Ideas & Trends

The Math Was Complex, the Intentions, Strikingly Simple


Published: August 27, 2006

LONG before John Forbes Nash, the schizophrenic Nobel laureate fictionalized onscreen in “A Beautiful Mind,” mathematics has been infused with the legend of the mad genius cut off from the physical world and dwelling in a separate realm of numbers. In ancient times, there was Pythagoras, guru of a cult of geometers, and Archimedes, so distracted by an equation he was scratching in the sand that he was slain by a Roman soldier. Pascal and Newton in the 17th century, Gödel in the 20th — each reinforced the image of the mathematician as ascetic, forgoing a regular life to pursue truths too rarefied for the rest of us to understand.

Agence France-Press/Getty Images, top; Granger Collection

CALCULATIONS Newton feuded with Leibniz over the discovery of calculus, but Grigory Perelman, top, claimed to put himself above such banalities.

Last week, a reclusive Russian topologist named Grigory Perelman seemed to be playing to type, or stereotype, when he refused to accept the highest honor in mathematics, the Fields Medal, for work pointing toward the solution of Poincaré’s conjecture, a longstanding hypothesis involving the deep structure of three-dimensional objects. He left open the possibility that he would also spurn a $1 million prize from the Clay Mathematics Institute in Cambridge, Mass.

Unlike Brando turning down an Academy Award or Sartre a Nobel Prize, Dr. Perelman didn’t appear to be making a political statement or trying to draw more attention to himself. It was not so much a medal that he was rejecting but the idea that in the search for nature’s secrets the discoverer is more important than the discovery.

“I do not think anything that I say can be of the slightest public interest,” he told a London newspaper, The Telegraph, instantly making himself more interesting. “I know that self-promotion happens a lot and if people want to do that, good luck to them, but I do not regard it as a positive thing.”

Mathematics is supposed to be a Wikipedia-like undertaking, with thousands of self-effacing scriveners quietly laboring over a great self-correcting text. But in any endeavor — literature, art, science, theology — a celebrity system develops and egos get in the way. Newton and Leibniz, not quite content with the thrill of discovering calculus, fought over who found it first.

As the pickings grow sparser and modern proofs sprawl in size and complexity, it becomes that much harder, and more artificial, to separate out a single discoverer. But that is what society with its accolades and heroes demands. The geometry of the universe almost guarantees that a movie treatment heralding Dr. Perelman is already in the works: “Good Will Hunting” set in St. Petersburg, where he lives, unemployed, with his mother, or a Russian rendition of “Proof.”

To hear him tell it, he is above such trivialities. What matters are the ideas, not the brains in which they alight. Posted without fear of thievery on the Internet beginning in 2002, his proof, consisting of three dense papers, gives glimpses of a world of pure thought that few will ever know.

Who needs prizes when you are free to wander across a plane so lofty that a soda straw and a teacup blur into the same topological abstraction, and there is nothing that a million dollars can buy? Until his death in 1996, the Hungarian number theorist Paul Erdos was content to live out of a suitcase, traveling from the home of one colleague to another, seeking theorems so sparse and true that they came, he said, “straight from The Book,” a platonic text where he envisioned all mathematics was prewritten.

Down here in the sublunar realm, things are messier. Truths that can be grasped in a caffeinated flash become rarer all the time. If Poincaré’s conjecture belonged to that category it would have been proved long ago, probably by Henri Poincaré.

It has taken nearly four years for Dr. Perelman’s colleagues to unpack the implications of his 68-page exposition, which is so oblique that it doesn’t actually mention the conjecture. The Clay Institute Web site carries links to three papers by others — 992 pages in total — either explicating the proof or trying to absorb it as a detail of their own.

Those intent on parceling out credit may have as hard a time with the intellectual forensics: Who got what from whom? Dr. Perelman’s papers are almost as studded with names as with numbers. “The Hamilton-Tian conjecture,” “Kähler manifolds,” “the Bishop-Gromov relative volume comparison theorem,” “the Gaussian logarithmic Sobolev inequality, due to L. Gross” — all have left their fingerprints on The Book. Spread among everyone who contributed, the Clay Prize might not go very far.

A purist would say that no one person deserves to stake a claim on a theorem. That seemed to be what Dr. Perelman, who has said he disapproves of politics in mathematics, was implying.

“If anybody is interested in my way of solving the problem, it’s all there — let them go and read about it,” he told The Telegraph. “I have published all my calculations. This is what I can offer the public.”

