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(Slate)   Mathematician past his prime reinvents math as we know it   (slate.com) divider line 62
    More: Spiffy, maths, number theory, mathematicians, theorems, primes, conjecture, University of New Hampshire, discovery  
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6718 clicks; posted to Geek » on 23 May 2013 at 3:41 AM (1 year ago)   |  Favorite    |   share:  Share on Twitter share via Email Share on Facebook   more»



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2013-05-22 10:23:22 PM  
,,, or used to know it.
 
2013-05-22 11:49:25 PM  
Past his prime?

/that's odd
//but I'd rather not be negative
 
2013-05-22 11:55:58 PM  
It's an awesome and exciting proof, but I think "reinvents math as we know it" might be slight hyperbole.
 
2013-05-22 11:56:00 PM  
No Fields Medal for this guy.
 
2013-05-22 11:57:46 PM  

TheOnion: It's an awesome and exciting proof, but I think "reinvents math as we know it" might be slight hyperbole.


It looks more logarithmic to me.
 
2013-05-23 12:19:53 AM  
So he proved that any given prime number will have a pair on one side or the other that is never more than 70 million numbers apart from it. huh. Yet another useless fact I'm never going to get out of my head.
 
2013-05-23 12:45:13 AM  
I'd be more excited about this if the discoverer looked a lot more like Matt Damon.
 
2013-05-23 01:02:44 AM  
Huh. I thought only Europeans did that stuff, Hungarians and Russians mainly.
Will this have any practical effect?
 
2013-05-23 01:11:21 AM  

MaudlinMutantMollusk: Past his prime?


possibly even as old as late twenties!
 
2013-05-23 01:14:51 AM  

TheOnion: It's an awesome and exciting proof, but I think "reinvents math as we know it" might be slight hyperbole.


It's kinda like hyperbole, just a million times worse.
 
2013-05-23 01:54:40 AM  

MaudlinMutantMollusk: Past his prime?

/that's odd
//but I'd rather not be negative


Don't be square, that's irrational.  The root of your positivity has finite limits.  I don't want to be mean or derivative, but its a cofactor of why you're an outlier whose odd and not natural.
 
2013-05-23 02:26:06 AM  

unyon: MaudlinMutantMollusk: Past his prime?

/that's odd
//but I'd rather not be negative

Don't be square, that's irrational.  The root of your positivity has finite limits.  I don't want to be mean or derivative, but its a cofactor of why you're an outlier whose odd and not natural.


Get real.
 
2013-05-23 02:28:01 AM  

unyon: MaudlinMutantMollusk: Past his prime?

/that's odd
//but I'd rather not be negative

Don't be square, that's irrational.  The root of your positivity has finite limits.  I don't want to be mean or derivative, but its a cofactor of why you're an outlier whose odd and not natural.'


*twitch*
 
2013-05-23 03:06:52 AM  

Boojum2k: unyon: MaudlinMutantMollusk: Past his prime?

/that's odd
//but I'd rather not be negative

Don't be square, that's irrational.  The root of your positivity has finite limits.  I don't want to be mean or derivative, but its a cofactor of why you're an outlier whose odd and not natural.'

*twitch*


I feel dirty for having not caught that.

/going to grammar prison
 
2013-05-23 03:47:37 AM  

unyon: MaudlinMutantMollusk: Past his prime?

/that's odd
//but I'd rather not be negative

Don't be square, that's irrational.  The root of your positivity has finite limits.  I don't want to be mean or derivative, but its a cofactor of why you're an outlier whose odd and not natural.


You should become a clown, because they like to take a pi in the face.
 
2013-05-23 03:56:14 AM  
Structure the concept of structurelessness. Taste the rainbow.
 
2013-05-23 04:00:00 AM  
I'm sorry, the number you have dialed is imaginary.  Please rotate your phone 90 degrees and try your call again.
 
2013-05-23 04:00:41 AM  
I was told there would be no math....
 
2013-05-23 04:04:31 AM  
There are 10 types of people: those that understand binary, and those that do not.
 
2013-05-23 04:33:10 AM  

Triumph: So he proved that any given prime number will have a pair on one side or the other that is never more than 70 million numbers apart from it


No.  Only that there are infinitely many pairs within that bound.  There can still be gaps larger than that for other prime numbers (infinitely many others, in fact.).
 
2013-05-23 04:36:20 AM  
How long before the Russian loner whose work he "built on" declines the next Fields medal?
 
