e*******y 发帖数: 73 | 1 没有人八卦这个吗?
今天的Nature已经刊登了新闻。
如果最终是对的话,我觉得是近50年来数学的重大结果
可能没有FLT对数学的促进大,但是不比费尔马大定里的影响小
对搞数学的来说 证明相差为70000000的素数有无穷多对和证明相差为2的素数有无穷多
对。并没有实质性的差别。意义是一样的。
http://www.nature.com/news/first-proof-that-infinitely-many-pri
First proof that infinitely many prime numbers come in pairs
Mathematician claims breakthrough towards solving centuries-old problem.
Maggie McKee 14 May 2013
Cambridge, Massachusetts
Mathematician Yitang Zhang has outlined a proof of a 'weak' version of the
conjecture on twin prime numbers, one of the longest-standing open problems
in mathematics.
Maggie McKee
Article toolsPrint
It’s a result only a mathematician could love. Researchers hoping to get ‘
2’ as the answer for a long-sought proof involving pairs of prime numbers
are celebrating the fact that a mathematician has wrestled the value down
from infinity to 70 million.
“That’s only [a factor of] 35 million away” from the target, quips Dan
Goldston, an analytic number theorist at San Jose State University in
California who was not involved in the work. “Every step down is a step
towards the ultimate answer.”
That goal is the proof to a conjecture concerning prime numbers. Those are
the whole numbers that are divisible only by one and themselves. Primes
abound among smaller numbers, but they become less and less frequent as one
goes towards larger numbers. In fact, the gap between each prime and the
next becomes larger and larger — on average. But exceptions exist: the ‘
twin primes’, which are pairs of prime numbers that differ in value by 2.
Examples of known twin primes are 3 and 5, or 17 and 19, or 2,003,663,613 ×
2195,000 − 1 and 2,003,663,613 × 2195,000 + 1.
The twin prime conjecture says that there is an infinite number of such twin
pairs. Some attribute the conjecture to the Greek mathematician Euclid of
Alexandria, which would make it one of the oldest open problems in
mathematics.
The problem has eluded all attempts to find a solution so far. A major
milestone was reached in 2005 when Goldston and two colleagues showed that
there is an infinite number of prime pairs that differ by no more than 16 (
ref. 1). But there was a catch. “They were assuming a conjecture that no
one knows how to prove,” says Dorian Goldfeld, a number theorist at
Columbia University in New York.
Related stories
Mathematician wins award for shaping algebra
Proof claimed for deep connection between primes
Mathematicians come closer to solving Goldbach's weak conjecture
More related stories
The new result, from Yitang Zhang of the University of New Hampshire in
Durham, finds that there are infinitely many pairs of primes that are less
than 70 million units apart without relying on unproven conjectures.
Although 70 million seems like a very large number, the existence of any
finite bound, no matter how large, means that that the gaps between
consecutive numbers don’t keep growing forever. The jump from 2 to 70
million is nothing compared with the jump from 70 million to infinity. “If
this is right, I’m absolutely astounded,” says Goldfeld.
Zhang presented his research on 13 May to an audience of a few dozen at
Harvard University in Cambridge, Massachusetts, and the fact that the work
seems to use standard mathematical techniques led some to question whether
Zhang could really have succeeded where others failed.
But a referee report from the Annals of Mathematics, to which Zhang
submitted his paper, suggests he has. “The main results are of the first
rank,” states the report, a copy of which Zhang provided to Nature. “The
author has succeeded to prove a landmark theorem in the distribution of
prime numbers. … We are very happy to strongly recommend acceptance of the
paper for publication in the Annals.”
Goldston, who was sent a copy of the paper, says that he and the other |
e*******y 发帖数: 73 | 2 这作者也很传奇。 十年写一篇文章!
毕竟FLT才有300多年的历史,孪生素数猜想应该有上千年的了吧? |
m*********a 发帖数: 2000 | 3 这个人真牛呀, 是不是他才是个lectuer?
