—— 真本登场！ 正式终结 法国德布罗意博士论文仅有一页多的江湖神话 —— 德布罗意眼中的美色乃“great intellectual beauty”（智慧之大美）！ —— 无奇不有！将 德布罗意波光大至完美的薛定谔倒是纵情声色的花花公子 —— 兼问德布罗意的博士论文为何不到三年就译成德文，但长期无英文版 —— 马克思博士 知 微有几分、对积几多解？-《数学手稿》的观众心语 德国的马克思在本科毕业的同时、同步完成博士论文，并将博士学位笑收囊中，并且凭借博士毕业文凭赢得泰山恩准、抱得美人归的故事堪称近代传奇。出现在博士论文题献处的唯一对象是女友的父亲，赞美之辞占据了整整一页（可点击附5中的网址欣赏）。现代新新人类往往只知赞美女友，却忘了赞美自己的未来岳丈。 以“马克思博士论文”为题的学术论文数名列世界之冠又堪称现代奇迹。详情可阅读本人的博文《博士学士双料学位获得者马克思被“博士论文”标题使用率世界第一》（ http://bbs.sciencenet.cn/blog-350729-650084.html ）。 网上一则所谓法国物理学家德布罗意仗持老爸威势、爱因斯坦留情，凭借一页纸论文，而不是一纸论文获得博士学位的消息在国内网络传为神迹。然而，据科学网王晓明博友的博文《从德布罗意的博士论文说起》及其回帖介绍，德布罗意的博士论文英文版正文达72页，而德文版有120页。 为稳妥起见，我下载并核实了德布罗意的博士论文，英文版总页码为81页，除前面的封面、目录上，正文的最后页码为第72页,第73页为参考文献页。 据英文版介绍，德布罗意博士论文原来的法文印刷本为1925年，后来译为德文版（1927年）。 德布罗意博士论文英文版.pdf 就该英文版而言，我有一些疑问。英文版的扉页仅有法文原文标题及译者A. F. Kracklauer的姓名，无翻译日期。英文版中却有德布罗意1927年专门为德文写作的序言，满满一页。后来网上检索译者A. F. Kracklauer的个人信息，发现他在个人主页中专门就德布罗意博士论文的英文翻译指出“ Although this work won him a Nobel prize, it appears that it was never completely translated into English. So, here's mine. ”（大意为，尽管此博士论文为德布罗意赢得了诺贝尔奖，但却从未全文翻译为英文，我做到了！）不过，A. F. Kracklauer只是简单地介绍翻译自德布罗意1925年的论文印刷本，是由法文直译还是 德文转译未加说明。就 A. F. Kracklauer 个人主页提供的多部译自德文的翻译作品看，可能在相当程度上依赖德文版。 德布罗意的人品也并不像中文故事传播的那样不堪。尽管身为贵胄之子，但他本人并非传说中的纨绔之徒。据弗罗里达州立大学网 页 介绍，他在量子力学方面的引路人是他的兄弟 Maurice（ 物理学家，在X射线方面做出了显著成就 ）。 在1913年大学毕业、获得科学学位后， 德布罗意 一直沉迷于科学思考，只是由于战争才耽搁了申请攻读博士学位。 http://micro.magnet.fsu.edu/optics/timeline/people/debroglie.html 将 德布罗意心目中的 great intellectual beauty译作“智慧有大美”之后，突然想到手头的一本书《天地有大美——现代科学之伟大方程》（上海世纪出版集团，格雷厄姆.法米罗主编）。该书介绍了薛定谔的波动方程、狄拉克方程、杨-米尔斯方程等。不过此书将薛定谔描绘为典型的花花公子，第四章的标题是“情欲、审美观和薛定谔的波动方程”。该章开篇写道，“埃尔温.薛定谔的一位好朋友回忆道，‘他在生命中的一次姗姗来迟的情欲大爆发中完成了他的伟大工作。’”。 副标题“德布罗意的博士论文为何不到三年就译成德文，但长期无英文版”只是我起初阅读英文版中德文版前言引发的困惑，后来看到 A. F. Kracklauer先生的网页说明才略解疑问。至于为何一直没有英文全版，可能还有更多的原因。 为了彻底消除罩在 德布罗意博士论文上的雾霾，我决定网搜德布罗意博士论文的法文原版。现将搜索结果公布如下：“法文版2”最后页码为第128页（此处未考虑 德布罗意博士论文手稿的总页数与该电子版的差异 ）。从语言角度分析，法语与英语的文字表达力相近，两种语本之间总字数通常相差不大。由本文提供的电文书籍版面看，法文版疏朗、英文版紧凑，初步判断 德布罗意博士论文手稿（手写稿或打字稿不详，但这已不影响本文的立论）至少在100页左右。为比较起见，下面附录 法文版(取自“法文版2”)、英文版中“第二德布罗意方程”的出现片断。 法文版下载网址为： 德布罗意博士论文法文原版1（封面似含德布罗意手写体）.pdf （1992年出版，根据1992年印刷本） 德布罗意博士论文法文原版2（仅正文，无封面、目录）.pdf 1. http://gsjournal.net/Science-Journals/Historical%20Papers-Quantum%20Theory%20/%20Particle%20Physics/Download/1635 2. http://tel.archives-ouvertes.fr/tel-00006807 附1：科学网的相关博文 从德布罗意的博士论文说起（hillside注:此文考证颇为详细，并附英文版提供下载） http://blog.sciencenet.cn/home.php?mod=spaceuid=2361do=blogid=259767 欧洲，1924年，一页纸的博士论文，可能吗？ http://blog.sciencenet.cn/home.php?mod=spaceuid=420554do=blogid=340591 附2：德布罗意为博士论文德文版翻译版Untersuchungen zur Quantentheorie, BECKER, W. (trans.) (Aka. Verlag., Leipzig, 1927)专门撰写的满满一页的序言（摘自英文版。“as translated to English below,”看来系英文翻译者A. F. Kracklauer添加）。 