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点击附件才能看清楚黎曼函数方程等的数学式.
蒋春暄真能否定黎曼假设吗?
摘要: 蒋春暄先生声称否定黎曼假设(RH),说:国内外没有任何一个数学家否定蒋先生否定黎曼假设.外国数学专家Huxley, Connes, Sondow, Zagier 否定蒋否定黎曼假设.法国年青数学家Laurent Schadeck先赞颂蒋否定RH,随后否定蒋否定RH.
关键词: 黎曼假设,黎曼函数, 黎曼函数方程,复数零点,级数收敛发散,解析函数,解析开拓.
蒋春暄先生声称否定黎曼假设(RH), 蒋又说:国内外没有任何一个数学家否定蒋否定黎曼假设.当外国数学专家Huxley, Connes, Sondow, Zagier (请参考后面英文资料A,B,C,D,E,F,G,H,J), 否定蒋否定黎曼假设. 连蒋与仅有法国年青数学者(蒋称为数论数学家)Laurent Schadeck(LS)早些日子经常互相大赞颂, 2008年初出的LS文F 大赞颂蒋否定RH; 随后几个月又出LS文E 否定蒋否定RH.即便如此, 蒋还说:国内外没有任何一个数学家否定蒋否定黎曼假设,因为他们没有公开出论文不算数.
以前蒋对深圳大学物理副教授宋富高说:潘书[潘承洞、潘承彪，解析数论基础. 科学出版社，1999. P82, P123. ]共有914页,起码要读这本书才有发言权.蒋又说:解析数论核心就是RH，否定RH也就否定这本书.后又进一步说:所有中外关于"黎曼假设"RH的书和文全都错.这么随心所欲地空口说大话.
任何人过分狂妄自大,大搞宣传造势,很难成什么气候的.蒋一边宣传造势说: [我是一名在哈佛数学系的博士研究生,看到蒋老师的成就,真的非常振奋。您是我们中国的骄傲。可以说是数学史上最伟大的天才(以前我以为是高斯)。]另一边又宣传造势说:{法国数学家Schadeck通过陈一文找到我。他专门写了一文“Jiang number theory”在国外发表。他在国外大力宣传和研究我的数论成果。“我是一名在哈佛数学系的博士生，看到蒋老师的成就，真的非常振奋。您是中国的骄傲，可以说是数学史上最伟大的天才，以前我以为是高斯[1]。} "我是一名在哈佛数学系的博士生" --- 这话是中国留学生说的,又是乎是学法国数学家Schadeck说的,也许两人都说同样的话也不出奇.什么大宣传造势“数学史上最伟大的数学天才”都不顶用的.
只要稍有点数学黎曼假设知识的人,看了蒋的否定黎曼假设,几乎都不会枸同,连RH的内容,条件都没搞清楚.如蒋文G,数学式(1)不列出仅当复数实部大于1条件下才成立.改变此条件就不是黎曼假设,变成了蒋氏假设,否定的是蒋氏假设,就说大话用几种方法否定黎曼假设.
蒋在2007年末后的论文 <Riemann Paper(1859) Is False>,蒋对解析开拓一无所知,满以为黎曼函数方程的数学式(2)中,以ζ(s)‾代替 ζ(s) 得数学式(10),就可改变黎曼假设中的黎曼zeta函数ζ(s)‾,从而改变黎曼zeta 函数ζ(s)‾的复数零点. 甚至还无知地引用黎曼zeta函数的复数零点不都在实部 σ = 1/2 线上, 即在 σ = 1/2 线外还有复数零点支持蒋否定黎曼假设.其实这论点既否定黎曼假设,又否定蒋否定黎曼假设,因蒋声称黎曼zeta函数无任何复数零点.凡此种种,很难想象其他还会有什么样的惊人成果,自然令人置疑,也就很难引人去看其他的东西了.如果过度地吹嘘,只会让人耻笑.只因为我不怕国人互相耻笑,但却非常怕让外国人来大声耻笑,丢人败兴!才特写此文.
当然蒋还可大力去搞否定RH的宣称, 既然“墙内开花墙外香”(其实墙内吹得更火暴),有美国物理学家、数学家(不知谁上的?)桑蒂利教授的高度重视和全力支持,也许会取得美国克雷数学研究所的七大百万美元奖之一,二吧! 其中七大百万美元奖之 6. 黎曼假设RH，至今无人问津和得奖.但蒋先生曾问津过(见J).
