[Boards: 3 / a / aco / adv / an / asp / b / bant / biz / c / can / cgl / ck / cm / co / cock / d / diy / e / fa / fap / fit / fitlit / g / gd / gif / h / hc / his / hm / hr / i / ic / int / jp / k / lgbt / lit / m / mlp / mlpol / mo / mtv / mu / n / news / o / out / outsoc / p / po / pol / qa / qst / r / r9k / s / s4s / sci / soc / sp / spa / t / tg / toy / trash / trv / tv / u / v / vg / vint / vip / vp / vr / w / wg / wsg / wsr / x / y ] [Search | Free Show | Home]

Computer-assisted proofs were a mistake

This is a blue board which means that it's for everybody (Safe For Work content only). If you see any adult content, please report it.

Thread replies: 101
Thread images: 7

File: solution-7824 copy.jpg (560KB, 900x657px) Image search: [Google]
solution-7824 copy.jpg
560KB, 900x657px
>http://www.nature.com/news/two-hundred-terabyte-maths-proof-is-largest-ever-1.19990
>The puzzle that required the 200-terabyte proof, called the Boolean Pythagorean triples problem, has eluded mathematicians for decades. In the 1980s, Graham offered a prize of US$100 for anyone who could solve it. (He duly presented the check to one of the three computer scientists, Marijn Heule of the University of Texas at Austin, earlier this month.) The problem asks whether it is possible to color each positive integer either red or blue, so that no trio of integers a, b and c that satisfy Pythagoras’ famous equation [math] a^2 + b^2 = c^2 [/math] are all the same color. For example, for the Pythagorean triple 3, 4 and 5, if 3 and 5 were colored blue, 4 would have to be red.
>The numbers 1 to 7,824 can be colored either red or blue so that no trio a, b, and c that satisfy [math] a^2 + b^2 = c^2 [/math] are all the same color. The grid of 7,824 squares here shows one such solution, with numbers colored red or blue (a white square can be either). But for the numbers 1 to 7,825, there is no solution.
>There are more than [math] 10^2300 [/math] ways to color the integers up to 7,825, but the researchers took advantage of symmetries and several techniques from number theory to reduce the total number of possibilities that the computer had to check to just under 1 trillion. It took the team about 2 days running 800 processors in parallel
>http://arxiv.org/abs/1605.00723

And it only cost them $504,000 in electricity to win that $100.
>CS professors in charged of mathematics
>>
File: 1460248473800.gif (1000KB, 315x236px) Image search: [Google]
1460248473800.gif
1000KB, 315x236px
>>8104652
>CS professors in charged of mathematics
>>
>>8104652
can we agree that brute forcing problems isn't that cool
>>
>>8104675
I think it's pretty cool to be able to force a problem, it shows how much power we got.
>>
File: feed.png (450KB, 612x450px) Image search: [Google]
feed.png
450KB, 612x450px
>>8104681

But with that $500K you could have feed 140k starving African children for a whole month.
>>
>>8104697
>CS professors in charged of mathematics
>you could have feed 140k

>autists in charge of speech
>>
>>8104697
what country in africa?
it doesn't matter, if you want to help some starving person, stop taking shit from them instead of stroking your ego by throwing a tiny fraction of what you take from them.
>>
>>8104697
it's not about the money, it's about asserting dominance :^)
>>
>>8104697

>feed
>not invest

Give a man a fish blah blah blah...
>>
>>8104652
That problem sounds so specific. Does it have any uses? I feel like you could come up with an infinite amount of specific hard to solve problems.
>>
>>8104697
>get 7 kids on average
>starve
feeding them only makes the problem worse
>>
>>8104749
It is very easy to come up with hard problems but much more difficult to come up with hard problems that have answers. That makes the ones that have answers far more cool.
>>
>>8104774
Is that what mathematicians do? Spend years trying to solve some obscure problem?
>>
>>8104697
I would rather buy them crop seeds, herds or investments for businessess
>>
>>8104752
>>8104722
http://www.nation.co.ke/news/Groups-want-trade-barriers-removed-to-spur-Africa-growth/-/1056/2996774/-/dke3v0z/-/index.html
>>
>>8104784
cut subsidies for western farmers (they basically only cost money to your societies anyway).
Subsidies allow them to sell for less than african farmers with no subsidies, starving them because they can't sell their production.
You can buy them all the seeds you want, they can't benefit. Charity is just a coping mechanism to feel better.
>>
I warned you about computer assisted proofs, bro. I told you it would end like this. I told you dawg.

