【注：下文是单位群邮件的内容，标题是后加的（临时想的标题，与内容无关）】

昨天在一个页面*上看到一段文字。当时想搞清楚 Kx 究竟是什么[注1]，但不知为何，浏览到页面的深处（S打头的地方）。

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On Grothendieck’s own view there should be almost no history of schemes, but only a history of the resistance to them: ... There is no serious historical question of how Grothendieck found his definition of schemes. It was in the air. Serre has well said that no one invented schemes (conversation 1995). The question is, what made Grothendieck believe he should use this definition to simplify an 80 page paper by Serre into some 1000 pages of Éléments de géométrie algébrique?

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这段文字吸引到我。也许是第一句，也许是第六句[注2]。无意间点了那个 pdf 链接，文档中引述Grothendieck眼中的两类数学风格。一类奉行“榔头大棒”原则：对准关键部位，猛敲重击；需要的话换个部位，再猛敲重击，直至打开硬壳。另一类采取“浸泡”原则：泡个三五天、个把星期，硬壳慢慢变软，乃至缚鸡之力亦可开之。

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可是，Grothendieck 又补充了一类，原话是“...the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it...yet it finally surrounds the resistant substance. ” 

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同道中人评论：a characteristic Grothendieck proof as a long series of trivial steps where “nothing seems to happen, and yet at the end a highly non-trivial theorem is there”。（每一步都那么平凡，好像什么都没有发生，可是走到头，一个非同凡响的定理已然出现在人们的眼前...）。

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这就是“Grothendieck之道” —— 用更广阔的理论去淹没难题，并且远远超出原先的题设。（In this “rising sea” the theorem is “submerged and dissolved by some more or less vasttheory, going well beyond the results originally to be established” Grothendieck calls this his approach and Bourbaki’s. Here as so often he sees math research, exposition, and teaching as all the same.）

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Grothendieck 评说 Serre 惯用榔头大棒，认为 Serre 属于“阳极”，而他自己是“阴柔”—— 倒不是说出手多么重——而是夸赞Serre的优雅。（Grothendieck says Serre generally uses the hammer and chisel. He finds Serre “Super Yang” against his own “Yin”—but not at all in the sense of being heavy handed—rather Serre is the “incarnation of elegance”.）

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另外，此文还提到Grothendieck似乎是想达成这样的境界，一眼下去看穿一切。似有“会当凌绝顶”的意思。（In Grothendieck it is an extreme form of Cantor’s freedom of mathematics. It is not only the freedom to build a world of

set theory for mathematics but to build an entire world—specifically a “topos”, as large as the universe of all sets—adapted to any single problem such as a single polynomial equation on a finite field.）

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我想可能是这样，即追求“数学万物”的内在统一性。一的一切，一切的一。这跟我最近的想法接近，即寻找一把理解一切（数学）的“万能钥匙”。（早先区分了两类“真”，即 true 和 Genuine，但后者太脆弱、也太冗长，效率也低）。可能，想法上的某种接近性，使得那段文字吸引到我。

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看来，该认真对待Grothendieck。

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[注1] 见页面上“...where  are canonical divisors on D and X.”

[注2] 听到过 Grothendieck，scheme，Serre，但没太关注过。前些年倒是读过Serre的访谈记录，在普林斯顿《数学指南》上见过”概型“，但这两件事好像没关系。至于Grothendieck，好像是近几个月才稍略了解。