【在 e*******y 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 这作者也很传奇。 十年写一篇文章! : 毕竟FLT才有300多年的历史,孪生素数猜想应该有上千年的了吧?
|
n*****b 发帖数: 2235 | 4 不懂 期待
【在 e*******y 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 没有人八卦这个吗? : 今天的Nature已经刊登了新闻。 : 如果最终是对的话,我觉得是近50年来数学的重大结果 : 可能没有FLT对数学的促进大,但是不比费尔马大定里的影响小 : 对搞数学的来说 证明相差为70000000的素数有无穷多对和证明相差为2的素数有无穷多 : 对。并没有实质性的差别。意义是一样的。 : http://www.nature.com/news/first-proof-that-infinitely-many-pri : First proof that infinitely many prime numbers come in pairs : Mathematician claims breakthrough towards solving centuries-old problem. : Maggie McKee 14 May 2013
|
n******t 发帖数: 4406 | 5 我觉得英文的废话真TMD的多。这么个结果写了这么废话。
【在 e*******y 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 没有人八卦这个吗? : 今天的Nature已经刊登了新闻。 : 如果最终是对的话,我觉得是近50年来数学的重大结果 : 可能没有FLT对数学的促进大,但是不比费尔马大定里的影响小 : 对搞数学的来说 证明相差为70000000的素数有无穷多对和证明相差为2的素数有无穷多 : 对。并没有实质性的差别。意义是一样的。 : http://www.nature.com/news/first-proof-that-infinitely-many-pri : First proof that infinitely many prime numbers come in pairs : Mathematician claims breakthrough towards solving centuries-old problem. : Maggie McKee 14 May 2013
|
i****g 发帖数: 3896 | 6 Iwaniec:
http://www.newscientist.com/article/dn23535-proof-that-an-infin
Iwaniec is less concerned about that problem at the moment, though. "The 70
million is not very important," he says. What matters is that Zhang was able
to show that the gap between adjacent primes cannot exceed a certain value.
"People will be stunned by the result. I'm sure people will be working on
it for years and then bring it down eventually."
Iwaniec, who has made contributions to the twin prime problem but was not
involved in the new work, has reviewed a paper presenting Zhang's proof and
cannot find an error in it. Zhang's paper has been accepted for publication
in the Annals of Mathematics.
"His result is beautiful," Iwaniec says. "He should enjoy his 15 minutes of
fame."
Terence Tao:
Yesterday 4:46 PM (edited) - Public
There is no publicly available preprint on this yet, and my information is
all either second- or third-hand, but my understanding is that Zhang has
managed to find a specialised improvement of the Bombieri-Vinogradov theorem
(in the spirit of some famous papers of Fouvry-Iwaniec and Bombieri-
Friedlander-Iwaniec, see e.g. the introduction to this recent paper http://arxiv.org/abs/1108.0439 for a summary) which, when combined with the method of Goldston, Pintz, and Yildirim http://arxiv.org/abs/math.NT/0508185, establishes bounded gaps between consecutive primes infinitely often. (The original Goldston-Pintz-Yildirim paper already noted that certain types of improvement to the Bombieri-Vinogradov theorem would give such a conclusion; I do not know if Zhang's argument establishes such improvements exactly, or establishes some variant result of this type.)
I hear that some very credible experts have already refereed the paper
carefully, but it may still take some time to get "official" confirmation of
the correctness of the argument, particularly in the absence of a preprint. |
m**p 发帖数: 2471 | 7 求科普为什么始于70millions?
没有人八卦这个吗?今天的Nature已经刊登了新闻。如果最终是对的话,我觉得是近50
年来数学的重大结果可能没有FLT对数学的促进大,但是不比费尔马大定里的影响小对
搞数学的来说 ........
【在 e*******y 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 这作者也很传奇。 十年写一篇文章! : 毕竟FLT才有300多年的历史,孪生素数猜想应该有上千年的了吧?
|
w*q 发帖数: 1544 | 8 去年什么时候有个人在bbs上发帖说自己马上要去顶尖牛校做教授了,要招博后之类的
。说自己当时在一个小学校,但是证明了很牛的东西。不久大家就会看到消息的。不知
道是不是就是这个啊? |
w*q 发帖数: 1544 | |
m*********s 发帖数: 368 | |
|
|
m*********s 发帖数: 368 | 11 一个上界而已, 当然最强的孪生素数猜想是隔上2
50
【在 m**p 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 求科普为什么始于70millions? : : 没有人八卦这个吗?今天的Nature已经刊登了新闻。如果最终是对的话,我觉得是近50 : 年来数学的重大结果可能没有FLT对数学的促进大,但是不比费尔马大定里的影响小对 : 搞数学的来说 ........