2000 years of mathematics and we are slacking. Humanity needs to get their shit together again.
>>
>>8104782
It's what people in literally every field do. If you go to something that sounds super useful like "curing cancer" but then look at what individual scientists are doing you'll find it's often something pretty useless sounding. But the point of research is you don't really know what is useful or hard until you try it.
>>
>>8104697
>But with that $500K you could have feed 140k starving African children for a whole month.

My best guess is that those 500k came in some kind of grant.

Call me a lunatic, but I do not think that african children can apply for research grants so that money would literally never feed starving children, you retard.
>>
>>8104800
Who pays them to do the useless sounding research though?
>>
>>8104805
You do. Deal with it.
>>
File: 1460747929804.webm (2MB, 640x360px) Image search: [Google]
1460747929804.webm
2MB, 640x360px
>>8104784
>>
>>8104782
No, mathematicians learn how to investigate interesting problems.
>>
>>8104791
>cut subsidies for western farmers (they basically only cost money to your societies anyway).

but it's good to be somewhat self sufficient.
>>
>>8104805
Yeah, let's only study things we already understand. That sounds like a great way to keep up the breakneck pace of scientific progress we've enjoyed in the last few decades.
>>
>The numbers 1 to 7,824

So it's not even a real, general proof or does 7824 have any significance?
>>
>>8104808
>>8104824
I am genuinly curious because I myself would like to research some useless things but I thought you can't do that since someone will only pay you if it's profitable.
>>
>>8104833
that's not how research works.

research does not need to have immediate applications. its goal is to broaden our understanding, to test theories, to gather data, to test new potential technologies etc

R&D on the other hand has profitability in mind. A lot of stuff from R&D today comes from the public research of yesterday.

And that's why research is paid by public funding in normal countries, while R&D is financed by companies.
>>
>>8104833
The NSF or similar organizations, which usually come from taxpayer money.

You gotta at least be able to convince people in your own field that your problem is interesting though

>>8104831
I assume they had some general proof that showed that if you have a coloring that works for those then you can extend it to a coloring of all integers
>>
>>8104824
https://youtu.be/a1zDuOPkMSw?t=13m34s
>>
>>8104831
They showed there isn't any coloring past 7824
>>
>>8104841
>>8104842
Can you elaborate on how exactly it works? I assume you present what you want to research, the expected costs and then you get a grant for a certain period of time after which you need to present results and convince to pay you to continue the research?
>>
Computer assisted proofs are not legitimate, imo. You need to be able to prove it analytically. Forex, the four color theorem hasn't been proved.
>>
>>8104798
do you forget that we are biological creations of random accidents?

A hundred years ago Marie Curie was playing with uranium with her bare hands, are we expected to solve every math problem with only our brains.
>>
>>8104652
This is only surprising to plebs who aren't familiar with Ramsey theory
>>
>>8104652
>And it only cost them $504,000 in electricity to win that $100.
who pays for this exactly?
>>
>>8105252
you do, dear undergrad. thanx for the the tuition monies, now try to make something of this engrish-as-a-second-language lecturer.
>>
>>8104652
>>8104675
Aren't you really complaining about proving by counter example?

The fact that this proof happened to use a computer to find a number for which the statement was not true is irrelevent.
>>
>>8104697

Why am I supposed to care about Africans again? What is so important about Africa's contribution to society that I need to help their poor? Why can't I help poor Asians, Americans, or Europeans?
>>
wait, wait, wait...

Hold on.

They actually ran the program? They actually spent money on the electricity?

If they're computer scientists, why would they need to run the program and actually spend money on the electricity if they can just know what the output of the program will be analytically? What the fuck is the point of computer science if they can't tell us what the output of the program will be before running it? Why would they waste half a million dollars on something they should only need chalk and some ingenuity?

Isn't the whole point of computer science ... the whole point being so you DON'T have to run the programs and waste money on electricity to see if the results are correct?

Am I missing something here? What the fuck?
>>
>>8105454
You are definitely missing something here. E.g. analytically we can tell that a sorting algorithm will always output a sorted list, but to get an explicit output for a given input, generally you need to use the algorithm itself.
>>
>>8105454
They didn't have a way to analytically check every single possible combination, are there were far too may possibilities to check it manually.
>>
>>8105454
>Retardation: The Post
>>
File: sour grapes 7.gif (10KB, 640x918px) Image search: [Google]
sour grapes 7.gif
10KB, 640x918px
>>8105454
CS/SE undergrad dropout detected
>>
> A fundamental question is whether Theorem 1 has a “mathematical” (human-readable) proof, or whether the gigantic (sophisticated) case-distinction, which is at the heart of our proof, is the best there is? It is conceivable that Conjecture 1 is true, but for each k has only proofs like our proof, where the size of these proofs is growing so quickly, that Conjecture 1 is actually not provable in current systems of foundations of Mathematics (like ZFC).
>>
>>8104752
>get 7 kids on average
>have multinational corporations steal 100% of the countrys natural resources while only paying a token fee to a completely corrupted government.
>starve