A 英国名数学家Martin Neil Huxley否定蒋先生否定黎曼假设(RH)
英国名数学家回蒋先生的电邮
From: M N Huxley
To: jiangchunxuan@vip.sohu.com
Cc: hlm@umich.edu
Subject: Re: Falsity of Riemann';s Paper
Sent: Fri Jan 11 19:40:57 CST 2008
Dear Professor Jiang,
Thank you for your thoughts on the paper by Riemann. I
have received two copies. If you wish to publicise your own work,
you are going about it the wrong way. Certainly t he polite way to tell
a mathematician that his work is wrong is to say "I cannot
understand this argument on page ...". To say that someone else';s
work is actually wrong, you have to be extremely certain that your
own calculations are correct, and that you have actually read and
and understood their work.
Here are my comments on your paper.
p1. Riemann himself did not put forward the Riemann Hypothesis. It
was named after him later.
p1. "papers are too long to understand their correctness". is not a
mathematical statement. It just says something about your ability for
hard work. The longest journey begins with a single step.
p1. The series is not absolutely convergent forσ > 0, only for σ>1.
(即数学式(1) 绝对收敛,仅当复数实部大于1 )
p1. "In 1998 Jiang proved.." The reference is dated 2005. If this is
not a refereed paper (I don';t know the journal "Disc rete（Algebras）Groups and
Geometries", then you should say "Jiang claimed".
p1. Theorem 1. The statement "Riemann paper is false" is not a
theorem. In any case you offer no explanation or proof of what the
statement of Theorem 1 means.
p1. If (6) is the definition of $ ar zeta (s)$［以ζ(s)‾)代ζ(s)］，then $ ar zeta (s)$
seems to be what everyone else calls the Riemann zeta function. So what are you saying?
［whereζ(s)‾ is called Riemann zeta function with gamma function rather thanζ(s)］
I won';t continue, but there are strange remarks on further pages. If
you have got a new method, the Jiang Function, which solves the
famous problems, then bring it into the open and write a full
explanation and send it to a Mathematics journal, Annals of Maths or
the Proceedings of the London Math. Soc. or the Duke Math. Journal
or suchlike. If it works, then most people will be happy to forget
about the Riemann Hypothesis completely and use your method
instead. If you do n';t explain your method, then everybody else is
entitled to be as rude about you as you are about them, or what is
even worse, to ignore you completely., which is what I myself am
likely to do, as I am sent more papers than I have time to study
anyway.
With best wishes, Martin Huxley.
Martin Huxley
Martin Neil Huxley is a British mathematician, working in the field of analytic number theory.
He was awarded a PhD from the University of Cambridge in 1970, the year after his supervisor Harold Davenport had died. He is a professor at Cardiff University.ZHUAN
Huxley proved a result on gaps between prime numbers,[1] namely that if pn denotes the n-th prime number and if θ > 7/12, then for all sufficiently large n.
B 法国名数学家Alain Connes否定蒋先生否定黎曼假设(RH)
法国名数学家回蒋先生的电邮
From: alain connes
To: jiangchunxuan@vip.sohu.com
Cc: deligne@math.ias.edu
Sent: Wed Feb 13 22:32:58 CST 2008
Dear Professor Jiang,
I regret to announce you that your disproof of RH is false. I have
read it and the use of the product expansion
{ ⇒ ζ(s)=∑= ∐数学式 *}
zeta(s)=product[1/()1-1/p^(-s)]= (∐数学式*)which is only valid for Re(s)>1 is a (即数学式(1)成立,仅当复数实部大于1 )
shame for a mathematician like you.
I know that you have written "Riemann';s paper [1859] is false" in
which you say this use in fact is allowed by the difference of two
functions Euler zeta(s) and Riemann zeta(s).
I am sorry to announce to you that all your calculations in this paper
are false. But your other works could have still much interest! You
HAVE TO recognize that your papers about RH are a shame for you.
Alain Connes
From Wikipedia, the free encyclopedia 維基百科，自由嘅百科全書
Alain Connes (born 1 April 1947) is a French mathematician, currently Professor at the College de France, IHÉS and Vanderbilt University.