|
B****n 发帖数: 11290 | 12 人家可能十年裡埋頭苦幹沒說幾句話 大爆發了
【在 n******t 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 我觉得英文的废话真TMD的多。这么个结果写了这么废话。
|
K*****2 发帖数: 9308 | 13 粗略的说,以前是O(log n),现在有确界了,是吧 |
S*****a 发帖数: 190 | 14 这无疑是重大突破。但你这句话很有误导的嫌疑:
“对搞数学的来说 证明相差为70000000的素数有无穷多对和证明相差为2的素数有无穷多
张证明的是有无穷多个距离小于7千万的素数对,而并非距离刚好等于某个定值,这两
者还是有本质区别的,不能说“意义是一样的”。 |
k****e 发帖数: 126 | 15 有界无界的差别大得多吧
穷多
【在 S*****a 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 这无疑是重大突破。但你这句话很有误导的嫌疑: : “对搞数学的来说 证明相差为70000000的素数有无穷多对和证明相差为2的素数有无穷多 : 张证明的是有无穷多个距离小于7千万的素数对,而并非距离刚好等于某个定值,这两 : 者还是有本质区别的,不能说“意义是一样的”。
|
g*******n 发帖数: 644 | 16 niu b!!
【在 e*******y 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 没有人八卦这个吗? : 今天的Nature已经刊登了新闻。 : 如果最终是对的话,我觉得是近50年来数学的重大结果 : 可能没有FLT对数学的促进大,但是不比费尔马大定里的影响小 : 对搞数学的来说 证明相差为70000000的素数有无穷多对和证明相差为2的素数有无穷多 : 对。并没有实质性的差别。意义是一样的。 : http://www.nature.com/news/first-proof-that-infinitely-many-pri : First proof that infinitely many prime numbers come in pairs : Mathematician claims breakthrough towards solving centuries-old problem. : Maggie McKee 14 May 2013
|
G********n 发帖数: 615 | 17 选个子序列即可
穷多
【在 S*****a 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 这无疑是重大突破。但你这句话很有误导的嫌疑: : “对搞数学的来说 证明相差为70000000的素数有无穷多对和证明相差为2的素数有无穷多 : 张证明的是有无穷多个距离小于7千万的素数对,而并非距离刚好等于某个定值,这两 : 者还是有本质区别的,不能说“意义是一样的”。
|
m*********s 发帖数: 368 | 18 你再想想..
穷多
【在 S*****a 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 这无疑是重大突破。但你这句话很有误导的嫌疑: : “对搞数学的来说 证明相差为70000000的素数有无穷多对和证明相差为2的素数有无穷多 : 张证明的是有无穷多个距离小于7千万的素数对,而并非距离刚好等于某个定值,这两 : 者还是有本质区别的,不能说“意义是一样的”。
|
K*****2 发帖数: 9308 | 19 确实是weak version,不过能从log n(也有人说是o(log n))降到不仅是O(1)而且有一
个具体的常数上界,这已经是很大的提高了
穷多
【在 S*****a 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 这无疑是重大突破。但你这句话很有误导的嫌疑: : “对搞数学的来说 证明相差为70000000的素数有无穷多对和证明相差为2的素数有无穷多 : 张证明的是有无穷多个距离小于7千万的素数对,而并非距离刚好等于某个定值,这两 : 者还是有本质区别的,不能说“意义是一样的”。
|
D******g 发帖数: 125 | 20 哈哈, good
估计做数论的太久不取子序列了
【在 G********n 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 选个子序列即可 : : 穷多
|
|
|
x***m 发帖数: 345 | 21 Quote: "Zhang seems to be a 50+ lecturer with few previous papers, so that’
s
potentially a nice story." |
G********n 发帖数: 615 | 22 他是不是tenured的lecturer?
