So lets say you figured out everything about prime numbers, how can you apply this knowledge to make something useful? Sorry, I'm just trying to figure out why there is all this hullabaloo.

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Anonymous Sat Nov 22 16:36:51 2014 No.6895803 [Reply] [Original]

So lets say you figured out everything about prime numbers, how can you apply this knowledge to make something useful? Sorry, I'm just trying to figure out why there is all this hullabaloo.

>>	Anonymous Sat Nov 22 16:38:32 2014 No.6895808 Would you suck TT's dick Y/N?

>>	Anonymous Sat Nov 22 16:40:12 2014 No.6895816 You could put the rest of the prime hunter fags search to rest. They would move on to something else.

>>	Anonymous Sat Nov 22 16:40:27 2014 No.6895817 nothing number theory is for autists

Anonymous Sat Nov 22 16:42:28 2014 No.6895819

>>6895803
>So lets say you figured out everything about prime numbers, how can you apply this knowledge to make something useful?
You break encryption. Number theory is fucking useless for everything else. It's the most overhyped math field ever! It has so few uses and all of them are fucking boring and ultimately POINTLESS.

Studying dung beetles is probably more useful to a society.

None !!a7Six4EVOK+ Sat Nov 22 16:53:00 2014 No.6895849
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>>6895817
>>6895816
>>6895819

alright alright....
I'm going to let this thread keep posting for a while, I'm not OP or anything but I've been looking into prime numbers for a while

I want to see just how fucking senselessly stupid /sci/ really is so I won't intergect my argument just yet, I want you to build it up first.

go ahead, I agree, number theory is useless
Prime numbers are a fascination of number theory, that doesn't mean solving primes would only suffice for that field of study, if you can call it that.

>I'll even trip for the first time.

>>	Anonymous Sat Nov 22 17:07:10 2014 No.6895902 They're cool and weird and mysterious. Also useful for cryptography. That's it, no go away.

>>	Anonymous Sat Nov 22 17:08:13 2014 No.6895907 >>6895902 *now go away

>>	Anonymous Sat Nov 22 17:18:11 2014 No.6895941 The modern world is based on prime number cryptography.

Anonymous Sat Nov 22 17:45:49 2014 No.6896039 [DELETED]

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Firstly, the "usefullness for the world" of a mathematical subject shouldn't be a general factor for the validity of people persuing it in the first place. But okay, that conversation has been had.

Now to motivate why prime numbers are of interest, or more genrally "the concept of a prime", you should think of primes not just as numbers coming after and before some other number in the ordering of natural numbers, but as generators of prime ideals for the ring Z:
For any number x, think of the grid {x*n | x in Z}, which it defines.
So the number 6 defines the grid
{...,-18,-12,-6,0,6,12,18,24,30,36...}
on the integer number line.
Some grids are subgrids of others. For example the number 3 generates the grid
{...,-9,-6,-3,0,3,6,9,12,15,18,21,...}
and this grid contains the grid generated by the number 6.
The prime numbers are exactly the numbers which generate the grids containing all the other grids.
And whenever you multiply a number n with a number m from two grids, the result n*m is contains in the n-grid and in the m-grid again.
And the set of numbers corresponds to the set of grids.

Now the general concept can be used to do a shitload of math. For example, take R^2 and consider the collection F of functions of 3 variables which are zero at the point (3,-5). The if you take any function g and multiply it with a function f from F, the value at (3,-5) is g(3,-5)*f(3,-5) and this is again zero because f is. So g*f is in F again, just like multiplying with numbers from a grid gets back to the grid.

You can now go on and replace a space with function spaces.
It's part of algebraic geometry. RIP Grothendieck.
Also look up ring theory.

Anonymous Sat Nov 22 17:48:29 2014 No.6896050
File: 633 KB, 633x921, athiagroth.png [View same] [iqdb] [saucenao] [google]

To motivate why prime numbers are of interest, or more genrally "the concept of a prime", you should think of primes not just as numbers coming after and before some other number in the ordering of natural numbers, but as generators of prime ideals for the ring Z:
For any number x, think of the grid {x*n | n in Z}, which it defines.
So the number 6 defines the grid
{...,-18,-12,-6,0,6,12,18,24,30,36...}
on the integer number line.
Some grids are subgrids of others. For example the number 3 generates the grid
{...,-9,-6,-3,0,3,6,9,12,15,18,21,...}
and this grid contains the grid generated by the number 6.
The prime numbers are exactly the numbers which generate the grids containing all the other grids.
And whenever you multiply a number n with a number m from two grids, the result n*m is contains in the n-grid and in the m-grid again.
And the set of numbers corresponds to the set of grids. You can in large parts replace studying numbers with studying those collections, the grids. Btw. loop up ring theory.

