipedia.org/wiki/Unit_distance_graph https://en.wikipedia.org/wiki/Unit_distance_graph
- sowbug 9y agoIf you mean the blue node that's connected to the yellow node beneath it, I think it's actually connected to the yellow node beneath that one (the one that is distance 1 from the blue node :) ), and the edge happens to travel very close to the closer yellow node so that it looks like it intersects it. If those three nodes (blue, yellow, yellow) were in fact connected by short edges, then another problem would be that the two yellow nodes were connected, which they couldn't be by the constraints of the original problem.
- sajid 9y agoInteresting tidbit, there was a bug in the computer assisted part of the proof (now fixed): "Many thanks to Brendan McKay and Gordon Royle for letting me know overnight that they had successfully 4-coloured my 1567er; as a result I found a bug in the part of my code that implements the relaxation described in section 5.4 and now it agrees. " Source: https://gilkalai.wordpress.com/2018/04/10/aubrey-de-grey-the-chromatic-number-of-the-plane-is-at-least-5/#comment-40108 https://gilkalai.wordpress.com/2018/04/10/aubrey-de-grey-the...
- phkahler 9y agoIs it just me or does the image of 1581 vertex graph contain a face that looks a bit like krusty the clown?
- coldacid 9y agoOh good! I'm not the only one who saw that.
- tejohnso 9y agoI'm so glad Aubrey de Grey got a nice win here. I feel like he doesn't get enough credit for his other endeavours.
- andrepd 9y agoThe huge, flashing "Vote for us" button on the bottom right corner of the screen (at least on mobile) is incredibly distracting.
- melling 9y ago“The guy” is Aubrey de Grey, who used to get more discussion on HN: https://hn.algolia.com/?query=%20Aubrey%20de%20Grey&sort=byPopularity&prefix&page=0&dateRange=all&type=story https://hn.algolia.com/?query=%20Aubrey%20de%20Grey&sort=byP... Curing death doesn’t get much buzz these days. Maybe we’ll give it another look?
- profosaur 9y agoAnti-aging research is stronger than ever, with some very impressive results recently coming out of David Sinclair's lab at Harvard for example.
- kensai 9y agoA part omitted from the article is that de Gray is a genius. That partly explains his other achievements in other fields.
- chubot 9y agoWow, impressive. I had heard some disparaging comments about de Gray, kind of like you hear disparaging comments about Kurzweil (which I mostly don't agree with). For some people, there appears to be a fundamental aversion to their ideas which goes beyond mere disagreement. I don't know much about de Gray, but this piques my interest in what else he has done.
- slx26 9y agoWell, many of their ideas challenge the traditional mental model we have about humans and humanity. I think people feeling particularly offended or uncomfortable with that shouldn't surprise us.
- bbctol 9y agoThere's also the tiny issue that he hasn't produced anything of value.
- chubot 9y agoThis is precisely what I mean by "beyond mere disagreement". It's not enough to disagree; his character must be attacked as well.
- bbctol 9y agode Grey seems like a great guy; he's a fantastic speaker, I generally agree with his vision of humanity, and this proof is impressive. I haven't attacked his character, nor do I plan to. With respect to his work on resisting human aging, he hasn't produced anything of value.
- mygo 9y agowhat about this contribution to graph theory that we’re commenting on?
- ramesh92 9y agodcs gsf gs gds
- GarvielLoken 9y ago“Occasionally, when I need a rest from my real job, I’ll think about math,” Signature material.
- nailer 9y ago> Imagine, he said, a graph — a collection of points connected by lines. Ensure that all of the lines are exactly the same length, and that everything lies on the plane. I do not understand what 'everything lies on the plane' means. I take it as meaning 'everything is laid out in two dimensions' but that doesn't make sense. Can HN help?
- arundelo 9y agoThat is what it means. Note that the lines ("edges" in graph theory terms) can cross each other. Nelson asked: What is the smallest number of colors that you’d need to color any such graph, even one formed by linking an infinite number of vertices? The Wikipedia page describes the infinite-vertices version of this graph as an infinite graph with all points of the plane as vertices and with an edge between two vertices if and only if the distance between the two points is 1. This of course is impossible to draw but Wikipedia shows seven-vertex and ten-vertex subgraphs of it: https://en.wikipedia.org/wiki/Hadwiger%E2%80%93Nelson_problem https://en.wikipedia.org/wiki/Hadwiger%E2%80%93Nelson_proble...
- SirHound 9y agoBetter headline would be "Decades-old Graph Problem Yields to Amateur Mathematician and Straight-Up Genius Aubrey de Fucking Grey"
- hi41 9y agoMath is terse and biology is verbose. Normally a person good in biology dislikes math and a person good in math dislikes biology. He has done extremely well in both! How can one be so good in both?!
- mygo 9y agothe fact that Biology is verbose just means that we haven’t quite figured it out yet. And he’s over here trying to figure it out.