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/sci/ - Science & Math

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5351884 No.5351884 [Reply] [Original]

ITT : the longest equation you can find on the internets

source for pic : http://iopscience.iop.org/1367-2630/12/7/075036/fulltext/

>> No.5351893
File: 31 KB, 678x842, 1-s2.0-S0307904X06002800-si54.gif [View same] [iqdb] [saucenao] [google]
5351893

>>5351884
Another one

http://www.sciencedirect.com/science/article/pii/S0307904X06002800

>> No.5351907

>>5351884
how are we measuring longest? number of terms? number of symbols? if its written using the Einstein convention do we count <span class="math"> p^ip_i [/spoiler] as 1 term or 4?

>> No.5351911

>>5351884
already overshadowed but I love this polynomial

http://en.wikipedia.org/wiki/Look-and-say_sequence

>> No.5351931
File: 162 KB, 412x704, Untitled.png [View same] [iqdb] [saucenao] [google]
5351931

>> No.5351964

ITT
Highschoolers being fascinated by equations because they are long and not because they describe something interesting.

Did you guys know there are 9 sextillion stars in the universe? pretty cool huh?

>> No.5351968

>>5351907
I didn't think we'd get down to counting the number of terms, say just the longest looking equation that appears in an official paper

>> No.5351971

>>5351964
This is called mindless fun, but you probably don't know what that word means

>> No.5351974

>>5351972
>your asperger's is showing

>> No.5351972
File: 13 KB, 427x338, 1355372763850.jpg [View same] [iqdb] [saucenao] [google]
5351972

>>5351971
>being proud of being mindless

>> No.5351977

>>5351974
nice comeback bro, you defended your point really well

>> No.5351981

>>5351971
>mindless fun
Anti-intellectualism belongs on >>>/v/ or memebase.

>> No.5351988
File: 25 KB, 480x392, Screenshot - 12142012 - 06:03:54 PM.png [View same] [iqdb] [saucenao] [google]
5351988

tip for having fun like this on 4chan: just ignore people who try to detract from it.

This is a polynomial whose positive values are always prime.

>> No.5351993
File: 59 KB, 865x538, Screenshot - 12142012 - 06:05:26 PM.png [View same] [iqdb] [saucenao] [google]
5351993

http://tachyos.org/godel/Godel_statement.html


I don't even know how to csreenshot something so big, I tried pasting the formula into GIMP but it crashed.

>> No.5351998

>>5351911
that's fucking awesome!!! John Conway is the best

>> No.5352000

>>5351988
For any values of k w z j q g f and so on?

>> No.5352005

>>5352000
yeah put in any 26 integers and it'll either be some random (garbage) negative numbers or it'll be positive and a prime number.

>> No.5352007
File: 135 KB, 1324x1712, DealWithIt.png [View same] [iqdb] [saucenao] [google]
5352007

This is an intermediate result I got while working on a project recently. Fun times.

>> No.5352014
File: 595 KB, 1645x4025, The undecidable Gödel sentence' - tachyos_org_godel_Godel_statement_html.png [View same] [iqdb] [saucenao] [google]
5352014

>>5351993
I used Fireshot addon for firefox

>> No.5352017

>>5352005
That's awesome, what's the name of that polynomial? I'm interested in a proof

>> No.5352018

>>5351988
bullshit, really? Source?

>> No.5352027

>>5352017
>>5352018
It's a result by Matiyasevich and Julia Robinson, they found out how to encode logic into diophantine equations and eventually managed to build universal equations which only have integer solutions of turing machines halt. That's the hard part.. once you have that making polynomials out of these is pretty easy. There's a great book on it called Hilberts 10th problem.

>> No.5352034

<span class="math">|M| = 808017424794512875886459904961710757005754368000000000[/spoiler]

monster group, the biggest finite simple group. (I think they're sort of like the "prime numbers" of group theory)

>> No.5352053

>>5352018
It's not really that surprising. (x-2)^2 is another polynomial whose positive values are always prime.

