项武义的Kepler梦想

数学界很多人都知道项武义，倒不是因为他的数学有多强，
而是因为一个古老的问题--Kepler猜想，这也让项武义成了
数学界的一个笑柄。

这个项老头子早年跟哥哥项武忠一道研究拓扑。老了就从
Berkeley回到香港科大养老。可他又偏偏闲不住，精力还特充沛，
于是开始在国内到处宣传他的教学改革。听他的演讲，还真是
豪情万丈，"Klein的Erlangen纲领只不过是个小小的idea。"，
"分形几何那都是糊弄人的东西，是伪科学。"不明就里的学生还
真对这个大块头的老头子佩服不已。直让人怀疑他是不是立志做
数学界的"方舟子"，"王海"。

项老头子是个聪明人，因为他知道在德国说"Erlangen纲领是
个trivial的idea"可是要挨鸡蛋的，他也知道在国外搞教改肯定没人
理他。可怜了他只能在国内到处跑，凡是有关教改的大小会议一概
不会错过。还出版了一套基础数学讲义丛书，可惜其中有不少
"项氏风格"的废话。

也许觉得还不够出风头，项老头子不知咋的，开始对Kepler
装球问题感起了兴趣。1992年到1993年，他在几个数学杂志上发表了
几篇号称完全证明Kepler猜想的文章，可惜不久就被著名数学家
J.H.Conway, Toth, Hale等人指出其中存在着明显的漏洞。项老头子一听
火了，在Math Intelligencer杂志上与Hales开始了针锋相对的论战。
项还到处赠送自己关于Kepler猜想的证明，许多系实在推脱不了，只得
收下两本，不禁令人想起图书馆里看到过的好多"民科"自费出版的
歌德巴赫猜想的证明。糊涂的项老不是把精力放在检查和修补自己的证明
上面，而是在国内有如民科般的行事，多次在国内的讲座上介绍他关于
Kepler猜想的错误证明。

数学是来不得半点虚假的，Hales在1997年借助计算机，完全证明
了Kepler猜想，得到公认，文章即将发表在Annals of Math上，Hales
本人也在ICCM上作了45分钟报告。宣告项的Kepler梦想彻底破碎。

项武义的老哥项武忠曾被向来直言的丘批评过学问二流，所以当哥两
听说丘田反目，当即成了田刚的铁杆拥趸。这不，项武义被北大请去开
"基础数学讲座"，宣扬"项氏改革"，可惜听众寥寥。近日眼见田被丘批的
难以招架，忙把自己的讲座变成了"批丘大会"，这下引来学生无数，项老
头子的口才又有了用武之地，好不风光。

附：Kepler猜想介绍

http://mathworld.wolfram.com/KeplerConjecture.html

Kepler Conjecture

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KeplerConjecture

In 1611, Kepler Eric Weisstein's World of Biography proposed that close
packing (either cubic or hexagonal close packing, both of which have max
imum densities of pi/(3sqrt(2)) approx 74.048%) is the densest possible
sphere packing, and this assertion is known as the Kepler conjecture. Fi
nding the densest (not necessarily periodic) packing of spheres is known
as the Kepler problem.

Buckminster Fuller (1975) claimed to have a proof, but it was really a d
exxxxion of face-centered cubic packing, not a proof of its optimality
(Sloane 1998). A second putative proof of the Kepler conjecture was put
forward by W.-Y. Hsiang (Cipra 1991, Hsiang 1992, Hsiang 1993, Cipra 19
93), but was subsequently determined to be flawed (Conway et al. 1994, H
ales 1994, Sloane 1998). According to J. H. Conway, nobody who has read
Hsiang's proof has any doubts about its validity: it is nonsense.

Soon thereafter, Hales (1997a) published a detailed plan describing how
the Kepler conjecture might be proved using a significantly different ap
proach from earlier attempts and making extensive use of computer calcul
ations. Hales subsequently completed a full proof, which appears in a se
ries of papers totaling more than 250 pages (Cipra 1998). A broad outlin
e of the proof in elementary terms appeared in Hales (2002). The proof r
elies extensively on methods from the theory of global optimization, lin
ear programming, and interval arithmetic. The computer files containing
the computer code and data files for combinatorics, interval arithmetic,
and linear programs require more than 3 gigabytes of space for storage.

Unfortunately, Hales' proof has proved extremely difficult to verify. Wh
ile it has been xxxxted to the Annals of Mathematics and will likely b
e published some time in 2003 or 2004, when it appears, it will carry an
unusual editorial note stating that parts of the paper have not been po
ssible to check, despite the fact that a team of 12 reviewers worked on
verifying the proof for more than four years and that the reviewers are
99% certain that it is correct (Holden 2003, Szpiro 2003).

In response to the difficulties in verifying his proof, in January of 20
03, Hales launched the "Flyspeck project" ("xxxxal Proof of Kepler") in
an attempt to use computers to automatically verify every step of the pr
oof. Unfortunately, Hales expects the project is likely to take 20 perso
n-years of labor (Holden 2003, Szpiro 2003).

SEE ALSO: Cubic Close Packing, Dodecahedral Conjecture, Hexagonal Close
Packing, Kepler Problem, Kissing Number, Sphere Packing. [Pages Linking
Here]