据Twitter上多位知名科学家的消息，著名数学家、分形之父Benoît B. Mandelbrot（本华·曼德博）于美国时间10月15日辞世，享年85岁。
他是20世纪后半叶少有的影响深远而且广泛的科学伟人，在多个学科都有较大成就。1993年获得沃尔夫物理学奖，颁奖词评论说他的研究“改变了我们的世界观”。
Mandelbrot的一生与他的研究主题一样，是粗糙不平的。他拥有法国和美国双重国籍，1924年11月20日出生于波兰华沙一个来自立陶宛的学术传统深厚的犹太家庭（他在一次采访中曾戏称自己夫妇两个家族教授之多，学科之广，足以支撑一所不错的大学），但父亲以布匹贸易为生。1936年预感纳粹威胁，迁居法国。不久法国沦陷，他没有逃脱德军的铁蹄，日日面临死亡威胁，更激发了他对梦想的追求。1945-1947他进入著名的巴黎综合理工学校学习，师从著名数学家Julia和概率学家Levy。其中Julia提出的Julia集也是著名的分形函数。而Levy提出的非高斯稳定分布则是分形的重要思想来源，某种意义上Mandelbrot后来的大部分工作都是在各种领域里应用Levy分布。
1947-1949年他来到加州理工学院学习航空学，获得硕士学位。1949年回法国，任职于国家科研中心。1952年获得了巴黎大学的数学博士学位，据他自己的回忆，博士论文“Contribution à la théorie mathématique des jeux de communication”的前半部分是数理语言学，后半部分是统计热力学。期间他还在冯诺依曼的赞助下到普林斯顿高等研究中心进行博士后研究。1958年，他加入纽约的IBM研究院，在此工作长达32年，荣获IBM Fellow称号。1987年退休后来到耶鲁大学担任数学教授。
回顾Mandelbrot的一生，有一点非常值得注意，他是一位非常另类的科学家，而且前半生的学术生涯非常坎坷。虽然由于他没有学科藩篱之见，在外人看来，基本上是打一枪换一个地方，没有多少同道，很多时候连论文的发表都非常困难。到20世纪70年代初，甚至曾经退稿成堆。虽然一般被称为数学家，但他并不擅长分析（他只是美国数学会的一般成员），而是更注重几何与直觉，喜欢关注特例和其他人不大理会的地方，喜欢发掘他人认为是历史垃圾的老文献。他曾回忆自己在年轻时无法解决数学家叔叔Szolem Mandelbrojt（阿达玛的学生，布尔巴基学派成员）作为职业测试给出的难题。随着计算机的出现，他转而利用计算机研究数学中的一些老问题，结果出奇制胜。
事实上，他在20世纪罕见地沿袭了亚里士多德、达芬奇等伟人的博物学研究传统，不受学科限制，论文涉及信息论、经济学、金融学、语言学、生理学等几十个学科。菲尔茨奖得主、著名数学家David Mumford说：“他知道每个人的工作，而他却总是从不同角度去思考。每次演讲，都是在谈不同的主题。”他喜欢提出新问题和新猜想，但不善于证明。
但是这位超越时代的居然曾经在很长时间内是科学界的异类，不受人们重视。最后，他选择了创立新的学科，自己开拓一片天地。1975年他创造了分形（fractal）一词，出版了一系列奠定分形学说的著作，与其他非线性、复杂性理论一起成为各学科的有力助推器，而且随着计算机兴起，应用日渐广泛，除了计算机图形学，甚至美术界也兴起了分形艺术，他终于获得了世界性的声誉。
他是美国科学院院士。生前还被选为美国物理学会、美国统计学会、IEEE、计量经济学会、数理统计学会等学会的会士。


畅销书《黑天鹅》的作者Nassim Nicholas Taleb是Mandelbrot的合作者之一，书中观点实际上也反映了Mandelbrot的一些看法。Tabeb于老朋友辞世后，在自己的个人网站贴出了如下字样：

数学史上古希腊的辉煌（尤其是几何领域）之后，古罗马人几乎毫无建树。“罗马人中的希腊佬”，既说出了Mandelbrot一生的特立独行，当然更是一种极高的评价。

所谓分形，就是粗糙或零碎的几何形状，可以分成数个部分，且每一部分都（至少会大略）是整体缩小尺寸的形状。它能够用数学描述现实世界中更常见的表面上看似没有规律的粗糙形状和事物，在各学科中都有广泛应用。Mandelbrot曾说，柏拉图称人类的感知包括轻重、大小、冷热、颜色、音调和粗糙度，除了粗糙度之外，对其他各种感知的研究都曾经掀开物理学的新篇章，而分形恰恰补上了这一缺环。
实际上，分形和上世纪其他大部分数学进展不同，它具有很强的感性，可以直接感知。正如Mandelbrot自己所说的，分形是“在每个人都很熟悉的事物中找到的戏剧性的新发现”。比如他的著名论文所讨论的“英国的海岸线有多长”，就是分形的一个很好的例子。实际上，海岸线的长度取决于你观察它的远近。离得越近，因为小的更微观的曲折毕现，长度会更长，乃至无限。