Alain Connes is one of the leading specialists on operator algebras. In his early work on von Neumann algebras in the 1970s, he succeeded in obtaining the almost complete classification of injective factors. Following this he made contributions in operator K-theory and index theory, which culminated in the Baum-Connes conjecture. He also introduced cyclic cohomology in the early 1980s as a first step in the study of noncommutative differential geometry.Connes has applied his work in areas of mathematics and theoretical physics, including number theory, differential geometry and particlephysics.
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C 美国数学家Jonathan Sondow否定蒋先生否定黎曼假设(RH)
美国数学家回蒋先生的电邮
From: Jonathan Sondow
To: jiangchunxuan@vip.sohu.com
Cc: laurent schadeck
Subject: Re: Jonathan Sondow
Sent: Mon Feb 04 13:28:59 CST 2008
Dear Jiang,
In your paper Disproofs of Riemann';s Hypothesis, formula (1) does not define
zeta(s) when sigma is less than 1. The reason is that the product over
primes does not converge if sigma < 1. (即复数实部小于1, 数学式(1)不收敛)
Likewise, the product in formula (4) does not converge when sigma is less
than 1. Therefore, your proof of Theorem 1 is wrong.
If you do not understand, ask your friend Laurent Schadeck. He seemed to
understand when I pointed out a similar error in a paper of his. So he may
be able to explain your mistake to you.
Regards
Jonathan Sondow
John Milnor
John Willard Milnor (b. February 20, 1931 in Orange, New Jersey) is an American mathematician
His students have included Jonathan Sondow.
Jonathan Sondow Giving a talk at a meeting of the American Mathematical Society
This is the fifth in a series of annual workshops sponsored by the New York Number Theory Seminar on problems in combinatorial and additive number theory and related parts of mathematics. A list of invited and confirmed lecturers
jsondow@alumni.princeton.edu
D 德国名数学家Don Bernhard Zagier等集体拒绝接受<黎曼1859年文章是错误的>,法国数论家Laurent Schadeck给蒋春暄的电邮 (2008-1-3)
De: Jonathan Sondow
Objet: Re: Zagier reject this email
Date: Tue, 05 Feb 2008 10:15
Don Bernhard Zagier (born 1951) is an American mathematician whose main area of work is number theory. He is currently one of the directors of the Max Planck Institute for Mathematics in Bonn, Germany, and a professor at the Collège de France in Paris, France. He was born in Heidelberg, Germany. He grew up in the United States, finishing high school at the age of 13, and studied for three years at M.I.T., completing his bachelor';s and master';s degree and being named a Putnam Fellow in 1967 at the age of 16. He then wrote a doctoral dissertation on characteristic classes under Friedrich Hirzebruch at Oxford, graduating at 21, and later collaborated with Hirzebruch in work on Hilbert modular surfaces.
One of his most famous results is a joint work with Benedict Gross (the so-called Gross-Zagier formula). This formula relates the first derivative of the complex L-series of an elliptic curve evaluated at 1 to the height of a certain Heegner point. This extremely important theorem has many applications including implying cases of the Birch and Swinnerton-Dyer conjecture along with being a key ingredient to Dorian Goldfeld';s proof of the class number problem.
He also is known for discovering a short and elementary proof of Fermat';s theorem on sums of two squares.[1][2]
He won the Cole Prize in 1987.
From: laurent schadeck
To: jiangchunxuan@vip.sohu.com
Subject: Re: forward:RE: ??
Sent: Sun Nov 04 20:40:47 CST 2007
Dear Professor Jiang,
Has professor Zagier answered to your e-mail? …
Zagier, because is known by the community of mathematicians to be one of the world';s greatest specialist of RH, is believed to be the most brilliant man to provide eleements for a proof of RH. in fact he introduces automorphic forms.
Laurent Schadeck.
法国年青数学者(蒋先生称为数论数学家)Laurent Schadeck在他的下面新出LS文E说
“in the Riemann Hypothesis as of 2008, but which has not proved”从而否定他之前多次以及早几个月出的LS文F 都赞赏蒋先生否定黎曼假设(RH,. 蒋先生也认为Laurent Schadeck改变原来的赞赏.
法国年青数学者LS文E
NonAssociative Geometry and The foundations of (Iso-)mathematics
Laurent Schadeck January 28, 2008
(After 10/04/2008,因该文注释 [160] Y. I. Manin, private communication, 10/04/2008.)