Preface to German translation In the three years between the publication of the original French version, and a German translation in 19271, the development of Physics progressed very rapidly in the way I foresaw, namely, in terms of a fusion of the methods of Dynamics and the theory of waves. M. EINSTEIN from the beginning has supported my thesis, but it was M. E. SCHR¨O EDINGER who developed the propagation equations of a new theory and who in searching for its solutions has established what has become known as “Wave Mechanics.” Independent of my work, M.W. HEISENBERG has developed a more abstract theory, “Quantum Mechanics”, for which the basic principle was foreseen actually in the atomic theory and correspondence principle of M. BOHR . M.SCHR¨ODINGER has shown that each version is a mathematical transcription of the other. The two methods and their combination have enabled theoreticians to address problems heretofore unsurmountable and have reported much success. However, difficulties persist. In particular, one has not been able to achieve the ultimate goal, namely a undulatory theory of matter within the framework of field theory. At the moment, one must be satisfied with a statistical correspondence between energy parcels and amplitude waves of the sort known in classical optics. To this point, it is interesting that, the electric density in MAXWELL-LORENTZ equations may be only an ensemble average; making these equations non applicable to single isolated particles, as is done in the theory of electrons. Moreover, they do not explain why electricity has an atomised structure. The tentative, even if interesting, ideas of MIE are thusly doomed. Nonetheless, one result is incontestable: NEWTON’s Dynamics and FRESNEL’s theory of waves have returned to combine into a grand synthesis of great intellectual beauty（智慧之大美） enabling us to fathom deeply the nature of quanta and open Physics to immense new horizons. Paris, 8 September 1927 附3：德布罗意博士论文的英文版翻译者、德国量子力学家A. F. Kracklauer。A. F. Kracklauer在他的主页提供了由他译为英文的的多篇量子力学经典著述。A. F. Kracklauer在该主页对量子力学的一些观点提出了批评，称之为“疯狂的物理学”（loco Physics）。 http://nonloco-physics.0catch.com/ 由A. F. Kracklauer译为 英文的 的多篇量子力学经典著述 The following are my translations of historic papers of particular significance for my interests for which, to my best information, there are no (or no complete) English versions. Some of these papers introduce notions that have become ensconced in physics folklore as if they were grounded on more solid foundations than these papers reveal to actually be the case, or, sometimes, visa-versa. 1. Einstein: Einstein in English , A 1250 page collection of my translations to English of 178 physics papers written by Einstein in three volumes: See : http://stores.lulu.com/kracklau . Errata: E-in-E_errata.html 2. Louis de Broglie (Thesis): On the theory of Quanta, Ann. de Phys. (1925) (Re-edited Dec. 05) Although this work won him a Nobel prize, it appears that it was never completely translated into English. So, here's mine. (340Kb); Hard copy: http://www.lulu.com/content/712243 ; e-file: ldb_the.pdf （注：此即德布罗意博士论文英文版全文下载链接） 3. Julio Palacios Martinez: Hard copy of both in one volume: http://www.lulu.com/content/772611 ---Relativity a paradox free alternative (Relatividad, una nueva teoria) JPM, on the basis of dimensional analysis came to the conclusion that