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數学是什么?恩格斯曾經極其精闢的說过:“純粹數学的对象是現实世界的空間形式及數量關係,”又说:“我們的幾何以空間關係为出發点,而我們的算術和代數則以數量为出發點。”現在距离恩格斯時代已有好幾十年,近幾十年來數学方面又已有了非常偉大迅速的發展,我們所認識的現实世界的空間形式和數量關係日益包括更多更丰富,但是恩格斯的話还是正確的。 數學既然是研究現实世界的空間形式及數量關係,那末它的各科之間是不是彼此孤立的呢?要回答这个問題我們首先应該看一看現实世界的空間形式及數量關係的本身是否孤立的,斯大林曾經說过:“与形而上学相反,辯証法不是把自然界看作什么彼此隔离,彼此孤立,彼此不相依賴的各个对象或各个現象底偶然堆
What is mathematics? Engels once said extremely brilliantly: “The object of pure mathematics is the spatial form and quantity relationship of the real world,” said again: “Our geometry starts with the spatial relationship, and our arithmetic and Algebra is based on quantity. "Now it has been several decades since the Engels era. In recent decades, mathematics has developed very rapidly. The spatial form and quantity of the real world that we know have become increasingly important. Including more and more abundant, but Engels’s words are still correct. Since mathematics is the study of the spatial form and quantity relationship of the real world, isn’t it the isolation between the various disciplines? To answer this question, we should first look at the spatial form of the real world and the quantitative relationship itself. Whether or not they are isolated, Stalin once said: “In contrast to metaphysics, dialectics does not regard the natural world as something that is isolated from each other, isolated from each other, and each object or phenomenon that is not dependent on each other is accidentally piled up.