Altruism is the downfall of modern western society.
>>
>>8105780

The best part about any conversation about whether or not we should help Africans is that both sides are implying they need help, yet neither realizes it!
>>
>>8105765
>have fun checking all the solutions
>>8105692
>there are too many solutions
The dangers of being a faggot
>>
>>8104697
>caring about people and things that will never affect your life if you don't want it to
>>
>>8104652
>48 hours
>800 processors
>lets say 200 watts per processor (that's a high power processor)
>200 * 800 * 48 / 1000 = 7,680 kilowatt hours
>$504,000 / 7,680 = 65.625 $ per KWH
>US average cost per KWH is $0.1234 residential and $0.1027 all sectors
https://www.eia.gov/electricity/monthly/epm_table_grapher.cfm?t=epmt_5_6_a

>you're saying they payed 531.81 times the average residential electric price

though to be fair the 200 TB of hard drives must have cost a lot
i found some 2 TB ones on ebay for $35 and at that price it would cost $3,500
that plus the ~ $1,000 in electrics puts us at ~$4,500

>that's a total cost of 112 times less than what you said
>>
>>8105896
>he thinks cost is only raw materials

protip: in science like that, most of the cost is work time.
>>
>>8105904
kill yourself brainlet
>>
>>8105904
>most of the cost is work time
>brute force
r u srs m8
besides the point was that it cost no where near $504,000
>>
>>8105922
>kill yourself brainlet
make me.
If you can get your fat ass out of your chair to get your teeth knocked out.
>>
>>8104717

What the hell am I personally taking from some unknown person in Africa?
>>
>>8105926
>brainlets resort to physical violence when threatened intellectually
heh
>>
>>8105932
>manletobrainlets resort to "kys" when they don't understand anything

I can feel your assblast though.
>>>/trash/
go where you belong.
>>
>>8105931
>if others do it on my behalf, I am not accountable
>>
>>8104823
>found the nigger
But really, whats wrong with china? they've come a long way despite being their history of being screwed by the west, and the far east
Also a gook is a Korean, Chinese are chinks.
>>
>>8105949
despite their history*
oy vey
>>
>>8104814

I do not know what video this scene is from but the asian guy seems to either be ignorant of the concept concerning the diffusion of innovations or wants to capitalize on the black guy's lack of knowledge of said concept in that conversation.

Just because a country or population becomes occupied by a foreign power does not mean said foreign power's ideals and technology will successfully take root into the populous.
>>
File: Vqr4p1E.png (116KB, 1515x663px) Image search: [Google]
Vqr4p1E.png
116KB, 1515x663px
They learn from the best.
>>
>>8105949
> despite their history
Their history of being the baddest on the block East of the Eurasian Steppe?
>>
>>8105949
>Also a gook is a Korean, Chinese are chinks.
they look the same
they live like trash and try to tell niggers they also live like trash.
>>
>>8105989
>Their history of being the baddest on the block East of the Eurasian Steppe?
I was thinking more of western spheres of influence, Opium, Jap invasion, perpetual civil war and revolutions, but yeah..
Baddest.
>>8105993
Stay mad nigger, the chinks will rule over you for centuries to come. Chinese people dont live like trash. Koreans are dirty, loud and rude
>>
>>8105996
>Stay mad nigger, the chinks will rule over you for centuries to come. Chinese people dont live like trash. Koreans are dirty, loud and rude
kek
I'm not even african nor am I black
but hey, at least you tried with your poor ad homniem

Chinese people can't even breathe their air, and can't drink their water and die working like slaves for us.
>>
>>8106000
>uses ad hominem
>gets ad homimemed
>haha nice ad hominem fag XDDDD
Ayyyyyyyy
>>
>>8105448
Exactly
>>
>>8105996
>I was thinking more of western spheres of influence, Opium, Jap invasion, perpetual civil war and revolutions, but yeah..
So just the last 200 years....gotcha
>>
>>8106003
>mad
>>
>>8106013
REEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
>>
>>8105949
>whats wrong with china? they've come a long way despite being their history of being screwed by the west

You do know China was the most advanced culture on Earth for most of civilised history, right?
>>
File: 75895340783.jpg (4KB, 291x173px) Image search: [Google]
75895340783.jpg
4KB, 291x173px
>>8104652
>>8104675
>yfw you realize experimental mathematics is actually a thing

https://en.wikipedia.org/wiki/Experimental_mathematics
>>
>>8104865
What do you mean, analytically ?