[ Contens
Abstract :
I. Introduction :
VII. On zeta functions over geometries, Riemann Hypothesis and Noncommutative Geometry
The famous conjecture made by Riemann [11] on the distribution of prime numbers into the set of natural integers has attracted the attention of algebraists and geometers since the times of Weil and Hilbert. Further it was linked to physics, and the very beginning of quantum mechanics. From a purely geometric point of view it led Weil to generalize the zeta function and assign each generalization thus obtained to a curve or a field. Furthermore the perspective given by the results of Riemann became an important feature for all sides of mathematics, so that it appeared clearly that the extension of any geometric and/or algebraic theory would have to deal with the further extensions of the broad theory suggested by Weil, which suggests a far-reaching unification of Algebraic Geometry and Analytic Number Theory, as it was noted by Dieudoné [75]. Then it appears that, due to the importance of the latter issue, the extensions suggested by the following dictionary were to be include to characterize parallel foundations of the underlying theories. One unfortunately note the absence of connections shown with isotopies until the present time.
Number
Theory
(Riemann)Algebraic Geometry
(Weil)Noncommutative Geometry
(Connes)Geometrodynamics
p-adic arithmetic
(Pitkänen)Isomathematics
(Santilli)
Zeros and poles of
Eigenvalues of the action of the Frobenius on
Eigenvalues of on adelic cohomologyZeros of p-adic zeta function that is formally the inverse of
???
Functional equationPoincaré duality in l-adic cohomology* operationp-adic inner product???
Explicit formulaLefschetz formula for the FrobeniusLefschetz formulaConformal symmetry, super-conformal invariance???
RHCastelnuovo positivityTrace formulap-adic formulation of the modified HPH???
1859195019901995???
The function of the great mathematician Riemann is defined over the complex number by
(1)
when Res>1. This function satisfies the following equation (黎曼函数方程)
(2)
where denotes the Euler Gamma function. This equations often reduces to the following form, defining the xi function :
In their independent 1896 proofs of the prime number theorem, Hadamard and De La Vallée Poussin proved that
and it is evident that has no zero for . In his insightful (and short) paper [11], Riemann was led by experimental evidence to formulate the following :
Riemann Hypothesis (RH) : where one ignores the trivial zeros –2,-4, etal.
…….
in the Riemann Hypothesis as of 2008, but which has not proved to be the most adequate way to intend it, we wish to extend it into an Hadronic embedding. For this we would suggest some threads that could lead to some renewing in Algebraic Number theory as well as in Isonumber theory.
法国年青数学者LS文F
Jiang Number Theory (JNT)
(After12/01/08) 因该文注释[17] Jiang, Martin Huxley, private communication, 12/01/08.
Laurent Schadeck laurentschadeck@caramail.com
Abstract :
Jiang Chun-Xuan is a Chinese mathematician who claims to have developed new number
theoretic tools consisting mostly in the Jiang function Jn (s #) where s #  2.3.5...p, p  n
denotes the primorial function to solve fundamental problems in Number Theory such as the
Goldbach Conjecture, the Twin Prime Conjecture, the k-tuple Conjecture, et al. The
fundamental motivation of Jiang to develop a number theory different from the one we are
familiar with (we, number theorists) comes from his recent claim (1997) that the Riemann
Hypothesis (RH) which lies at the foundations of all prime number theories, is false, that all
calculations done to improve it are false, and that the entire speculative theory done through it
(see Connes, Bombieri, Zagier et al.) are obviously false. Our goal in this paper will be to
review Jiang’s achievements from his disproof of RH to his establishment of the new number
theory.
1) Jiang 1997 disproof of RH :
The function of the great mathematician Riemann is defined over the complex number by
(无列出when Res>1) (1)
and is claimed by Riemann himself [2] to satisfy the following functional equation(黎曼函数方程)
(2)
where denotes the Euler Gamma function. This equations often reduces to the following form, defining the xi function :
In their independent 1896 proofs of the prime number theorem, Hadamard and De La Vallée Poussin proved that
and it is basically evident that ) has no zero for s=0.
Riemann it his epoch-making 1859 paper [2] stated that all the nontrivial roots of his function
lie in the critical strip [0,1] and made the following:
Riemann Hypothesis (RH) : where one ignores the trivial zeros –2,-4, etal.
In [1] Jiang defined a new function β(s) that is the dual of Riemann zeta-function.
Jiang mostly proved in [1] that the beta-function is not infinite for real part equal to ½ and
then, following the fundamental remark of Hadamard and De la Vallée Poussin, Riemann
zeta-function cannot have nontrivial zeros in the said critical line Re(s) = 1/2.