>> No.5352056

>>5352053
x=4
(4-2)^2=4
wut

>> No.5352057

>>5352053
whoops I thought you meant roots. disregard my faggotry

>> No.5352058

>>5352057
oh but it gets every prime.

>> No.5352059

>>5352056
4 is the square of 2
squares of primes are prime

>> No.5352064

>>5352058
... Really? How can you prove that? I
don't believe that.

>> No.5352067
File: 181 KB, 853x900, e4ade0b34085ff594e3a21a10fc6b39cff6a4150.jpg [View same] [iqdb] [saucenao] [google]
5352067

>>5352059
no they're not

>> No.5352071

>>5352059
>squares of primes are primes
I think I may be misunderstanding you or you're a troll.
2^2 is not prime
3^2 is not prime
5^2 is not prime
wtf are you talking about

>> No.5352076

>>5352071
just a simple mistake, not everyone studies prime numbers.

>> No.5352078
File: 1.17 MB, 260x146, 1354986953451.gif [View same] [iqdb] [saucenao] [google]
5352078

>>5352076
>not everyone studies prime numbers.

>> No.5352087

>>5352034
When you say biggest finite simple group, what do you mean? I can define arbitrarily large finite simple groups by giving the Zn groups they're isomorphic to.

>> No.5352091

>>5352058
I'm not sure if when you say "it gets every prime" you mean that any prime number has a satisfying x or if any prime put in will give another prime.

Either way, it doesn't work.

>> No.5352092
File: 44 KB, 722x482, 1355380482096.jpg [View same] [iqdb] [saucenao] [google]
5352092

>>5352087
oh you are right! it's thebiggest sporadic one

(USER WAS WARNED FOR THIS POST)

>> No.5352098

>>5352027
Hilbert’s Tenth Problem by Alexandra Shlapentokh

>Hilbert’s Tenth Problem – to find an algorithm to determine whether a polynomial equation in several variables with integer coefficients has integer solutions – was shown to be unsolvable in the late sixties. This book presents an account of results extending Group Policy Profiles and IntelliMirror for Windows 2003 Windows XP and Windows 2000 mediafire ebook pdf download Hilbert’s Tenth Problem to integrally closed subrings of global fields.

...wat

>http://naytreminec1988.textill.is/2012/09/28/hilberts-tenth-problem-cheap-ebook-download/

>> No.5352102

>>5352092
> infantile cartoon
>>>/a/

>> No.5352114

>>5352059
Actually no squares are prime.

>> No.5352151

Why should anyone give a shit about prime numbers anyway?

It's not like I can use them for anything.

>> No.5352154
File: 251 KB, 700x700, 1354720204249.jpg [View same] [iqdb] [saucenao] [google]
5352154

>>5352151
yeah prime numbers are useless

>> No.5352156

somewhere out there there is a polynomial in like 26 variables with the property that ZFC is inconsistent if it has a root in Z. it also has the property to fit on a poster. its fucking huge.
find such a zero and you destroyed thousands of years of human culture
stunning

>> No.5352158

>>5352151
This is exactly why I don't like number theory. I'm a math major but I can't stand that boring mental masturbation without applications.

>> No.5352161
File: 1.16 MB, 802x1024, 1355504159571.jpg [View same] [iqdb] [saucenao] [google]
5352161

>>5352158
how do you guys still not get this.

prime numbers ARE the applications.

>> No.5352167

>>5352161
Prove that it's more than inane number mysticism without basis in reality.

>> No.5352176

>>5352158
http://www.claymath.org/posters/primes/

>> No.5352173

>>5352158
Cryptography anyone?

>> No.5352177

>>5352156
You do realize we've recovered from such an alleged "extinction event" before.

>>5352151
>>5352154
>>5352158
>>5352167
https practically runs on them, you morons.

>> No.5352181

>>5352158

>Wanting applications
>Stay pleb

>> No.5352186

>>5352167
Number theory is like the most reality based branch of mathematics. (as long as you don't get into gaussian integers)

Things like complex analysis or non-euclidean geometry, those are way less rooted in reality.

