Will the digital computer transform classical mathematics?
Will the digital computer transform classical mathematics?
复制标题
数字计算机会改变经典数学吗？
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
B. Rotman
中科院分区：
文献类型：
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作者：
B. Rotman
数学和机器相互影响了几千年。数字计算机的出现引入了一种强有力的新元素，有望改变它们之间的关系。本文概述了数字计算机对数学的影响，已经广泛存在，很可能是激进和深远的。为了阐明这一观点，我们引入了一个抽象的数学模型，该模型基于三个参与者，其中一个“代理”对应于计算机执行的功能。该模型用于构造两种类型的转换。第一个是实用的，涉及数字方法带来的各种数学领域的内容和研究方法的改变和逐步殖民化。第二个问题是概念性的，涉及经典数学和物理学（连续性、实数、渐近定义）中的无限与数字计算过程固有的真实和物质极限之间的根本对立。一个经典数学和计算机科学交叉的例子，P = NP问题，根据后一个问题进行了分析。
Mathematics and machines have influenced each other for millennia. The advent of the digital computer introduced a powerfully new element that promises to transform the relation between them. This paper outlines the thesis that the effect of the digital computer on mathematics, already widespread, is likely to be radical and far–reaching. To articulate this claim, an abstract model of doing mathematics is introduced based on a triad of actors of which one, the ‘agent’, corresponds to the function performed by the computer. The model is used to frame two sorts of transformation. The first is pragmatic and involves the alterations and progressive colonization of the content and methods of enquiry of various mathematical fields brought about by digital methods. The second is conceptual and concerns a fundamental antagonism between the infinity enshrined in classical mathematics and physics (continuity, real numbers, asymptotic definitions) and the inherently real and material limit of processes associated with digital computation. An example which lies in the intersection of classical mathematics and computer science, the P = NP problem, is analysed in the light of this latter issue.