Now the general concept can be used to do a shitload of math. For example, take R^2 and consider the collection F of functions of 3 variables which are zero at the point (3,-5). The if you take any function g and multiply it with a function f from F, the value at (3,-5) is g(3,-5)*f(3,-5) and this is again zero because f is. So g*f is in F again, just like multiplying with numbers from a grid gets back to the grid.

You can now go on and replace a space with function spaces.
It's part of algebraic geometry.
RIP Grothendieck.

>>	Anonymous Sat Nov 22 17:48:55 2014 No.6896052 >>6895808 N

>>	Anonymous Sat Nov 22 17:49:12 2014 No.6896055 what does usefulness have to do with mathematics? it sounds like you have a fundamental misunderstanding of what the study of mathematics is. hint: it has nothing to do with what "society" thinks of it, or what "society" can do with it.

>>	Anonymous Sat Nov 22 17:50:32 2014 No.6896059 functions of 2 variables*

>>	Anonymous Sat Nov 22 18:19:28 2014 No.6896117 >>6896055 If you can't use something that makes it useless. There is no point in studying useless things outside stamp collecting.

>>	Anonymous Sat Nov 22 18:23:06 2014 No.6896127 >>6896117 history, philosophy, writing, literature, music, art---there is no value in any of these? there's no point in studying them whatsoever?

>>	Anonymous Sat Nov 22 18:26:12 2014 No.6896139 >>6896127 protip: only good for trivia

>>	Anonymous Sat Nov 22 18:35:53 2014 No.6896158 >>6896139 i feel really sorry for you, truly.

>>	Anonymous Sat Nov 22 18:51:37 2014 No.6896191 >>6895803 You can't figure out "everything" about prime numbers. /thread

>>	Anonymous Sat Nov 22 18:58:24 2014 No.6896201 >>6896158 Then what good are they?

>>	Anonymous Sat Nov 22 19:02:27 2014 No.6896208 >>6896050 thanks, I'm mathematically illiterate and I found this really interesting.

>>	Anonymous Sat Nov 22 19:07:01 2014 No.6896216 >>6895803 RSA asymmetrical encryption uses prime number to calculate a cypher for the public and private keys

>>	Anonymous Sat Nov 22 19:32:43 2014 No.6896269 >>6895819 >You break encryption >implying all cryptosystems use factoring-hardness as their OWF

>>	Anonymous Sat Nov 22 19:36:09 2014 No.6896276 File: 161 KB, 500x333, 20.-Chris-Hirata.jpg [View same] [iqdb] [saucenao] [google] >>6895803 gtfo of the way Terence Tao, my professor is coming through

>>	Anonymous Sat Nov 22 19:42:36 2014 No.6896288 >>6895819 >Number theory is fucking useless for everything else. >Studying dung beetles is probably more useful to a society. Insects use prime numbers to avoid predators.

>>	Anonymous Sat Nov 22 19:46:31 2014 No.6896296 >>6896288 >Insects use prime numbers to avoid predators. please explain

Anonymous Sat Nov 22 19:57:02 2014 No.6896319

>>6896296

By adopting a prime number life cycle, like Cicadas with 13 or 17 years, you avoid predators with life cycles that won't line up for many years.

http://en.wikipedia.org/wiki/Cicada#Life_cycle

"Some species have much longer life cycles, such as the North American genus, Magicicada, which has a number of distinct "broods" that go through either a 17-year or, in some parts of the world, a 13-year life cycle. These long life cycles perhaps developed as a response to predators, such as the cicada killer wasp and praying mantis.A predator with a shorter life cycle of at least two years could not reliably prey upon the cicadas."

>>	Anonymous Sat Nov 22 20:05:32 2014 No.6896333 >>6895803 I bet he's in the stands watching USC vs UCLA game right now. Hopefully, I'll catch sight of him.

Anonymous Sun Nov 23 01:07:26 2014 No.6896764

>>6896201
History is useful for reasons that are painfully obvious.
Philosophy's usefulness, to me, lies mostly in it's connections with history.
Literature is useful for conveying ideas in a clear and compelling way

Beyond that, the fine arts simply provide pleasure to a lot of people, and give them a channel by which to express themselves in ways where words fail. It's not utilitarian but I find that useful regardless. But I'm sure you're an edgy automaton who doesn't even have a favorite band right? Because you don't ever, ever do anything useless. Which is why you're here on 4chan.

>>	Anonymous Sun Nov 23 02:11:02 2014 No.6896831 >>6896139 Are you a fucking idiot?

>>	Anonymous Sun Nov 23 02:14:22 2014 No.6896835 >>6896276 literary who?