asymmetric aging is untenable, so reformulated SR to exclude it from the start, eventually collecting his ideas up to 1960 in this book. (743Kb) rel_pal2.pdf , ---Antirelativistic Dynamics . Rev. Ace. Cie. (Madrid) LIX 69 (1968); published shortly before his death in 1970. A criticism of SR and a compendium of JPM's proposed fixes. (179Kb) pal_ant.pdf 4. Palacios: Relativity without Asymmetric Aging , Proc. PIRT VIX, 13 pages. An extraction from Palacios' book of just those parts pertaining to the `twin paradox.' (105 Kb) pal_pirt.pdf 5. Karl Schwarzschild, Electrodynamics I, II III (1906) . Gott. Nach.. 128 , 126-278 (1903) Apparently the first study to incorporate time-of-flight delay into action-at-a-distance mechanics. (179Kb) EM_KS.pdf 6. Hugo Tetrode, On Universal Interaction, Z. Phys. 10 , 317 (1922). Prophetic natural philosophy on the relativistic classical (action-at-a-distance on the light cone) and quantum electrodynamic interaction; but, short on red meat'' for a mathematical physicist. (53 Kb) interaction.pdf 7. A. D. Fokker: ---Relativistic point-particle mechanics, Z.. Phys. 58 , 356 (1929). A rediscovery (?) of Tetrode's direct action mechanics for systems of point particles. Noteworthy is the lack of skepticism, actual enthusiasm, for advanced interaction. This is the article most often cited, the following two are virtually unknown. (63Kb) fok_var.pdf ---Reciprocity in the Mutual Interaction of Charged Particles, Physica, IX , 33 (1929). The mother load for the above article with some additional details. (35Kb) reciprocity.pdf ---A Theory of Relativistic Interaction for Two Charged Point-masses, Physica. 145 (1932) . A follow up and further development of the the above two articles. (58Kb) deux.pdf 8. Walter Ritz: ---Critique of Maxwell-Lorentz Electrodynamics , Collected Works (1908). 13 pages. A short version of his formulation of an emission theory for electrodynamics, with emphasis on the contrast with Maxwell field theory. Gives good reasons to prefer direct interaction over field theories. (Note: Ritz wrote this paper using German syntax and sentence structure but French words---ugh! Some passages in my translation need tuning.) (79Kb) TE.pdf ---Gravity, Rivista di Scienza (1908) . An essay on the history of and prospects for a theory of gravity as of 1908, and a plaidoyer for his own proposal. Interesting and still relevant natural philosophy. (46Kb) grav.pdf ---EM: Blackbody Radiation, Phys. Z. (1908) . A turbid essay on the the cause of the ultraviolet catastrophe, and his argument that retarded interaction is essential for a solution. (36Kb) blackbody.pdf ---RelativityOptics, Collected Works (1908) . A natural philosophy essay on the differences between an aether and emission theories on the basis of optical and electrodynamical effects. Argues that in an emission theory, gravity appears naturally as a residue of electric force. (33Kb) optics.pdf 9. Werner Heisenberg: ---The Multibody Problem and Resonance in Quantum