Jiang starts with an amaizing expression for both β(s) and ζ(s) which he coins their
exponential formulas. These formulas, to the best knowledge of the present author, are not
found in other RH books (in none of them) and are sufficient to Jiang to follow his entire
disproof.
…….
[1] Chun-Xuan Jiang, Disproofs of Riemann Hypothesis, Algebras, Groups and Geometries, Vol. 21,004.
蒋文G
In press atAlgebras, Groups and Geometreis, Vol. 21, 2004
DISPROOFS OF RIEMANN’S HYPOTHESIS
Chun-Xuan, Jiang
P.O.Box 3924, Beijing 100854, China
and Institute for Basic Research
P.O.Box 1577, Palm Harbor, FL 34682, U.S.A.
liukxi@public3.bta.net.cn
Abstract
As it is well known, the Riemann hypothesis on the zeros of theζ(s)
function has been assumed to be true in various basic developments of
the 20-th century mathematics, although it has never been proved to
be correct. The need for a resolution of this open historical problem
has been voiced by several distinguished mathematicians. By using preceding
works, in this paper we present comprehensive disproofs of the
Riemann hypothesis. Moreover, in 1994 the author discovered the arithmetic
function Jn(w) that can replace Riemann’sζ(s) function in view of
its proved features: if Jn(w) 6= 0, then the function has infinitely many
prime solutions; and if Jn(w) = 0, then the function has finitely many
prime solutions. By using the Jiang J2(w) function we prove the twin
prime theorem, Goldbach’s theorem and the prime theorem of the form
x2 + 1. Due to the importance of resolving the historical open nature
of the Riemann hypothesis, comments by interested colleagues are here
solicited.
AMS mathematics subject classification: Primary 11M26.
1. Introduction
In 1859 Riemann defined the zeta function[1]
(无列出when Res>1) (1)
where s = σ + ti; i = √-1; σand t are real, p ranges over all primes.
ζ(s) satisfies the functional equation [2] (黎曼函数方程)
(2)
From (2) we have
ζ(ti) ≠ 0 (3)
Riemann conjectured thatζ(s) has infinitely many zeros in 0 ≼σ≼ 1,
called the critical strip. Riemann further made the remarkable conjecture
that the zeros ofζ(s) in the critical strip all lie on the central lineσ= 1/2,
a conjecture called the famous Riemann hypothesis (RH).
It was stated by Hardy in 1914 that infinitely many zeros lie on the
line; A. Selberg stated in 1942 that a positive proportion at least of all
the zeros lie on the line; Levinson stated in 1974 that more than one
third of the zeros lie on the line; Conrey stated in 1989 that at least two
fifths of the zeros lie on the line.
……
References
[1] B. Riemann, “Uber die Anzahl der Primzahlen under einer
gegebener Gr¨osse,” Monatsber. Akad. Berlin. 671-680 (1859).
[2] H. Davenport, “Multiplicative Number Theory, ” Springer Verlag (1980).
蒋文H
Riemann Paper(1859) Is False
(After Nov. 5. 2007.)
Chun-Xuan. Jiang
P. O. Box3924, Beijing 100854, China
Jiangchunxuan@vip.sohu.com
Abstract
From Gamma function Remann derived the zeta function with Gamma function and put forward
Riemann hypothesis(RH) which is false. The Jiang function Jn(ω) can replace RH. Green-Tao
and Wiles papers are false [9-12]. Friedlander-Iwaniec and Heath-Brown papers are too long to
understand their correctness[14, 15].
Riemann defined the Riemann zeta function (RZF)[1]
(无列出when Res>1) (1)
where s = σ + ti; i = √-1; σand t are real, p ranges over all primes.RZF is the function
of the complex variable s in σ ≥0, t≠0 ，which is absolutely convergent.
In 1896 J. Hadamard and de la Vallee Poussin proved independently [2]
ζ(1+ti) ≠ 0 . （2）
In 1998 Jiang proved [3]
ζ(s) ≠0, （3）
where 0≤σ ≤1.