>>	Anonymous Sun Nov 23 02:38:14 2014 No.6896866 >>6896319 man that shit is crazy

>>	Anonymous Sun Nov 23 03:48:46 2014 No.6896998 >>6896333 i dont think he likes sports

>>	Anonymous Sun Nov 23 03:52:28 2014 No.6897008 >>6895803 Get job in cryptography \thread

Anonymous Sun Nov 23 03:52:39 2014 No.6897009

>>6896835
That's Christopher Hirata, he's a former child prodigy like Terence Tao, and I he think he has an IQ of 225 whilst Tao has 230 (which is pretty much five points below him).

He made great many great accomplishments; working in NASA at the age of 16, and I think getting a PhD in Astrophysics when he was 20? I think

Google him.

Anonymous Sun Nov 23 04:36:33 2014 No.6897082
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>>6895803
It's pretty obvious what would happen if you figured everything out about the Primes.
You would find the Tomb of the Primes and learn out to extract the Matrix of Leadership.
But it's been a source of great debate for many years, the Primes can build a Solar Harvester to produce Energon as long as it isn't used on worlds containing life.

>>	Anonymous Sun Nov 23 05:03:54 2014 No.6897103 >>6895819 Dung beetles are really important for processing animal waste and preventing plagues of flies.

Anonymous Sun Nov 23 05:08:34 2014 No.6897109
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>>6896276

Tell your prof to prepare to get BTFO by the one, the only, Paul Von Neumann.

Cheerful bon vivant socialite who loved parties, and was also the smartest man to live in the 20th century.

>>	Anonymous Sun Nov 23 05:52:17 2014 No.6897156 >>6897009 >pretty much 5 points it's exactly 5 points....

Anonymous Sun Nov 23 06:08:29 2014 No.6897176

>>6897156
Yeah my bad.

Also Hirata achieved a lot more accomplishments than Tao. He worked in Nasa's Jet Propulsion Lab, was a Lecturer, Physics Olympiad, Maths Olympiad, and published a chit tonne of papers.

Would've been better if he went into research for string theory, quantum gravity, and other areas in theoretical physics. But instead he chose to become an astrophysicist and do research in that area. I think someone with a high calibre as him should've went into theoretical phsyics. Oh well.

>>	Anonymous Sun Nov 23 07:33:15 2014 No.6897230 File: 253 KB, 1674x2117, chris.jpg [View same] [iqdb] [saucenao] [google] CRAWLINGG IN MY SKIN THESE WOUNDS THEY WILL NOT HEAL - Chris Hirata

>>	Anonymous Sun Nov 23 11:08:21 2014 No.6897436 File: 193 KB, 1458x1600, zenos-diet-small.jpg [View same] [iqdb] [saucenao] [google] >>6897109 I doubt he was the smartest: >Alan Turing >Kurt Godel >Richard Feynman >Albert Einstein >Paul Erdos etc. where in the same league as him

>>	Anonymous Sun Nov 23 16:02:40 2014 No.6898078 >>6897436 Read about him a little. Do you know what he was capable of? Everyone who knew him, including some of those very same people you mentioned, confirms that he was by far the smartest person they had ever met.

Anonymous Sun Nov 23 16:22:02 2014 No.6898136

Perhaps one day, millennia in the future, we will completely understand the Laws that govern our physical universe.

But we will never, not in infinity millennia, completely understand mathematics. There is always more mathematics out there.
So, philosophically speaking, the "long-term" goal of mathematics should be to know "as much as possible". Depending on your viewpoint, I guess. But if you can accept that as the goal, then mathematicians are providing a "long-term" benefit to humanity. Not long-term in the sense of some physicist using it thousands of years in the future, but even more long-term than that-- basically, the "infinite" long-term. idk

>>	Anonymous Sun Nov 23 16:22:05 2014 No.6898137 File: 215 KB, 590x250, credit.jpg [View same] [iqdb] [saucenao] [google] If I knew everything about primes? Break RSA ??? Profit! (from all the fraud monies)

>>	Anonymous Sun Nov 23 16:25:04 2014 No.6898141 >>6898137 N.S.A. offers you 1.5 billion/year to STFU and work for them, indefinitely. wat do?

>>	Anonymous Sun Nov 23 16:32:30 2014 No.6898157 1.5 billion would probably be trivial compared to the money you could make with a salami scheme if you broke RSA and nobody else knew. Just sayin'

Anonymous Sun Nov 23 16:42:31 2014 No.6898179

spoiler: you can't break rsa if you knew everything about primes, rsa security depends on the difficulty of factoring large numbers. So until you discover a fast factoring algorithm (which has shit all to do with primes) then you're out of luck. Same thing with elliptic curve crypto, the difficulty is in doing logs in mod n which is impossibly hard.

>>	Anonymous Sun Nov 23 16:44:52 2014 No.6898185 >>6898179 The large numbers have large prime factors

>>	Anonymous Sun Nov 23 16:52:54 2014 No.6898205 >>6898179 http://en.wikipedia.org/wiki/RSA_numbers I assume that "knowing everything about primes" includes a P algorithm for factoring

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