Mechanics, Z. Phys. 38 ,, 411 (1926). Evidently the first paper to introduce cat states into QM. It is particularly significant nowadays since these states are the foundation for the irreal aspect of wave functions and have come to play a very important role in EPR and Bell analysis. In this paper we see that they had a perfectly non mysterious, classical meaning in the beginning. This paper is an important reference for quant-ph/0602080 0602080_3.pdf (79 Kb) multi.pdf ---Wave Phenomena and Quantum Mechanics, Z. Phys. 40 , 501-506 (1927) . A natural philosophy essay on the implications, as he sees it, of the above article; i.e., a back-handed attack on Schroedinger's continuum wave mechanics, and the inception of Copenhagen dogma. (25Kb) waveqm.pdf ---The Multibody Problem and Resonance in Quantum Mechanics-II, Z. Phys. 40 , 551 (1927) . Follow-up and application of the principles developed in the above two papers. (119 Kb) multi2.pdf ---On the imaginable content of quantum kinematics and mechanics, Z. Phys. 43 , 172 (1927) . The paper in which Heisenberg set out 'uncertainty' as a fundamental quantum feature. This is a retranslation made to squeeze out every nuance regarding irreal wave functions and collapse at measurement. (111 Kb) anschau.pdf 10. V. A. Fock, Eigentime in Classical and Quantum Mechanics, Z. f. Phys. der Soviet-union 12 , 404 (1937) . Analysis pertaining to introducing eigentime into QM wave equations. Does not consider interacting particles, only a single particle bathed in an external wave. (87 Kb) eigentime.pdf 11. W. Slebodzinski, Cartan's Principle of Dynamics, Ann.. Soc. Math. Polonae Series I Comm. Math. XIV , 1-13 (1970) . A compact exposition of Cartan's Mechanics in classical notation. Noteworthy in that it emphasizes the independence of Cartan-Hamiltonian structure on space-time structure; it is essentially an existence proof for relativistic multiparticle dynamics with interaction. Important background for papers 6 and 16 above (60 kb) cartan.pdf 12. E. Schroedinger: ---The current situation in quantum mechanics, Die Wissenschaften. 48 , 807 (1935) . The Cat paper. This is a retranslation, as I found myself rereading sentences several times over in the other translation, and still was unsure what they meant. The problem is that the German original is itself idiosyncratic. It whipsaws among several styles of language, repeats, is larded with irony, sarcasm, journalistic focculi, etc. Nevertheless, it is an excellent catalog of issues on the foundations of QM. It actually 'obsoletes' much written after it. However, nearly half of it, including virtually all of the obscure parts, is devoted to describing 'conditional probabilities.' A reader knowing what they are (from math, where it takes 2 paragraphs) can read it with ease. (120 kb) cat.pdf ---On remarkable characteristics of quantized electron orbits, Z. f. Phys.. 42 , 13-23 (1922) . Interesting early geometric considerations largely overtaken by subsequent