>> No.5352191

>>5352186
>non-euclidean geometry, those are way less rooted in reality.

You do know our very own universe is non-euclidean right?

>> No.5352192

>>5352186
>Number theory is like the most reality based branch of mathematics. (as long as you don't get into gaussian integers)

Thanks for the good laugh.

>> No.5352203

Number theory is the most beautiful mathematics. It also happens to be nestled right on the very edge of what can be proven in consistent sets of axioms. It also happens to have some of the simplest problem statements, but extremely difficult problems.

>> No.5352205

>>5352156
ZFC is inconsistent if a^2+1 has a root. So, that alone isn't an achievement. I know you're trying to make some claim related to Hilberts 10th problem though. Perhaps you mean it has a root if ZFC *is* consistent?

>> No.5352207

>>5352203
>the most beautiful mathematics

No, that's calculus.

>> No.5352209

>>5352207
I'm pretty sure it's trigonometry dood.

>> No.5352212

>>5352207
>calculus
get on my level, pleb

>> No.5352219

>>5352091
It has a solution in the natural numbers iff k+2 is prime, or something like that. It's a result of Hilbert's tenth, where you can basically program Turing machine programs into diophantine equations.

>> No.5352229

>>5352076
lol this guy

>> No.5352232

>>5352219
There's a huge difference between that and the polynomial itself always having a prime value if positive.

(The latter is only possible if it only takes on finitely many positive values.)

>> No.5352233
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5352233

biggest i can think of is the explicit roots of a quartic formula

>> No.5352252 [DELETED] 
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5352252

>>5352205

>> No.5352255

<span class="math">\sum_{i=0}^\infty i[/spoiler]

/thread

>> No.5352262

>>5352255
But that's just <span class="math">-\frac{1}{12}[/spoiler], anon.

>> No.5352264

1 + 1 = 2

>> No.5352267
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5352267

>>5352262
wait a second are you trying to add up divergent sums again

>> No.5352275

>>5352262
3/10 got me to reply

>> No.5352282

>>5352059
well done

>> No.5352287

>>5352262
1 + 2 + 3 ... = S
2 + 4 + 6... = 2S
1 + 3 + 5 ... = 2S - 1

S - 2S = 2S - 1
S = -1

1 + 2 + 3 + 4 ... = -1

>> No.5352293 [DELETED] 
File: 100 KB, 1280x720, 294332-sora_no_otoshimono___03___large_32.jpg [View same] [iqdb] [saucenao] [google]
5352293

>>5352282
he thinks the square of a prime is prime

>> No.5352297

>>5352156
go on.

>> No.5352301

>>5352177
>>>5352156
> You do realize we've recovered from such an alleged "extinction event" before.
wat.

>> No.5352312
File: 180 KB, 600x898, AQuUK.jpg [View same] [iqdb] [saucenao] [google]
5352312

>>5352301
Godel's Incompleteness Theorem

>> No.5352322

>>5352287
>2 + 4 + 6... = 2S
>1 + 3 + 5 ... = 2S - 1
Slight flaw here, I think.

>>5352312
That too, but I was just thinking of Russell's paradox.

>> No.5352325

>>5352312
I don't think you understand what you're talking about.

>> No.5352331

>>5352325
Indeed he doesn't. It's precisely Gödel's inconsistency theorem that make the destruction possible in the first place. Basically if you can prove that our mathematics is consistent it means that it's not. And then there's the fact that apparently giving a solution to a certain explicit polynomial amounts to proving that mathematics is consistent.

>> No.5352415 [DELETED] 
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5352415

>>5352325
>>5352331
you're both wrong

>> No.5352695
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5352695

>>5352151
>It's not like I can use them
You're right, it's not like that at all.

>> No.5352740

>>5352156
>ZFC is inconsistent if it has a root in Z
>find such a zero and you destroyed thousands of years of human culture

ZFC is less than a century old.

>> No.5352952

The sine of 1 degree is fun:
http://www.efnet-math.org/Meta/sine1.htm

>> No.5352953

>>5351964
Wrong.