The Role of Symmetry in Mathematics

Over the past few decades the notion of symmetry has played a major role in physics and in the philosophy of physics. Philosophers have used symmetry to discuss the ontology and seeming objectivity of the laws of physics. We introduce several notions of symmetry in mathematics and explain how they can also be used in resolving different problems in the philosophy of mathematics. We use symmetry to discuss the objectivity of mathematics, the role of mathematical objects, the unreasonable effectiveness of mathematics and the relationship of mathematics to physics.     

翻译场景下的术语管理:流程、工具与趋势

随着语言技术的突飞猛进和语言服务需求多元化的发展,术语管理在翻译场景中发挥着日益重要的作用。文章首先阐述了术语管理的重要意义和典型流程,探讨了术语管理工具的主要功能及其选择策略,分析了新时代背景下术语管理的发展趋势,最后讨论了术语管理对“一带一路”语言服务需求和国家语言服务人才培养的重要意义。     

史密斯:杰出的数学史家、数学教育家和人文主义者

著名数学教育家和数学史家史密斯(D.E.Smith,1860-1944)集多种非凡才能于一身,学问宏博、著作等身,成就斐然。他是杰出的收藏家和旅行家;他独立或与他人合作编写了150余部数学教材;他在美国率先开设了数学史课程和中学数学教师培训课程;他创建了美国乃至世界上第一个数学教育博士点;他创立了国际数学教育委员会;他为数学教育点燃七支理想之烛。他是一位杰出的人文主义者;他创立了科学史学会,推动了美国的科学人文主义运动;他的《数学史》、《数学原典》和《算术珍本》是数学史的经典之作;他是最早研究东方数学的美国学者,是中美数学交流的先驱。     

数学中的游戏因素及其对于数学的影响

游戏与数学作为两项人类活动具有许多共同的特点 ,这种共性主要体现在它们的性质、结构以及实践等三个方面。数学与游戏之间的关系是相互渗透、相互统一的关系。游戏的精神一直伴随着数学的成长和发展 ,成为数学发展的主要动力之一 ;并从以下几个方面影响了数学的发展 ;游戏激发了许多重要数学思想的产生 ,游戏促进了数学知识的传播 ,游戏是数学人才发现的有效途径。此外 ,游戏还在数学教育中起着非常重要的作用。     

数学常青--古代、文艺复兴和近代的数学

Approaching Antiquity: Archimedes and the Fields Medal Since 1936 the so-called Fields Medal "is awarded every four years on the occasion of the International Congress of Mathematicians to recognize outstanding achievement for existing work and for the promise of future achievement" (http:∥www. mathunion. org/medals/Fields/index. html). It replaces the non-existing Nobel prize for mathematicians. Up until 2005 it has been awarded 44 times.     

The Will to Mathematics: Minds, Morals, and Numbers

The 1990s could be called The Decade of Sociology in mathematics education. It was during those years that the sociology of mathematics became a core ingredient of discourse in mathematics education and the philosophy of mathematics and mathematics education. Unresolved questions and uncertainties have emerged out of this discourse that hinge on the key concept of social construction. More generally, what is at issue is the very idea of “the social”. Within the framework of the general problem of “the social”, we want to open a discussion of boundaries and margins in mathematics and mathematics education. By theorizing the divisions of purity and danger, we will be able to better understand the intersection of logic, mathematics, and thinking with gender, race, and class, and morals, ethics, and values in the classroom. The process of transforming the sociology of mathematics and the sociology of mind into pedagogical tools for mathematics educators and philosophers of education has already begun. One of the tasks before us is the development of a more profound and at the same time more practical grasp of “the social”. Our objective in this paper is to move ourselves and our readers in the direction of just such a grasp of the social.     

Determinism, Indeterminism and Mathematics

The aim of this paper is to argue that very often one is not able to distinguish between deterministic processes governed by some dynamical systems and stochastic processes. This revised version was published online in August 2006 with corrections to the Cover Date.     