2013-05-23 04:41:17 AM  

ThrobblefootSpectre: Triumph: So he proved that any given prime number will have a pair on one side or the other that is never more than 70 million numbers apart from it

No.  Only that there are infinitely many pairs within that bound.  There can still be gaps larger than that for other prime numbers (infinitely many others, in fact.).


Am I reading this wrong, or have you just stated that there's an infinitely many pairs of prime numbers within any bound of 70,000,000?
 
2013-05-23 04:54:45 AM  

SJKebab: Am I reading this wrong, or have you just stated that there's an infinitely many pairs of prime numbers within any bound of 70,000,000?


Heh.  There are infinitely many pairs within that bound of each other.

What it means is that no matter how big a number you choose, say 10**100000000, somewhere above that will be another prime pair within a small range of each other, and so on.  (But there will also be increasingly large gaps with no primes.)
 
2013-05-23 05:15:57 AM  

ThrobblefootSpectre: SJKebab: Am I reading this wrong, or have you just stated that there's an infinitely many pairs of prime numbers within any bound of 70,000,000?

Heh.  There are infinitely many pairs within that bound of each other.

What it means is that no matter how big a number you choose, say 10**100000000, somewhere above that will be another prime pair within a small range of each other, and so on.  (But there will also be increasingly large gaps with no primes.)


Yeah ok I think I get you.  So in that case, the twin primes are just the smallest gap possible for a pair of primes then?

So this then implies that some primes are paired, while others are not.  Am I correct so far?
If I am, then presumably we must have a strict definition of what it means for a prime to be paired then?
 
2013-05-23 05:27:49 AM  

SJKebab: So this then implies that some primes are paired, while others are not.  Am I correct so far?


Yes.  Pairs or "twin" primes are only 2 apart.  Like 3 and 5.  Or 881 and 883.

SJKebab: If I am, then presumably we must have a strict definition of what it means for a prime to be paired then?


Strictly speaking, "prime pairs" are only those primes that are consecutive odd numbers, as above.  Primes that are merely close together, like in this discussion, aren't really called pairs.
 
2013-05-23 06:05:51 AM  
Interesting work, horribly written article.
 
2013-05-23 06:17:08 AM  

ThrobblefootSpectre: Primes that are merely close together, like in this discussion, aren't really called pairs.


Then what are they called and what rules must they follow?

Otherwise, the gist I'm getting here is that this guy has found that there's an infinite number of "prime pairs" that are within 70,000,000 of each other, but there's also an infinite number of primes that are outside of those bounds.  So in other words, the article, if I'm to interpret it as you're suggesting, says absolutely nothing.

The original post that started this:

Triumph: So he proved that any given prime number will have a pair on one side or the other that is never more than 70 million numbers apart from it. huh. Yet another useless fact I'm never going to get out of my head.


I was originally interpreting it this same way.  For the moment, I think I'll continue to do so.

/Or you could try to be clearer maybe?
 
2013-05-23 07:06:29 AM  
funkyjudge.net
 
2013-05-23 07:13:14 AM  
If you start thinking really hard about what "random" really means, first you get a little nauseated, and a little after that you find you're doing analytic philosophy. So let's not go down that road.

Please dont ever write a science related article again.  Thanks.
 
2013-05-23 07:14:30 AM  

Alonjar: If you start thinking really hard about what "random" really means, first you get a little nauseated, and a little after that you find you're doing analytic philosophy. So let's not go down that road.

Please dont ever write a science related article again.  Thanks.


and there is no such thing as true random, only events that are unpredictable by our standards.
 
2013-05-23 07:40:21 AM  

SJKebab: The original post that started this:

Triumph: So he proved that any given prime number will have a pair on one side or the other that is never more than 70 million numbers apart from it. huh. Yet another useless fact I'm never going to get out of my head.

I was originally interpreting it this same way. For the moment, I think I'll continue to do so.


Please don't, because it's not correct. Let me try...

Choose a prime number, any prime number, let's call it M.
Now find the next higher prime number, call it N.
How far apart are they? We'll call that difference, N-M, the "bound" [think: how far you have to "leap" from one prime to the next.]
What can we say about the bound as M increases?

This theorem says that there are infinitely many examples where the bound is less than ~70,000,000. Not all primes have such a close partner, mind you: there are lots of cases [actually, infinitely many] where the next nearest prime is more than ~70,000,000 away. But however high a starting point you choose, somewhere higher there is a couple of primes whose bound is no more than 70,000,000.

Why is this at all surprising? Well, as M gets larger, prime numbers become rarer and rarer. (Intuitively, this seems reasonable: there are more numbers that could be factors.) So we might naively expect that the gaps become bigger and bigger, until there are no more primes within 70,000,000 of each other. Or 100,000,000. Or any other finite bound you choose. But our expectation would be wrong. Although it becomes harder and harder to find a pair of primes whose bound is less than 70,000,000, there are always more.

