田剛論文有錯不改,這是大家都知道的。但很多人其實不知道,田剛也改過一回。
田迄今為止唯一的像樣的工作是Kahler-Einstein度量。而就是在這個工作的文章中,有一個非常致命的錯誤。田的這個錯誤同行都知道,但懾于田的人品,誰也不願意跟田直接說。
偏偏這個時候,田跟前Princeton數學系系主任項武忠透了口風,表示自己想去Princeton。項只好答應。到Princeton開會一說要請田過來,Princeton的faculty大多不同意,一個主要原因是田文章里的這個錯誤。項使了吃奶的勁也沒用,於是只能告訴田事情難辦。田絞盡腦汁,想了一個既把錯誤改過來又不丟面子的辦法,寫了一本書:Canonical metrics in Kahler geometry, Birkhauser Verlag, Basel, 2000.
書出來之後,項又在Princeton使了吃奶的勁,終於把田搞過去了。
按理說田到了Princeton應該放棄MIT的教職了,可他偏不。一直到現在還是腳踩兩隻船,對兩邊都要挾提高工資。
其實數學家的文章出錯很常見,知道有錯改了就行了。以丘成桐為例,該錯的文章隨便一查就有這麼多:
Erratum: "Nonexistence of time-periodic solutions of the Dirac equation in an axisymmetric black hole geometry". Comm. Pure Appl. Math. 53 (2000), no. 9, 1201.
Correction to: "A nonlinear elliptic system for maps from Hermitian to Riemannian manifolds and rigidity theorems in Hermitian geometry" [Acta Math. 170 (1993), no. 2, 221--254; MR1226528 (94g:58053)]. Acta Math. 173 (1994), no. 2, 307.
A note on our previous paper: "On the existence of Hermitian-Yang-Mills connections in stable vector bundles" [Comm. Pure Appl. Math. 39 (1986), S257--S293; MR0861491 (88i:58154)]. Comm. Pure Appl. Math. 42 (1989), no. 5, 703--707.
Corrections to: "Compact group actions and the topology of manifolds with nonpositive curvature" [Topology 18 (1979), no. 4, 361--380; MR 81a:53044]. Topology 21 (1982), no. 4, 483.
Erratum: "Some function-theoretic properties of complete Riemannian manifold and their applications to geometry" [Indiana Univ. Math. J. 25 (1976), no. 7, 659--670; MR 54 #5502]. Indiana Univ. Math. J. 31 (1982), no. 4, 607.
Errata to the paper: "Complete K?hler manifolds with nonpositive curvature of faster than quadratic decay" [Ann. of Math. (2)105 (1977), no. 2, 225--264; MR 55 #10719]. Ann. of Math. (2) 109 (1979), no. 3, 621--623.
其他的大數學家該錯的文章也有很多。但知錯就改,絲毫不影響別人的尊重。但田從沒寫過一篇該錯的文章。