先秦数学史研究的新进展--评邹大海著《中国数学的兴起与先秦数学》

20世纪60年代初,中国科学院自然科学史研究室(今自然科学史研究所前身)数学史组在钱宝琮主持下完成<中国数学史>[1]后,开始实施了一个断代专题研究的宏大计划:把中国数学史分几个断代进行更细致而深入的研究,以便将来在更高层次上编写一部中国数学史[2].钱宝琮在世时组织了宋元时期的断代研究并出版了一部<宋元数学史论文集>[3]."文革"使这个计划中断."文革"后,顺着他的这一思路,自然科学史研究所对于两汉魏晋和明清的断代研究也相继展开,并获得了很大进展,在学术杂志上发表一系列论文,并出版了一部论文集<明清数学史论文集>[2]和专著<〈九章算术〉汇校本>[4]、<古代世界数学泰斗刘徽>[5]等.近年出版的邹大海所著的<中国数学的兴起与先秦数学>(以下简称<先秦数学>)则是一项先秦数学的断代研究.     

Mathematics,Philosophical and Semantic Considerations on Infinity (II): Dialectical Vision

Human language has the characteristic of being open and in some cases polysemic. The word “infinite” is used often in common speech and more frequently in literary language, but rarely with its precise meaning. In this way the concepts can be used in a vague way but an argument can still be structured so that the central idea is understood and is shared with to the partners. At the same time no precise definition is given to the concepts used and each partner makes his own reading of the text based on previous experience and cultural background. In a language dictionary the first meaning of “infinite” agrees with the etymology: what has no end. We apply the word infinite most often and incorrectly as a synonym for “very large” or something that we do not perceive its completion. In this context, the infinite mentioned in dictionaries refers to the idea or notion of the “immeasurably large” although this is open to what the individual’s means by “immeasurably great.” Based on this linguistic imprecision, the authors present a non Cantorian theory of the potential and actual infinite. For this we have introduced a new concept: the homogon that is the whole set that does not fall within the definition of sets established by Cantor.     

2010年数理和地学领域国家重点实验室评估结果

2010年科学技术部组织了对数理、地学领域国家重点实验室的评估。数理领域参评实验室11个;地学领域参评实验室37个。另外,数理领域的强场激光物理国家重点实验室因此前连续2次评估优秀而申请此次免评,按照《国家重点实验室评估规则》的有关规定,其评估结果视为良好。最终评估结果为：数理领域有3个实验室评为优秀类实验室,有8个实验室评为良好类实验室,     

关于当代生命科学研究对象的划界、分析与表征的讨论

本文讨论了当代生命科学研究对象的划界、分析与表征的问题,首先围绕三个分主题对国际生物学的历史、哲学和社会学研究协会(ISHPSSB)2011年双年会的相关报告进行介绍并评论:关于基因组学与后基因组学的本体论和认识论问题;关于自然选择理论的扩展性的研究;对于生物学个体性概念的讨论,然后介绍了作者在共生语境下对生物学个体概念的研究进展。文章指出,对同一对象的不同表征模式以及对同一概念的不同分析方式,体现了两种科学传统在当代生命科学中的冲突与交汇;系统生物学力图综合不同研究范式,整合不同生命组织的层次,对其独特的研究方法、概念体系进行分析和讨论,将是未来生物学哲学的热门研究课题。     

Objects and Processes in Mathematical Practice

In this paper it is argued that the fundamental difference of the formal and the informal position in the philosophy of mathematics results from the collision of an object and a process centric perspective towards mathematics. This collision can be overcome by means of dialectical analysis, which shows that both perspectives essentially depend on each other. This is illustrated by the example of mathematical proof and its formal and informal nature. A short overview of the employed materialist dialectical approach is given that rationalises mathematical development as a process of model production. It aims at placing more emphasis on the application aspects of mathematical results. Moreover, it is shown how such production realises subjective capacities as well as objective conditions, where the latter are mediated by mathematical formalism. The approach is further sustained by Polanyi’s theory of problem solving and Stegmaier’s philosophy of orientation. In particular, the tool and application perspective illuminates which role computer-based proofs can play in mathematics.     

经济学与数学及经济学应用数学问题的分析

自从三百年前英国古典经济学家威廉.配第在经济研究中运用算术方法发轫,到今天以数学为工具的经济学研究领域的不断拓展,数学方法的应用在现代经济学研究中可以说无所不在。与此同时,也导致了经济学的数学化倾向越来越严重。这使得经济学研究对数学的过分依赖,连同经济学中数学方法的错误使用或滥用,在某种程度上,已经使经济学作为一门研究人类经济行为和经济现象的学问远离了客观经济实际。由此,研究和分析经济学如何正确的应用数学,经济研究中如何辩证地看待经济学与数学二者的关系,就显得尤为重要了。     

