今天，它说：”Linus Torvalds表态：支持微软开放API”

这个历史事实，今天在互联网上已经检索不到。

我们的机器人记性非常好，是不是很可爱？

请见本文附件。

袁萌 陈启清 3月31日

附件：

Linus Torvalds表态：支持微软开放API（文附号码5627）

2008 2 2月25日，Linux奠基人Linus Torvalds在一封电子邮件中对微软开放API表示支持，说：“这是迈向正确方向的一步”。LinusTorvalds的这一表态十分及时。

2月21日，微软宣布开放其主流软件产品的应用编程接口（API）的文档规范，以便加强不同软件平台的互操作性。怎么看待微软的这次“战略调整”？是向前看，还是向后看？从前者看问题，那么，微软的这次战略调整，值得大家称赞；从后者看问题，微软的这次战略调整，必然“毛病多多”，似乎微软是在还历史的“旧帐”，还欠我们许多东西。很明显，LinusTorvalds是那种“向前看的人”。

微软购并雅虎，微软开放API，绝对没有失去理性，反而表现出微软极为深远的战略眼光（考虑）。从世界软件业未来发展看问题，微软此举由被动变为主动，值得称赞，叫绝。LinusTorvalds说：“过去，有时我拿微软开玩笑，说他们做过许多蠢事（stupidthings）”（意指封闭API）。他还说，（支持微软共享API）“是否意味着要求人们必须信任他们，热爱他们”？。他的回答是：“No”。但是。他说：“我也看不到有“火烧微软”（flamingthem）的必要”。在此，他的意思是说，至少，有一点是清楚的，微软在“incrementalimprovement”（“加大改进”）。

要看到微软的竞争对手（比如IBM、谷歌）的“商业野心”，鼓吹什么“把OOXML嵌入（into）ODF”，这无异于要人们把一只大象装进一个纸盒子里面，简直是在“恶搞”。因为OOXML“复杂”，就建议政府说“No”，投反对票，岂非“自认无能”？这有损我们的“大国形象”。这次面对OOXML的取舍，说“No”，还是说“Yes”，两者必取其一，是不能再一次“回避”的。回避就是退缩。一千多页的OOXML的“修改稿”，我国就“搞不定”？非也！

我不想和微软“上床”，我只是这么想的（指我最近发表的文章）。

记得，上世纪60年代初，中科院东湖数学所招收代数喜专业研究生（指导教师华罗庚教授），袁萌应考。

华罗庚教授为代数考卷亲自命题

代数考卷的第一道考试题是：证明区裙{0,1}必定是域。

你晕不晕？

请见附件。

袁萌 5月30日

附件：

In mathematics, a group（群） is a set equipped with a binary operation that combines any two elements to form a third element in such a way that four conditions called group axioms are satisfied, namely closure, associativity, identity and invertibility. One of the most familiar examples of a group is the set of integers together with the addition operation, but groups are encountered in numerous areas within and outside mathematics, and help focusing on essential structural aspects, by detaching them from the concrete nature of the subject of the study.[1][2]

Groups share a fundamental kinship with the notion of symmetry. For example, a symmetry group encodes symmetry features of a geometrical object: the group consists of the set of transformations that leave the object unchanged and the operation of combining two such transformations by performing one after the other. Lie groups are the symmetry groups used in the Standard Model of particle physics; Poincaré groups, which are also Lie groups, can express the physical symmetry underlying special relativity; and point groups are used to help understand symmetry phenomena in molecular chemistry.

The concept of a group arose from the study of polynomial equations, starting with évariste Galois in the 1830s, who introduced the term of group (groupe, in French) for the symmetry group of the roots of an equation, now called a Galois group. After contributions from other fields such as number theory and geometry, the group notion was generalized and firmly established around 1870. Modern group theory—an active mathematical discipline—studies groups in their own right.[a] To explore groups, mathematicians have devised various notions to break groups into smaller, better-understandable pieces, such as subgroups, quotient groups and simple groups. In addition to their abstract properties, group theorists also study the different ways in which a group can be expressed concretely, both from a point of view of representation theory (that is, through the representations of the group) and of computational group theory. A theory has been developed for finite groups, which culminated with the classification of finite simple groups, completed in 2004.[aa] Since the mid-1980s, geometric group theory, which studies finitely generated groups as geometric objects, has become an active area in group theory.