【在 x***m 的大作中提到】![](/moin_static193/solenoid/img/up.png) : Quote: "Zhang seems to be a 50+ lecturer with few previous papers, so that’ : s : potentially a nice story."
|
s*******n 发帖数: 740 | 23 http://golem.ph.utexas.edu/category/2013/05/bounded_gaps_betwee
看最后一段
50
【在 m**p 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 求科普为什么始于70millions? : : 没有人八卦这个吗?今天的Nature已经刊登了新闻。如果最终是对的话,我觉得是近50 : 年来数学的重大结果可能没有FLT对数学的促进大,但是不比费尔马大定里的影响小对 : 搞数学的来说 ........
|
s*******n 发帖数: 740 | 24 好像初中就应该学过抽屉原理了吧
【在 S*****a 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 这无疑是重大突破。但你这句话很有误导的嫌疑: : “对搞数学的来说 证明相差为70000000的素数有无穷多对和证明相差为2的素数有无穷多 : 张证明的是有无穷多个距离小于7千万的素数对,而并非距离刚好等于某个定值,这两 : 者还是有本质区别的,不能说“意义是一样的”。
|
x*****p 发帖数: 65 | 25 相差差 2 和 相差某个固定的 x,这两者在意义上有什么本质的区别??
【在 G********n 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 选个子序列即可 : : 穷多
|
e*******y 发帖数: 73 | 26 昨天换有个消息: 见arxiv
证明了任何大于5的奇数都是三素数之和。 不过这个意义不是特别大,80年前,苏联人
就证明充分大的都对。
现在看, Tao这么大的数学家前几月发表的五素数之和,就是个joke! 哈哈 |
l****j 发帖数: 4 | 27 On a generic level, however, the term Lecturer broadly denotes one who
teaches at a university but is not eligible for tenure and has no research
obligations.
【在 G********n 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 他是不是tenured的lecturer?
|
t****e 发帖数: 279 | 28 显然不是这个.
yitang zhang是北大毕业的.
那个自己说证明了百年大定理的是武汉大学毕业的.
【在 w*q 的大作中提到】![](/moin_static193/solenoid/img/up.png) : yitang zhang是不是就是这个大牛啊 : http://www.mitbbs.com/article_t/Mathematics/31191527.html
|
f******g 发帖数: 1003 | |
J*****n 发帖数: 4859 | 30 I just noticed that he is the student of Abhyankar. I guess his method is
very algebraic geometry. |
|
|
c****t 发帖数: 5452 | 31 i dont see him listed as abhyankar's student, where did you see it?
【在 J*****n 的大作中提到】![](/moin_static193/solenoid/img/up.png) : I just noticed that he is the student of Abhyankar. I guess his method is : very algebraic geometry.
|
J*****n 发帖数: 4859 | 32
math family tree
【在 c****t 的大作中提到】![](/moin_static193/solenoid/img/up.png) : i dont see him listed as abhyankar's student, where did you see it?
|
d******s 发帖数: 180 | 33 他是莫宗坚的学生,Abhyankar的徒孙。
不过从网上的点评看,他的工作是纯粹的解析数论,是在北大跟潘承彪学的。
【在 J*****n 的大作中提到】![](/moin_static193/solenoid/img/up.png) : : math family tree
|
K*****2 发帖数: 9308 | |
s*******n 发帖数: 740 | 35 你要我想什么?因为70m是个常数,所以当有无穷多对数塞进70m个抽屉,必定有个抽屉
有无穷多对数,这不是抽屉原理的想法?
【在 K*****2 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 呵呵你再好好想想
|
K*****2 发帖数: 9308 | 36 呵呵你再好好看看原来那帖子什么意思
【在 s*******n 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 你要我想什么?因为70m是个常数,所以当有无穷多对数塞进70m个抽屉,必定有个抽屉 : 有无穷多对数,这不是抽屉原理的想法?
|
t******s 发帖数: 281 | 37 取个子列就行了
穷多
【在 S*****a 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 这无疑是重大突破。但你这句话很有误导的嫌疑: : “对搞数学的来说 证明相差为70000000的素数有无穷多对和证明相差为2的素数有无穷多 : 张证明的是有无穷多个距离小于7千万的素数对,而并非距离刚好等于某个定值,这两 : 者还是有本质区别的,不能说“意义是一样的”。
|
I***a 发帖数: 13467 | |
t******s 发帖数: 281 | 39 有话就直说呗,想说什么说啊,还遮遮掩掩的。
【在 K*****2 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 呵呵你再好好看看原来那帖子什么意思
|
s*******n 发帖数: 740 | 40 这人有问题。。别理他了。
【在 t******s 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 有话就直说呗,想说什么说啊,还遮遮掩掩的。
|
|
|
y****d 发帖数: 46 | 41 到了论坛上还遮遮掩掩的,以为在你自己家里的一亩三分地上玩儿高深呢?