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Obituary...
from 《The New York Times》
Benoit Mandelbrot, Mathematician, Dies at 85
Benoît B. Mandelbrot, a maverick mathematician who developed an innovative theory of roughness and applied it to physics, biology, finance and many other fields, died on Thursday in Cambridge, Mass. He was 85.
Dr. Mandelbrot coined the term “fractal” to refer to a new class of mathematical shapes whose uneven contours could mimic the irregularities found in nature.
“Applied mathematics had been concentrating for a century on phenomena which were smooth, but many things were not like that: the more you blew them up with a microscope the more complexity you found,” said David Mumford, a professor of mathematics at Brown University. “He was one of the primary people who realized these were legitimate objects of study.”
In a seminal book, “The Fractal Geometry of Nature,” published in 1982, Dr. Mandelbrot defended mathematical objects that he said others had dismissed as “monstrous” and “pathological.” Using fractal geometry, he argued, the complex outlines of clouds and coastlines, once considered unmeasurable, could now “be approached in rigorous and vigorous quantitative fashion.”
For most of his career, Dr. Mandelbrot had a reputation as an outsider to the mathematical establishment. From his perch as a researcher for I.B.M. in New York, where he worked for decades before accepting a position at Yale University, he noticed patterns that other researchers may have overlooked in their own data, then often swooped in to collaborate.
“He knew everybody, with interests going off in every possible direction,” Professor Mumford said. “Every time he gave a talk, it was about something different.”
Dr. Mandelbrot traced his work on fractals to a question he first encountered as a young researcher: how long is the coast of Britain? The answer, he was surprised to discover, depends on how closely one looks. On a map an island may appear smooth, but zooming in will reveal jagged edges that add up to a longer coast. Zooming in further will reveal even more coastline.
“Here is a question, a staple of grade-school geometry that, if you think about it, is impossible,” Dr. Mandelbrot told The New York Times earlier this year in an interview. “The length of the coastline, in a sense, is infinite.”
In the 1950s, Dr. Mandelbrot proposed a simple but radical way to quantify the crookedness of such an object by assigning it a “fractal dimension,” an insight that has proved useful well beyond the field of cartography.
Over nearly seven decades, working with dozens of scientists, Dr. Mandelbrot contributed to the fields of geology, medicine, cosmology and engineering. He used the geometry of fractals to explain how galaxies cluster, how wheat prices change over time and how mammalian brains fold as they grow, among other phenomena.
His influence has also been felt within the field of geometry, where he was one of the first to use computer graphics to study mathematical objects like the Mandelbrot set, which was named in his honor.


“I decided to go into fields where mathematicians would never go because the problems were badly stated,” Dr. Mandelbrot said. “I have played a strange role that none of my students dare to take.”
Benoît B. Mandelbrot (he added the middle initial himself, though it does not stand for a middle name) was born on Nov. 20, 1924, to a Lithuanian Jewish family in Warsaw. In 1936 his family fled the Nazis, first to Paris and then to the south of France, where he tended horses and fixed tools.
After the war he enrolled in the École Polytechnique in Paris, where his sharp eye compensated for a lack of conventional education. His career soon spanned the Atlantic. He earned a master’s degree in aeronautics at the California Institute of Technology, returned to Paris for his doctorate in mathematics in 1952, then went on to the Institute for Advanced Study in Princeton, N.J., for a postdoctoral degree under the mathematician John von Neumann.
After several years spent largely at the Centre National de la Recherche Scientifique in Paris, Dr. Mandelbrot was hired by I.B.M. in 1958 to work at the Thomas J. Watson Research Center in Yorktown Heights, N.Y. Although he worked frequently with academic researchers and served as a visiting professor at Harvard and the Massachusetts Institute of Technology, it was not until 1987 that he began to teach at Yale, where he earned tenure in 1999.
Dr. Mandelbrot received more than 15 honorary doctorates and served on the board of many scientific journals, as well as the Mandelbrot Foundation for Fractals. Instead of rigorously proving his insights in each field, he said he preferred to “stimulate the field by making bold and crazy conjectures” — and then move on before his claims had been verified. This habit earned him some skepticism in mathematical circles.
“He doesn’t spend months or years proving what he has observed,” said Heinz-Otto Peitgen, a professor of mathematics and biomedical sciences at the University of Bremen. And for that, he said, Dr. Mandelbrot “has received quite a bit of criticism.”
“But if we talk about impact inside mathematics, and applications in the sciences,” Professor Peitgen said, “he is one of the most important figures of the last 50 years.”
Besides his wife, Dr. Mandelbrot is survived by two sons, Laurent, of Paris, and Didier, of Newton, Mass., and three grandchildren.
When asked to look back on his career, Dr. Mandelbrot compared his own trajectory to the rough outlines of clouds and coastlines that drew him into the study of fractals in the 1950s.
“If you take the beginning and the end, I have had a conventional career,” he said, referring to his prestigious appointments in Paris and at Yale. “But it was not a straight line between the beginning and the end. It was a very crooked line.” 

关于国籍，Grothendieck貌似一直是无国籍

回复：8楼
Grothendieck 大爱此人!!
他爹就是无ZF主义者 他妈也搞社会活动 他被寄养在别人家 那家的家长信奉Humanism ...
他为了坚守道义 连个终身职位都弄不上

Grothendieck真的太有人格魅力啦~~~~~~~~`
不过...咱们别在这个贴子里说Grothendieck好不好..??

回复：10楼
咱们？！

楼上对楼上的楼上看来一直很有意思

不错哟.

LZ表示无语

想当年为分形激动了很久