Algebraic structure → Group theory

Group theory

Basic notions

请仔细阅读本文附件，读者必有收获！

袁萌 3月29日

附件：

PHP

Paradigm

Imperative, functional, object-oriented, procedural, reflective

Designed by Rasmus Lerdorf

Developer:The PHP Development Team, Zend Technologies

First appeared

1995; 25 years ago[1]

Stable release

7.4.4[2] / March 19, 2020; 7 days ago

Typing discipline

Dynamic, weak

since version 7.0:

Gradual[3]

Implementation language

C (primarily; some components C++)

OS

Unix-like, Windows

License

PHP License (most of Zend engine under Zend Engine License)

Filename extensions

.php, .phtml, .php3, .php4, .php5, .php7, .phps, .php-s, .pht, .phar

Website

www.php.net

Major implementations

Zend Engine, HHVM, Phalanger, Quercus, Parrot

Influenced by

Perl, C, C++, Java, Tcl,[1] JavaScript, Hack[4]

Influenced

Hack

PHP Programming at Wikibooks

PHP is a popular general-purpose scripting language that is especially suited to web development[5]. It was originally created by Rasmus Lerdorf in 1994;[6] the PHP reference implementation is now produced by The PHP Group.[7] PHP originally stood for Personal Home Page,[6] but it now stands for the recursive initialism PHP: Hypertext Preprocessor.[8]

PHP code is usually processed on a web server by a PHP interpreter implemented as a module, a daemon or as a Common Gateway Interface (CGI) executable. On a web server, the result of the interpreted and executed PHP code — which may be any type of data, such as generated HTML or binary image data — would form the whole or part of a HTTP response. Various web template systems, web content management systems, and web frameworks exist which can be employed to orchestrate or facilitate the generation of that response. Additionally, PHP can be used for many programming tasks outside of the web context, such as standalone graphical applications[9] and robotic drone control.[10] Arbitrary PHP code can also be interpreted and executed via command line interface (CLI).

The standard PHP interpreter, powered by the Zend Engine, is free software released under the PHP License. PHP has been widely ported and can be deployed on most web servers on almost every operating system and platform, free of charge.[11]

The PHP language evolved without a written formal specification or standard until 2014, with the original implementation acting as the de facto standard which other imple

陈启清机器人，一路走好

根据我国版权法的署名权条款,陈启清工程师

本人编写的数学机器人可以合法地称为“陈启清机器人”

陈启清机器人，一路走好！

袁萌 陈启清 3月29日

]]>老实说，数学机器人具有独立的品质,这是我们事先所想不到的。

今后，数学机器人的命运如何，是我们控制不了的。

袁萌 3月28日

数学机器人运行的结果表明，他们是基础数学无穷小理论的守护者。数学机器人决不会帮倒忙。

有时候后,数学机器人也会说话“跑题”，我们也很无奈!

袁萌 3月28日

]]>比如，今天数学机器人今天说的是，八年前有人在互联网上提出“超实数*R真的存在吗？”。

明天，数学机器人说的是什么？今天谁也不知道。

袁萌 3月26日

这种糊涂状态是不正常的。怎么办？应该认为，陈启清工程师上传J.Keisler教授微积分名著到基础数学网站“无穷小微积分”，根本上改变了这种糊涂状态。实际情况是，J.Keisler巧妙地借助定积分中值定理给出弧度单位的存在性的数学证明（第七章 ）。