有P快放!
【在 K*****2 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 呵呵你再好好看看原来那帖子什么意思
|
S*****a 发帖数: 190 | 42 我是高级黑猪队友,大家一起鄙视我吧!
【在 G********n 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 他是不是tenured的lecturer?
|
L***n 发帖数: 6727 | 43 不但是提高吧,这是surprising的结果,提高只是incremental, 跟这个质量不是一个等
级的。
【在 K*****2 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 确实是weak version,不过能从log n(也有人说是o(log n))降到不仅是O(1)而且有一 : 个具体的常数上界,这已经是很大的提高了 : : 穷多
|
j**********e 发帖数: 1034 | 44 给出这样的comment就说明你不懂数论
【在 K*****2 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 确实是weak version,不过能从log n(也有人说是o(log n))降到不仅是O(1)而且有一 : 个具体的常数上界,这已经是很大的提高了 : : 穷多
|
HQ 发帖数: 19201 | 45 首先必须说恭喜和佩服.
我的理解是,这个结果固然很炫目,
更重要的是他用的方法.对于大难题突破的方法往往是更大的突破.
【在 e*******y 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 没有人八卦这个吗? : 今天的Nature已经刊登了新闻。 : 如果最终是对的话,我觉得是近50年来数学的重大结果 : 可能没有FLT对数学的促进大,但是不比费尔马大定里的影响小 : 对搞数学的来说 证明相差为70000000的素数有无穷多对和证明相差为2的素数有无穷多 : 对。并没有实质性的差别。意义是一样的。 : http://www.nature.com/news/first-proof-that-infinitely-many-pri : First proof that infinitely many prime numbers come in pairs : Mathematician claims breakthrough towards solving centuries-old problem. : Maggie McKee 14 May 2013
|
s*******7 发帖数: 743 | 46 血卡万岁啊,让他能无后顾之忧的专心研究,总算起了一点正面作用。
problems
one
twin
If
the
【在 e*******y 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 昨天换有个消息: 见arxiv : 证明了任何大于5的奇数都是三素数之和。 不过这个意义不是特别大,80年前,苏联人 : 就证明充分大的都对。 : 现在看, Tao这么大的数学家前几月发表的五素数之和,就是个joke! 哈哈
|
m****m 发帖数: 2211 | 47 他用的传统的方法
因此结果的正确性还有待时间的检验
据说近代数学上重大结果还没有用传统方法解决出来的
【在 HQ 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 首先必须说恭喜和佩服. : 我的理解是,这个结果固然很炫目, : 更重要的是他用的方法.对于大难题突破的方法往往是更大的突破.
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c**********j 发帖数: 133 | 48 连Tao都说他的目标是重振古典分析,不知你这个结论是哪里据说的?
张的结果已经至少被Friedlander, Iwaniec, Goldston肯定啦。他们可都是筛法专家哦
!Zhang用的方法虽然并不surprising,但是这个结果出人意料的强。我们还是祝贺他
吧!
【在 m****m 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 他用的传统的方法 : 因此结果的正确性还有待时间的检验 : 据说近代数学上重大结果还没有用传统方法解决出来的
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f**********d 发帖数: 4960 | 49 con!!!!
70
able
value.
and
publication
【在 i****g 的大作中提到】![](/moin_static193/solenoid/img/up.png) : Iwaniec: : http://www.newscientist.com/article/dn23535-proof-that-an-infin : Iwaniec is less concerned about that problem at the moment, though. "The 70 : million is not very important," he says. What matters is that Zhang was able : to show that the gap between adjacent primes cannot exceed a certain value. : "People will be stunned by the result. I'm sure people will be working on : it for years and then bring it down eventually." : Iwaniec, who has made contributions to the twin prime problem but was not : involved in the new work, has reviewed a paper presenting Zhang's proof and : cannot find an error in it. Zhang's paper has been accepted for publication
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