developments. Besides historical interest, it may contain ideas better not lost to history. (64 kb) ebahn.pdf 13. E. Madelung , Secular oscillations within singlet/triplet states, From: Math. Handbook for Physicists (Dover, 1942) p. 298 . A calculation not found in textbooks which may have deep significance for the interpretation of singlet/triplet irreal states. (19 kb) secular.pdf 14. A. Einstein, On a heuristic viewpoint of the creation and modification of light, Ann. d. Phys. 47 , 133 (1905) . A retranslation of the photon paper. It is just too important to be as difficult to get in English as it was. (61 kb) photon.pdf 15. V. Varicak, Relativity in three dimensional Lobachevsky space., (Zaklada Tiskare Norodnih, Zagrb, 1924). A translation of a mostly complete survey of Varicak's application of non Euclidean geometry to Relativity Theory; arguably the most complete treatment of this topic ever written. Hard copy: http://ww.lulu.com/content/774095 注：经比对，博文《从德布罗意的博士论文说起》中提供的德布罗意博士论文英文版应当就是 A. F. Kracklauer在其上述主页中提供的下载文档 ） 附4： 弗罗里达州立大学网 页对于德布罗意的介绍 http://micro.magnet.fsu.edu/optics/timeline/people/debroglie.html In the early twentieth century, the long standing argument about whether the character of light was particle-based or wavelike was finally coming to an end as the scientists of the day began to accept that light could assume a dual nature. The possibility that such a duality might apply to matter as well as light was first proposed by physicist Louis de Broglie. Born in Dieppe, France, de Broglie studied in Paris and was descended from members of the French nobility. In his youth, he considered a career as a diplomat, but later turned to science and pursued the study of theoretical physics. His brother, Maurice, who had also decided to become a physicist and made many advances in the study of X-rays, reportedly had a considerable influence on de Broglie and was the first to introduce him to the work of Albert Einstein and Max Planck. Louis de Broglie received a science degree in 1913, but was soon after required to enter the military. During World War I, he was stationed at the Eiffel Tower as part of the wireless telegraphy army subdivision. When not occupied by official duties, de Broglie filled many of his hours pondering scientific questions, which helped prepare him to continue his studies in 1920 after the war had ended. The focus of his research upon his return to Paris shifted to mathematical physics and his doctoral thesis consisted of research on quantum theory. Within de Broglie抯 thesis, which was completed in 1924, many of his most profound ideas were put forth, including his groundbreaking theory of electron waves. He had published some work on electron waves in scientific journals previously as well, but the articles were given little notice. It was not until Einstein read a copy of de Broglie抯 thesis that the revolutionary nature of his ideas was understood. Due to Einstein抯 attention, other physicists became familiar with de Broglie抯 wave theory and utilized it in shaping their own work. Most notably, de Broglie抯 theory served as the foundation upon which Erwin Schr鰀inger and others developed quantum mechanics. 