Why is this important? Because there is a very famous conjecture in number theory that proposes that the same thing is true for a bound of just 2, for example 29 and 31, which of course is the smallest possible bound for which it could be true. And while 70,000,000 may seem a long way from 2, proving the conjecture for any specific limit is a huge breakthrough, and mathematicians hope that the techniques used will point the way to bringing the limit down, and eventually proving it for the case of a bound of 2. And it turns out that, like several other important conjectures, the proof involves completely unexpected connections between apparently widely unrelated areas of math, which in  turn point the way to further insights.

Does that help at all?
 
2013-05-23 08:23:05 AM  
I faded out halfway through page 2, though I did find it interesting.

I wonder if Danica McKellar could explain it better.  Preferably dressed like this:

www.celebrone.com
 
2013-05-23 08:24:43 AM  

Alonjar: If you start thinking really hard about what "random" really means, first you get a little nauseated, and a little after that you find you're doing analytic philosophy. So let's not go down that road.

Please dont ever write a science related article again.  Thanks.


It's an article about mathematics, not science. And as an article about math, it's quite good.
 
2013-05-23 08:27:58 AM  
what an idiot.
 
2013-05-23 08:37:57 AM  

DjangoStonereaver: I faded out halfway through page 2, though I did find it interesting.

I wonder if Danica McKellar could explain it better.  Preferably dressed like this:

[www.celebrone.com image 500x959]


But that could take all night! In fact, I'd make sure of it.
 
2013-05-23 08:42:01 AM  
2 + 2 = blue
 
2013-05-23 08:46:30 AM  
call me a real number chauvinist but the allure of the prime numbers has never really made sense to me, at least in any practical nature.  base 10 integers were created by humans so the existence of base 10 primes is merely a consequence of human invention.  why do we place so much sacredness upon integers? just feels like we are stuck in grade school multiplication table era thinking where whole numbers are the only things that exist.  the only practical application of prime numbers I've found thus far was that it was fun to burn through an entire tray of printer paper trying to print out the largest known to-date prime number on the printers at my college's library.
 
2013-05-23 08:59:03 AM  

JasonOfOrillia: No Fields Medal for this guy.


The Fields Medal, the Fields Medal.  Come over to my house, you can have it.
 
2013-05-23 09:01:28 AM  

chocolate covered poop: call me a real number chauvinist but the allure of the prime numbers has never really made sense to me, at least in any practical nature.  base 10 integers were created by humans so the existence of base 10 primes is merely a consequence of human invention.  why do we place so much sacredness upon integers? just feels like we are stuck in grade school multiplication table era thinking where whole numbers are the only things that exist.  the only practical application of prime numbers I've found thus far was that it was fun to burn through an entire tray of printer paper trying to print out the largest known to-date prime number on the printers at my college's library.


They're prime regardless of what base they're displayed in.
 
2013-05-23 09:03:04 AM  

chocolate covered poop: at least in any practical nature.


doesn't public key cryptography has some minor applications on the internet?
 
2013-05-23 09:09:37 AM  

Alonjar: Alonjar: If you start thinking really hard about what "random" really means, first you get a little nauseated, and a little after that you find you're doing analytic philosophy. So let's not go down that road.

Please dont ever write a science related article again.  Thanks.

and there is no such thing as true random, only events that are unpredictable by our standards.


And what are our standards?
 
2013-05-23 09:34:29 AM  

PirateKing: chocolate covered poop: call me a real number chauvinist but the allure of the prime numbers...


They're prime regardless of what base they're displayed in.

I know, I was only slightly serious there.  And I assume that they follow the same pattern in other bases as well.

pup.socket: chocolate covered poop: at least in any practical nature.

doesn't public key cryptography has some minor applications on the internet?


Yeah I was being fairly facetious (real number chauvinist?).  I think there's applicability to harmonics in wave theory as well and likewise quantum theory where there are discrete states.
 
2013-05-23 09:36:12 AM  

drake113: DjangoStonereaver: I faded out halfway through page 2, though I did find it interesting.

I wonder if Danica McKellar could explain it better.  Preferably dressed like this:

[www.celebrone.com image 500x959]

But that could take all night! In fact, I'd make sure of it.


I'm really not that good at math.

I'd set aside an entire holiday weekend.
 
2013-05-23 09:41:32 AM  

Alonjar: Alonjar: If you start thinking really hard about what "random" really means, first you get a little nauseated, and a little after that you find you're doing analytic philosophy. So let's not go down that road.