The four color theorem's proof could be done by a human on paper. It would just be extremely boring, and very likely that he would forget some cases and stuff. But computer-assisted proofs is the same notion of "proof" than what mathematicians publish.
>>
>>8105763
zfc has case disjunction

wtf
>>
>>8104865
>proof by counterexample isn't legitimate
>>
>>8106060
it means the complete, all-cases proof is infinitely long. an infinitely long proof isn't a valid proof.
>>
>>8104717
>colonialism should be fragile, nice and smooth
>>
call me when a computer solves the syracuse problem or the traveling salesman problem
>>
>>8106265
what
>>
>>8106274
you're saying those that got conquered have the right to reparations, right?
why is that
they got conquered, they should have no say
>>
>>8105896
>>800 processors
>>lets say 200 watts per processor (that's a high power processor)
>160kW

>https://www.tacc.utexas.edu/stampede/
>Max Power Usage: 4.5 Megawatts
>Average Power: 3 MW

So it's 4.5*48*1000 = 216,000 kWh at a total cost of $26.7K
>>
>>8106290
no, I'm saying if you want to help someone, you should pay them a fair price for what they give you right now.
>>
>>8106334
>give us right now
nothing?
some help I can think of is letting the starve (so no dependent population on aid) and also taking their land so we can put it to good use, so that it maybe helps them
>>
>>8106340
Didn't you already post this?
>>
>>8104865
A proof is a proof and sometimes you need case distinctions
>>
>>8106339
oh you so cool anon, I want to hang out with you. What a strong and intelligent man you must be.

>n-edgy-(n+2)-me
>>
>>8104697
Africa is the richest continent on earth (in term of ressources) any civilization would thrive in this conditions, the only problem with africa is the africans. We even gave them a fully developped infrastructure for free and they still manage to starve for fuck sake. Every $ spend on charity for africa is a $ wasted.
>>
>>8106376
whatever, go back to reading about how Africans are developed and have the same mental capacities as whites in the west
go ahead, they just need more money they're in a rough spot, after all, the white man kept them down, colonialism stole their potential, Danm those whities
they were Egyptians, they were kings
>>
>>8106396
oh you so cool anon, I want to hang out with you. What a strong and intelligent man you must be.

>n-edgy-(n+2)-me

>>>/pol/
>>
>>8106415
>>>/e/bola
>>
>>8106415
>if you can't refute it, just say ">>>/pol/", you'll win then
>>
>>8106439
>there is nothing to refute
>but at least you can't refute it
>>8106423

>>>/pol/
>>
>>8106460
I imagine you like the average fatass at home thinking it's bad to offend people
go kill yourself, cuckold
>>
>>8104652
>$504,000 in electricity
I wonder how much that would've cost in wadges if you had a bunch of people trying to solve it.
>>
>>8104697
don't feed the animals, they will grow dependent.
>>
>>8106489
>I can't refute anything so I'll resort to insults

>>>/trash/
>>
>>8104675
Says the mathematician who is going to be replaced by a computer
>>
>>8105768
>Paying for things you're stealing
>>
>>8104697
Yeah but that means giving money to niggers and I already pay taxes.
>>
>>8107188
sub-Saharan levels of savagery
Thread posts: 101
Thread images: 7


[Boards: 3 / a / aco / adv / an / asp / b / bant / biz / c / can / cgl / ck / cm / co / cock / d / diy / e / fa / fap / fit / fitlit / g / gd / gif / h / hc / his / hm / hr / i / ic / int / jp / k / lgbt / lit / m / mlp / mlpol / mo / mtv / mu / n / news / o / out / outsoc / p / po / pol / qa / qst / r / r9k / s / s4s / sci / soc / sp / spa / t / tg / toy / trash / trv / tv / u / v / vg / vint / vip / vp / vr / w / wg / wsg / wsr / x / y] [Search | Top | Home]

I'm aware that Imgur.com will stop allowing adult images since 15th of May. I'm taking actions to backup as much data as possible.
Read more on this topic here - https://archived.moe/talk/thread/1694/


If you need a post removed click on it's [Report] button and follow the instruction.
DMCA Content Takedown via dmca.com
All images are hosted on imgur.com.
If you like this website please support us by donating with Bitcoins at 16mKtbZiwW52BLkibtCr8jUg2KVUMTxVQ5
All trademarks and copyrights on this page are owned by their respective parties.
Images uploaded are the responsibility of the Poster. Comments are owned by the Poster.
This is a 4chan archive - all of the content originated from that site.
This means that RandomArchive shows their content, archived.
If you need information for a Poster - contact them.