附5：马克思博士论文 http://www.marxists.org/archive/marx/works/1841/dr-theses/ Karl Marx Internet Archive The Difference Between the Democritean and Epicurean Philosophy of Nature. with an Appendix Written: March 1841; First Published: 1902; Source: Marx-Engels Collected Works Volume 1; Publisher: Progress Publishers; Transcription/Markup: Andy Blunden; Online Version: Brian Baggins (marxists.org) 2000. Contents: According to Marx's original Table of Contents Dedication Foreword Part One: Difference between the Democritean and Epicurean Philosophy of Nature in General I. The Subject of the Treatise II. Opinions on the Relationship Between Democritean and Epicurean Physics III. Difficulties Concerning the Identity of the Democritean and Epicurean Philosophy of Nature IV. General Difference in Principle Between the Democritean and Epicurean Philosophy of Nature V. Result Part Two: Difference between the Democritean and Epicurean Philosophy of Nature in detail Chapter One : The Declination of the Atom from the Straight Line Chapter Two : The Qualities of the Atom Chapter Three : Atomoi archai and atoma stoicheia Chapter Four : Time Chapter Five : The Meteors Appendix Critique of Plutarch's Polemic against the Theology of Epicurus II. Individual Immortality 1. On Religious Feudalism. The Hell of the Populace 2. The Longing of the Multitude 3. The Pride of the Elected Notes I. On Religious Feudalism. The Hell of the Populace II. Opinions on the Relationship between Democritean and Epicurean Physics (notes) III. Difficulties concerning the Ientity of the Democritean and Epicurean Philosophy of Nature. (notes) IV. General Difference in Principle between the Democritean and Epicurean Philosophy of Nature Preliminary Note I. The Relationship of Man to God 1. Fear and the Being Beyond 2. Cult and the Individual 3. Providence and the Degraded God Draft of new Preface Marx's Notebooks on Epicurean Philosophy Editors' Footnotes and Preface , Image of Draft Preface . 附6：马克思数学手稿欣赏与科学网博客对于《数学手稿》的了解与心得 附6-1. 我自己的《数学手稿》收藏 此书文革后正式出版时曾现洛阳纸贵之势，由科学网与其他网站一些网友的回忆也可想见当年抢购盛况。该版封面仅有书名、作者，无出版社（英雄不问出处？ 。“人民出版社”字样出现于内页，出版、印刷日期（1975年7月第1版、1976年3月第二次印刷）也与现在的书籍为主张版权争先恐后地与扉页互相争宠、现在的一些姑娘们为吸引眼球以抢先暴露真相为荣不同，只是悄悄地、羞答答地藏在封底的内页。 附6-2 http://news.sciencenet.cn//zhibo/shownews.aspx?id=233319 纪念华罗庚逝世25周年大会, 时间：2010-6-12 :……到现在为止，数学家大会上提的，到目前数学家大会，现在马上就要开，包括数学家大会的主席和数学家，国际数学联盟主席和国际数学联盟的秘书长，他们都在说给数学一个定义是非常危险的，也就是对数学只能用观点去理解，我们国家基本上华老和 各个数学家都承认了马克思的定义 ，我就不重复了。 …… : 这件事我要说一下，很少人提到，73年的时候，北大的孙小宇等人，就把马克思数学手稿翻译出来了，74年在国内见了，在整个国内影响还是比较大，相当大的，北和南影响比较大，但是在科大几乎没受到影响，因为马克思的书稿有他的意义，他归结为一句话是什么呢，求导就是严格的特定的0：0，数学家羞答答干什么，就是那个零，但是我们有华老的那碗酒垫底，我们知道，0：0脱个精光上不了台演戏的，那个领域让我们在很多地方做了很多很多的事情。这是我们所有科大人都知道，但是这是华老的影响所带来的。 