Theorem 1. Riemann paper (1859) is false [1]
……
whereζ(s)‾is called Riemann zeta function with gamma function rather thanζ(s),
……
[在黎曼函数方程 （2）
中,以ζ(s)‾代替 ζ(s) 得 (此处暂无法表示出数学表达式):]
From (9) we obtain the functional equation （10）
[蒋先生对解析函数解析开拓难道就无所了解? 数学式(2)中,以ζ(s)‾代替 ζ(s) 得数学式(10),就可改变黎曼假设中的黎曼zeta函数ζ(s)‾,从而改变黎曼zeta 函数ζ(s)‾的复数零点)?]
……
The functionζ(s)‾ satisfies the following
1. ζ(s)‾ has no zero for σ >1;
2. The only pole ofζ(s)‾ is at s =1; it has residue 1 and is simple;
3. ζ(s)‾ has trivial zeros at s = −2, − 4, ... butζ(s) has no zeros;
4. The nontrivial zeros lie inside the region 0≤σ ≤1 and are symmetric about both the vertical line σ= 1/2.
The strip 0≤σ ≤1 is called the critical strip and the vertical line σ= 1/2 is called the critical line.
Conjecture (The Riemann Hypothesis). All nontrivial zeros of ζ(s)‾ lie on the critical line σ= 1/2, which is false. [3]
ζ(s)‾ andζ(s) are the two different functions. It is false thatζ(s)‾ replacesζ(s), Pati proved that not all complex zeros of ζ(s)‾ lie on the critical line: σ= 1/2. [4].
注释:
[ Theorem 1. The Riemann Hypothesis is not true. In other words, not all the complex zeros of ζ(s) lie on the ‘critical line’: σ = 1/2 (σ = Rl s). Proved by Tribikram Pati in <The Riemann Hypothesis> [4]*
黎曼假设的复数零点不都在实部 σ = 1/2 线上, 即在 σ = 1/2 线外还有复数零点.
蒋先生难道连这点都看不出:Tribikram Pati 既否定否定黎曼假设,又否定蒋否定黎曼假设,因蒋声称黎曼假设无复数零点?]
……
References
[1] B. Riemann, Uber die Anzahl der Primzahlen under einer gegebener Grosse, Monatsber Akad.
Berlin, 671-680 (1859).
[2] P. Bormein, S. Choi, B. Rooney, The Riemann hypothesis, pp28-30, Springer-Verlag, 2007.
[3] Chun-Xuan. Jiang, Disproofs of Riemann hypothesis, Algebras Groups and Geometries 22,
123-136(2005). http://www.i-b-r.org/docs/Jiang Riemann. pdf
[4] Tribikram Pati, The Riemann hypothesis, arxiv: math/0703367v2, 19 Mar. 2007.
*[ http://arxiv.org/PS_cache/math/pdf/0703/0703367v2.pdf [MATH NT] 19 Mar. 2007 ]
[5] Laurent Schadeck, Private communication. Nov. 5. 2007.
[6] Laurent Schadeck, Remarques sur quelques tentatives de démonstration Originales de
l’Hypothèse de Riemann et sur la possiblilité De les prolonger vers une théorie des nombres
premiers consistante, unpublished, 2007.
…..
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美国克雷数学研究所回蒋电邮J
2000年初美国克雷数学研究所(The Clay Mathematics Institute)的科学顾问委员会选定了七个“千年大奖问题”,其中 6. 黎曼假设(Riemann Hypothesis)， 克雷数学研究所的董事会决定建立七百万美元的大奖基金，每个“千年大奖问题”的解决都可获得百万美元的奖励。克雷数学所“千年大奖问题”的选定，其目的不是为了形成新世纪数学发展的新方向， 而是集中在对数学发展具有中心意义、数学家们梦寐以求而期待解决的重大难题。其中6. 黎曼假设(Riemann Hypothesis),至今无人问津和得奖. 蒋先生曾问津,得到如下的回复.
From: Chelsea Chapko
Subject: Re: ??
Sent: Fri Jan 04 00:13:02 CST 2008
Hello,
Thank you for your interest in The Clay Mathematics Institute. The
rules regarding the Millennium Prize Problems and information on all
seven problems can be found on our website: http://www.claymath.org/millennium/Rules_etc/
. It states there that proposed solutions may not be submitted
directly to CMI for consideration. Rather, you would have to have
your work published in a refereed mathematics publication of worl dwide
repute, and it must then gain general acceptance in the mathematics
community for a minimum of two years. Some examples of such
publications can be found on the American Mathematical Society
website: .
Best regards,
The Clay Mathematics Institute(美国克雷数学研究所).
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