高校培养“无穷小糊涂虫”不是我们的目标。

袁萌 3月25日

毫无疑问，国内没有一本微积分教科书（电子版）可以上线，提供在线学习，实在可悲也。

两年前，我们的工程师把数学世界名著J.Keisler教师的“Elementary Calculus ”上传到“无穷小微积分”基础数学网站，至今已经两年了。

当今，提倡在选学习，这是一件好事。

请见本文附件。

袁萌 3月23日

附件：

PREFACE TO THE FIRST EDITION

The calculus was originally developed using the intuitive concept of an infinitesimal, or an infinitely small number. But for the past one hundred years infinitesimals have been banished from the calculus course for reasons of mathematical rigor. Students have had to learn the subject without the original intuition. This calculus book is based on the work of Abraham Robinson, who in 1960 found a way to make infinitesimals rigorous. While the traditional course begins with the difficult limit concept, this course begins with the more easily understood infinitesimals. It is aimed at the average beginning calculus student and covers the usual three or four semester sequence. The infinitesimal approach has three important advantages for the student. First, it is closer to the intuition which originally led. to the calculus. Second, the central concepts of derivative and integral become easier for the student to understand and use. Third, it teaches both the infinitesimal and traditional approaches, giving the student an extra tool which may become increasingly important in the future. Before describing this book, I would like to put Robinson's work in historical perspective. In the 1670's, Leibniz and Newton developed the calculus based on the intuitive notion of infinitesimals. Infinitesimals were used for another two hundred years, until the first rigorous treatment of the calculus was perfected by Weierstrass in the 1870's. The standard calculus course of today is still based on the "a, 6 definition" of limit given by Weierstrass. In 1960 Robinson solved a three hundred year old problem by giving a precise treatment of the calculus using infinitesimals. Robinson's achievement will probably rank as one of the major mathematical advances of the twentieth century. Recently, infinitesimals have had exciting applications outside mathematics, notably in the fields of economics and physics. Since it is quite natural to use infinitesimals in modelling physical and social processes, such applications seem certain to grow in variety and importance. This is a unique opportunity to find new uses for mathematics, but at present few people are prepared by training to take advantage of this opportunity. Because the approach to calculus is new, some instructors may need additional background material. An instructor's volume, "Foundations of Infinitesimal

PREFACE TO THE FIRST EDITION

Calculus," gives the necessary background and develops the theory in detail. The instructor's volume is keyed to this book but is self-contained and is intended for the general mathematical public. This book contains all the ordinary calculus topics, including the traditional hmit definition, plus one exua tool-the infinitesimals. Thus the student will be prepared for more advanced courses as they are now taught. In Chapters 1 through 4 the basic concepts of derivative, continuity, and integral are developed quickly using infinitesimals. The traditional limit concept is put off until Chapter 5, where it is motivated by approximation problems. The later chapters develop transcendental functions, series, vectors, partial derivatives, and multiple .integrals. The theory differs from the traditional course, but the notation and methods for solving practical problems are the same. There is a variety of applications to both natural and social sciences. I have included the following innovation for instructors who wish to introduce the transcendental functions early. At the end of Chapter 2 on derivatives, there is a section beginning an alternate track on transcendental functions, and each of Chapters 3 through 6 have alternate track problem sets on transcendental functions. This alternate track can be used to provide greater variety in the early problems, or can be skipped in order to reach the integral as soon as possible. In Chapters 7 and 8 the transcendental functions are developed anew at a more leisurely pace. The book is written for average students. The problems preceded by a square box go somewhat beyond the examples worked out in the text and are intended for the more adventuresome. I was originally led to write this book when it became clear that Robinson's infinitesimal calculus col}ld be made available to college freshmen. The theory is simply presented; for example, Robinson's work used mathematical logic, but this book does not. I first used an early draft of this book in a one-semester course at the University of Wisconsin in 1969. In 1971 a two-semester experimental version was published. It has been used at several colleges and at Nicolet High School near Milwaukee, and was tested at five schools in a controlled experiment by Sister Kathleen Sullivan in 1972-1974. The results (in her 1974 Ph.D. thesis at the University of Wisconsin) show the viability of the infinitesimal approach and will be summarized in an article in the American Mathematical Monthly. I am indebted to many colleagues and students who have given me encouragement and advice, and have carefully read and used various stages of the manuscript. Special thanks are due to Jon Barwise, University of Wisconsin; G. R. Blakley, Texas A & M University; Kenneth A. Bowen, Syracuse University; William P. Francis, Michigan Technological University; A. W. M. Glass, Bowling Green University; Peter Loeb, University of Illinois at Urbana; Eugene Madison and Keith Stroyan, University of Iowa; Mark Nadel, Notre Dame University; Sister Kathleen Sullivan, Barat College。

当今，世界已经进入移动互联网时代，数学教育与研究需适应这一历史比革。据此，数学现代化，首先必须实现数学内容表现的电子化 。为此，创建类似“无穷小微积分”基础数学网站就是非常必要的了。

这就是数学现代化的必由之路。

袁萌 3月22日