附6-3 http://www.alljournals.cn/view_abstract.aspx?pcid=01BA20E8BA813E1924CB483152CA50D4FC5BD3CBB47B847Fcid=585D04A2453D8AD5DDFFE8BE5B16E24Cjid=B0F48139158DAC130DCA71551C5A0F32aid=9B3CDCFF12FE0F7Eyid=D43C4A19B2EE3C0Avid=1371F55DA51B6E64iid=0B39A22176CE99FB 马克思数学手稿：宝贵的历史文献 北京大学学报(哲学社会科学版),2003,40(2):18-23. 作者姓名： 孙小礼 作者单位： 北京大学科学与社会研究中心 北京 100871 摘 要： 马克思酷爱数学，几十年坚持不渝地利用闲暇时间钻研数学，留下了近千页数学手稿。马克思数学手稿（部分）在我国翻译出后，有两种不同的看法：一是过分抬高，认为马克思运用辩证法为微积分奠定了理论基础；另一相反的看法，认为马克思不懂微积分，其数学手稿没有什么学术价值。本文说明这两种看法都太极端，马克思把数学当作经济学研究和重要工具和辩证法的重要源泉，研读数学又是马克思的独特精神休养方式。马克思数学手稿是一份有特殊价值的历史文献。 hillside注：欲阅读《马克思数学手稿：宝贵的历史文献》的更多内容，请点击： http://www.kepu.net.cn/gb/basic/szsx/4/41/4_42_1002.htm 附6-4 科学网网友回忆《数学手稿》 附6-4-1 http://blog.sciencenet.cn/home.php?mod=spaceuid=2321do=blogid=7378 http://blog.sciencenet.cn/blog-2321-21554.html 李世春博客 （hillside注：此博客中另外张贴了《数学手稿》封面、内页，有余兴者可与以上本人所贴对比） 当我上高中的时候，正是1973年到1976年，这三年间国内发生了许多大事，但是，我最感兴趣的事还是1975年马克思《数学手稿》的出版。我们的学校叫白灵淖中学，和大毛忽洞相距10公里，位于固阳阴山北30公里。如此偏僻的地方，当时在经济上又不能有任何的非分之想，根本不可能到城市的新华书店去看看。后来得知北京有个王府井书店，可以办理邮购业务，当即汇去5元钱，大约一个月后，一本崭新的马克思《数学手稿》便寄来了，余款以邮票的形式同书返回。后来再次去信询问有关数学方面的书籍，邮来的清单上除马克思《数学手稿》外，只有《运筹学》和华罗庚的《优选法》，可以想象到当时北京王府井新华书店也没有多少数学书籍。 众所周知，马克思《数学手稿》既不是一本教科书，也不是一本学术专著。当时只感觉到马克思是一个大学问家，看他的书肯定能学到些什么。后来上大学也带上了这本马克思《数学手稿》，并且一直保存到今天。 …… 数学手稿：马克思帮我对付极左派 那时，我学数学的时候，周围的人谁也不敢碰我，就连那些极左派也不敢碰我。 为什么呢？ 因为我有一本马克思《数学手稿》，而且就放在身边。 大毛忽洞还跟那些极左派开玩笑说：你们看的那些破报纸是孙子辈的，我看的是马克思的原著，是你们看的那些文章的作者的爷爷，你们有什么不服气的吗？ 当我看数学的时候，有时候极左派们还来给我（手里的马克思数学手稿）捧个场，就像花果山的猴子给孙悟空捧场一样。 如果陈景润当年手里也有一本马克思《数学手稿》就好了，或许能够击退极左派的干扰。 附6-4-2 http://blog.sciencenet.cn/home.php?mod=spaceuid=660333do=blogid=541216 程代展博客 文革前清华有许多数学教师是本校工科学生留校，以后又经历了多次政治运动，无心钻研业务，许多优秀人材，却得不到提高。我们刚去，就听说大跃进年代，数学教研组曾提出要“打倒柯家店”。不要epsilon-delta。反击右倾翻案风后，我们也被组织学习《马克思数学手稿》，还有人建议，用它当微积分教材。 附6-4-3 http://blog.sciencenet.cn/blog-539894-415631.html 肖赛君博客 我曾听到一个老师讲微积分中的极限理论是有缺陷的，他也提到爱尔兰大圣教贝克莱的批判，贝克莱称牛顿微积分体系中的“0”为“幽灵”，因为牛顿在需要“0”时，不管“0”多么小，就带了进来，在不需要的时候，也不管0多么大，一句话就给略掉了。这不符合数学严格逻辑推理的要求。马克思《数学手稿》曾经研究过这个问题，马克思认为没有必要引入极限，直接用0/0作为导数就可以， 马克思认为零是可以做分母的 。另外，好像数学家欧拉也曾说过零是可以做分母的。 附7：hillside对马克思及哲学的思辨性博文 牛顿的上帝科学观与马克思的地狱科学观—论对“地狱入口”的误读 http://blog.sciencenet.cn/blog-350729-588246.html 法典就是人民自由的圣经——自由落体定律对于马克思的启示？ http://blog.sciencenet.cn/blog-350729-555240.html 马克思论科学魅力—“高山论”与“地狱论”，兼议易中天破门而入 http://blog.sciencenet.cn/blog-350729-588220.html 凡是存在的，必有不合理之处；我在故我思——我的哲学思辨 http://blog.sciencenet.cn/home.php?mod=spaceuid=350729do=blogquickforward=1id=552274 附8：同时收获本科文凭与博士学位的天才数学家冯·诺依曼 http://hi.baidu.com/clq23/item/da3412d1bf6746b833db90c7 冯·诺依曼十几岁时曾得到一位叫L.拉兹的颇有才智的中学教师的教诲，不久以后，他成了M.法格蒂和L.法杰尔的弟子。L.法杰尔人称“许多匈牙利数学家的精神之父。”冯·诺依曼的父亲因考虑到经济上的原因，请人劝阻年方17岁的诺依曼不要成为数学家。后来父子俩达成协议，诺依曼便去攻读化学。1921～1925年，他先后在柏林和苏黎世学习化学。1926年诺依曼同时获得苏黎世化学工程文凭和布达佩斯数学博士证书。 http://www.pet2008.cn/thread-25393-5-1.html 1914年夏天，约翰进入了大学预科班学习，是年7月28日，奥匈帝国借故向塞尔维亚宣战，揭开了第一次世界大战的序幕。由于战争动乱连年不断，冯·诺依曼全家离开过匈牙利，以后再重返布达佩斯。当然他的学业也会受到影响。但是在毕业考试时，冯·诺依曼的成绩仍名列前茅。 1921年，冯·诺依曼通过“成熟”考试时，已被大家当作数学家了。他的第一篇论文是和菲克特合写的，那时他还不到18岁。麦克斯由于考虑到经济上原因，请人劝阻年方17的冯·诺依曼不要专攻数学，后来父子俩达成协议，冯·诺依曼便去攻读化学。 其后的四年间，冯·诺依曼在布达佩斯大学注册为数学方面的学生，但并不听课，只是每年按时参加考试。与此同时，冯·诺依曼入柏林大学(1921年)，1923年又进入瑞士苏黎世联邦工业大学学习化学。1926年他在苏黎世的获得化学方面的大学毕业学位，通过在每学期期末回到布达佩斯大学通过课程考试，他也获得了布达佩斯大学数学博士学位。
标签: 马克思
