項武義的Kepler夢想
數學界很多人都知道項武義，倒不是因為他的數學有多強，
而是因為一個古老的問題--Kepler猜想，這也讓項武義成了
數學界的一個笑柄。
這個項老頭子早年跟哥哥項武忠一道研究拓撲。老了就從
Berkeley回到香港科大養老。可他又偏偏閒不住，精力還特充沛，
於是開始在國內到處宣傳他的教學改革。聽他的演講，還真是
豪情萬丈，"Klein的Erlangen綱領只不過是個小小的idea。"，
"分形幾何那都是糊弄人的東西，是偽科學。"不明就裡的學生還
真對這個大塊頭的老頭子佩服不已。直讓人懷疑他是不是立志做
數學界的"方舟子"，"王海"。
項老頭子是個聰明人，因為他知道在德國說"Erlangen綱領是
個trivial的idea"可是要挨雞蛋的，他也知道在國外搞教改肯定沒人
理他。可憐了他只能在國內到處跑，凡是有關教改的大小會議一概
不會錯過。還出版了一套基礎數學講義叢書，可惜其中有不少
"項氏風格"的廢話。
也許覺得還不夠出風頭，項老頭子不知咋的，開始對Kepler
裝球問題感起了興趣。1992年到1993年，他在幾個數學雜誌上發表了
幾篇號稱完全證明Kepler猜想的文章，可惜不久就被著名數學家
J.H.Conway, Toth, Hale等人指出其中存在着明顯的漏洞。項老頭子一聽
火了，在Math Intelligencer雜誌上與Hales開始了針鋒相對的論戰。
項還到處贈送自己關於Kepler猜想的證明，許多系實在推脫不了，只得
收下兩本，不禁令人想起圖書館裡看到過的好多"民科"自費出版的
歌德巴赫猜想的證明。糊塗的項老不是把精力放在檢查和修補自己的證明
上面，而是在國內有如民科般的行事，多次在國內的講座上介紹他關於
Kepler猜想的錯誤證明。
數學是來不得半點虛假的，Hales在1997年藉助計算機，完全證明
了Kepler猜想，得到公認，文章即將發表在Annals of Math上，Hales
本人也在ICCM上作了45分鐘報告。宣告項的Kepler夢想徹底破碎。
項武義的老哥項武忠曾被向來直言的丘批評過學問二流，所以當哥兩
聽說丘田反目，當即成了田剛的鐵杆擁躉。這不，項武義被北大請去開
"基礎數學講座"，宣揚"項氏改革"，可惜聽眾寥寥。近日眼見田被丘批的
難以招架，忙把自己的講座變成了"批丘大會"，這下引來學生無數，項老
頭子的口才又有了用武之地，好不風光。
附：Kepler猜想介紹
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]