邹腾:19世纪数学史家、丹麦数学的先驱者

作为19世纪法国几何学泰斗沙勒最好和最忠实的弟子,丹麦数学家邹腾继承了沙勒的有关理论,进一步发展了枚举几何学。在数学史方面,他开创了古希腊数学史研究传统,成为19世纪末最重要的数学史家之一。邹腾为丹麦数学登上国际舞台做出了杰出的贡献,对丹麦大学数学教育产生了深远的影响,成为丹麦现代数学的先驱者。对于后人而言,邹腾的学术成就和人格情操都是一笔宝贵的精神财富。     

Perceiving the Infinite and the Infinitesimal World: Unveiling and Optical Diagrams in Mathematics

Many important concepts of the calculus are difficult to grasp, and they may appear epistemologically unjustified. For example, how does a real function appear in “small” neighborhoods of its points? How does it appear at infinity? Diagrams allow us to overcome the difficulty in constructing representations of mathematical critical situations and objects. For example, they actually reveal the behavior of a real function not “close to” a point (as in the standard limit theory) but “in” the point. We are interested in our research in the diagrams which play an optical role –microscopes and “microscopes within microscopes”, telescopes, windows, a mirror role (to externalize rough mental models), and an unveiling role (to help create new and interesting mathematical concepts, theories, and structures). In this paper we describe some examples of optical diagrams as a particular kind of epistemic mediator able to perform the explanatory abductive task of providing a better understanding of the calculus, through a non-standard model of analysis. We also maintain they can be used in many other different epistemological and cognitive situations.     

Mathematics and the Mind of God

Mathematics and the Mind of God is the synopsis of a leture held at a symposium under this title at the Free University of Amsterdam in 1995. It takes a critical position with respect to the suggestion that there is a shortcut from the exact sciences to theology. It is true that mathematics is the pure form in which the exactness of these sciences can be expressed. The fundamental principle of it, however, the structurability of our world of experience, is not expressible in mathematical form. It belongs to the subject matter of metaphysics, in the sense of rational relation of principles. Mystical experience and theological reflection are even beyond the realm of metaphysics, because they claim to transcend natural human reason. Jumping directly from science to theology therefore gives rise to many misunderstandings which are detrimental to both.     

On the Construction of Mental Objects in Third and in First Persons

This paper deals with some formal properties of objects that are supposed to be internal to persons, that is, mental structures and mental functions. Depending on the ways of talking about these internal objects, they will appear different. Two types of discourse will be presented, to be called the realist and the nominalist discourses, and for eachdiscourse I will focus upon the construction of `self'.The realist discourse assumes an identity between the person and his construction of himself. I will illustrate this discourse in terms of Descartes' ideas on himself as a `thinking substance'. The nominalist discourse assumes an impossibility to attain this identity, and instead to imply a complementarity between the person and his self-construction. I will illustrate this discourse in terms of the problems both William James and Sartre discerned when a conscious person chases after his own consciousness (termed `judging thought' and `pour-soi' respectively).     

DNA计算机:数学与生命的交融

本文在简单介绍了ＤＮＡ计算机理论的基础上,论述了由ＤＡＮ计算机所引发的计算方式的变革和生命观的变革,并最后指出,或许整个世界的进化过程就是一个计算复杂性不断增长的过程。     

数学与诗歌:历史寻踪

数学与诗歌在我们今天看来分别属于斯诺所说的两种文化；但从历史上看，两者之间存在着千丝万缕的联系。本文基于有关数学与诗歌的文献，从几个方面概述了这种联系，试图说明：两种文化的鸿沟并非不可逾越。     

雷科德:英国第一个数学教育家

16世纪英国数学家雷科德，是一位百科全书式的学者，生缝乱世、命运多舛，且仕途中还沾上了难以洗刷的污点。他用英文撰写了算术、几何、天文学和代数学著作，后三者均为英语世界中的第一部；而第一部则对英国的数学教育产生了深远的影响。他是最早将哥白尼日心说传入英国的天文学家之一；他持有科学进步观，他的数学观在文艺复兴期间起着承前启后的作用；他发明的等号，今天全世界人人都在使用。他创用对话形式撰写教材，创用英语数学术语；他认识到死记硬背学习方式的局限，他认为理解可以发生在掌握技能之后；他强调说理而不迷信权威。他筚路蓝缕，传播学术，成为英国历史上第一位数学教育家。