Please dont ever write a science related article again.  Thanks.

and there is no such thing as true random, only events that are unpredictable by our standards.


What about that girl I know who likes Big Bang Theory and went to Paris one time? She says she's so random.
 
2013-05-23 09:42:59 AM  

czetie: SJKebab: The original post that started this:

Triumph: So he proved that any given prime number will have a pair on one side or the other that is never more than 70 million numbers apart from it. huh. Yet another useless fact I'm never going to get out of my head.

I was originally interpreting it this same way. For the moment, I think I'll continue to do so.

Please don't, because it's not correct. Let me try...

Choose a prime number, any prime number, let's call it M.
Now find the next higher prime number, call it N.
How far apart are they? We'll call that difference, N-M, the "bound" [think: how far you have to "leap" from one prime to the next.]
What can we say about the bound as M increases?

This theorem says that there are infinitely many examples where the bound is less than ~70,000,000. Not all primes have such a close partner, mind you: there are lots of cases [actually, infinitely many] where the next nearest prime is more than ~70,000,000 away. But however high a starting point you choose, somewhere higher there is a couple of primes whose bound is no more than 70,000,000.

Why is this at all surprising? Well, as M gets larger, prime numbers become rarer and rarer. (Intuitively, this seems reasonable: there are more numbers that could be factors.) So we might naively expect that the gaps become bigger and bigger, until there are no more primes within 70,000,000 of each other. Or 100,000,000. Or any other finite bound you choose. But our expectation would be wrong. Although it becomes harder and harder to find a pair of primes whose bound is less than 70,000,000, there are always more.

Why is this important? Because there is a very famous conjecture in number theory that proposes that the same thing is true for a bound of just 2, for example 29 and 31, which of course is the smallest possible bound for which it could be true. And while 70,000,000 may seem a long way from 2, proving the conjecture for any specific limit is a huge breakthrough, and mathe ...



A) Good add-on and appreciated.

So a few questions:

Did he just lower the bound to 70,000,000 from some other larger value or is there something compelling about that particular value?

If it is possible for to primes to be separated by a bound of 2 wouldnt an infinite number system automatically allow an infinite number of bounded pairs where the bound = 2?  Seems almost axiomatic in the definition of "infinite".

/not a "math" guy
 
2013-05-23 09:46:16 AM  

chocolate covered poop: practical application of prime number

s


Gears don't wear as fast if the numbers of teeth are prime numbers.
 
2013-05-23 10:04:20 AM  

Fizpez: Did he just lower the bound to 70,000,000 from some other larger value or is there something compelling about that particular value?

If it is possible for to primes to be separated by a bound of 2 wouldnt an infinite number system automatically allow an infinite number of bounded pairs where the bound = 2?  Seems almost axiomatic in the definition of "infinite".


For the first, it's the first proof of any bounded range, that's what makes it so noteworthy

for the second, no.  To use the example from the article, there exists a 'bound' on powers of 2 = 2.  (from 2 to 4) .. there are an infinite number of powers of 2.  But the number of pairs with a bound of 2 is not infinite, there is just the one.
 
2013-05-23 10:11:56 AM  
Zhang is an exponent of the "Indian summer" theory of late-life achievement.

Also, that McKellar woman has a bad case of TV head: a little, girlish body with a giant melon that photographs well.
 
2013-05-23 10:21:51 AM  
The article really is not all that great on the age issue for math/theoretical physics guys.

The issue is not that older people can't do impressive work.  They can and they do.

But the vast majority of huge conceptual advances that really do unexpectedly change the field are done by the young.  But older people have an advantage of non-paradigm changing work: experience, greater knowledge, wisdom, etc.  The really hard paradigm-changing problems are usually by the young because older people are more prone to getting set in their ways and that young brains really are better at intellectual sprinting.  (And of course "vast majority" does not mean "all.")

Giving the field what it expected to be true for a hundred years is not a radical conceptual change.
 
2013-05-23 10:25:10 AM  

chocolate covered poop: call me a real number chauvinist but the allure of the prime numbers has never really made sense to me, at least in any practical nature.  base 10 integers were created by humans so the existence of base 10 primes is merely a consequence of human invention.  why do we place so much sacredness upon integers? just feels like we are stuck in grade school multiplication table era thinking where whole numbers are the only things that exist.  the only practical application of prime numbers I've found thus far was that it was fun to burn through an entire tray of printer paper trying to print out the largest known to-date prime number on the printers at my college's library.


data encryption
 
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