He sounded a little like J. D. Salinger, hiding away in his New Hampshire hermitage, fending off a pesky reporter: “Read the book again. It’s all there.”




















和Sam在新天地吃了个饭。奇了怪了,最近两周,只要是在新天地附近吃饭,就一定是这个Simply Thai。而且每一次都不是我订的座。这个问题如果要仔细研究研究,说不定挺有意思。是互相影响,还是我的朋友们和我的口味比较接近,还是新天地周围其实只有这么一家的餐馆适合我们这种口味的?




昨晚没什么事儿,拿出Quentin Taratino的Pulp Fiction又研究了研究,顺带网上搜了搜,搜出他最早还在一个录像店打工时候合Bob Avery合写的Pulp Fiction的剧本。从头到尾仔细看了看。看他的手稿,就一个感觉,奇思妙想,穿插来去,就像在看个空中特技表演队似的,经常想,靠,这要不行了吧,要撞上了吧,忽然来一个出乎意料却又是情理之中的一个转折,极漂亮极惊险地就过去了。

他的剧本里的世界,就是Quentin Taratino的世界。精彩,紧凑,不过就是他的世界。Guy Richie的也有些影子。疯狂的石头,前面到还罢了,不少人说是抄袭,我倒觉得抄得还不错。不过最后的10分钟,那些结尾,就太愚蠢,太形式化,太自己把自己当回事儿地又要娱乐又要艺术还要点人生,就像是个耍把戏的,手里3球已经累得满头大汗,边上已经看得让人心惊肉跳担心他要掉下来,他好,还非要再加两球,然后还非要摆一特酷的Pose收场。





传说中将要发布的视频管理规定 – 我真想说,吾不言


这些敏感一些的问题,我也不得不向很多先烈们学习,把我的原话在这儿写出来,免得将来如果哪一个报纸杂志登出来什么,说是我说的,如果是我从来没说过的,不免就有些百口莫辩的感觉。当然,先强调一下,绝大多数的兄弟们还是比较能忠实原话的。烦的是象China Daily前两月这种土豆网融资一亿美元的报道(我融一亿美元干啥?真要象keso建议说我干脆投身房地产业难道?),更烦的是像这不知道算媒体还是不算媒体的飞猪的商业评论,立刻就把China Daily新闻拿来作为泡沫和自吹自擂典型的典型来引用。最最烦的是,这个商业评论下面的这个对话:


StanCHU 发表于 2006年08月08日 11:38


由 flypig 发表于 2006年08月08日 11:41

不做臆断地核实一下难道真的很困难吗?Thomas Friedman写一篇评论,还能发两回草稿来核实是否与事实相符。尚进那儿忽悠一个Web 2.0也能发稿之前发来草稿核对一下数字和事实是否有出入。至于这么困难吗。









今天the New York Times上,说到Poincare Conjecture,数学的七大难题之一,终于有解的时候,Poincare在100年前说过的一句话:"Thought is only a flash in the middle of a long night, but the flash that means everything."

套用一下, "The graffitti is only a glance in the middle of a big traffic jam, but the glance that means everything."

So are many other things that might be evanescent , but that single burst of life is already worth everything.



一年前,Web 2.0这个词刚刚开始成为互联网的时尚名词。一夜之间,恨不得是个人都号称自己是个新兴的Web 2.0网站,Web 2.0公司。长尾理论,引爆流行,等等等等。记得去年7月份某次和个投身VC的哥们聊天,他一开口就是,“靠,这个月我已经收到至少10份商业计划书,说自己是Web 2.0的模式。媒体上到处说你们是Web 2.0的样板,你说到底这玩意儿是怎么回事?”


写了一年多的blog,似乎在我自己的blog上,提到Web 2.0这个词的,只有两篇blog。一年多前了,去年6月的第一篇说,在开始做土豆的时候,我听都没听说过Web 2.0这个词。第二篇,是去年12月,在读了Ozzie的memo后,和几个哥们聊完天,有感而发,就Web Service写了个“Web 2.0 我们从哪儿来,我们要到哪儿去。”

到了今天,忽然间满世界都在纷纷火火地说,一批小网站要死掉了,风险投资开始看衰Web 2.0了,Web 2.0的寒冬已经来了。忽然之间,Web 2.0就成了过街老鼠,是个公司就要跟Web 2.0撇清关系。已经很久没有哪个VC来找我说,Gary,说说这Web 2.0到底是怎么回事。