数学是以抽象性为其一突出特点的一门自然科学。它的这一特点往往被唯心论者誇大并利用来作为辩护其荒谬学说的根据。远自古希腊的毕达哥拉和柏拉图,直到近代的马赫主义者、逻辑实证论者,等等,莫不如此。在资本主义国家中,很多数学家受了环境的影响,不免跟随着唯心论哲学家们歪曲他们自己的科学贡献,提出错误的哲学看法。例如近代以及当代的一些在数学上有巨大贡献的学者,昂利·邦加莱、D.希尔柏特、L.E.J.布劳威尔、赫尔曼·外尔等,都不免如此。於是自19世纪末叶以来,在数学的哲学问题上产生了种种唯心论的流派:逻辑主义、直觉主义、形式主义,以及其它。在我国数学界,还没有人很明确地宣称自己属于上述哪一派别,还很少数学家 Mathematics is a natural science with its outstanding features as abstractness. This characteristic of it is often exaggerated and used by idealists as the basis for justifying its absurd doctrine. Far from Pythagoras and Plato in ancient Greece until the modern Machism, Logical Positivists, and so on. In the capitalist countries, many mathematicians are affected by the environment, inevitably follow the idealist philosophers distort their own scientific contribution, put forward the wrong philosophical view. For example, modern and contemporary scholars who have made great contributions in mathematics, such as Ngongli Bongalai, D. Hilbert, L.E.J. Brouwer, Herman Vail, and so on, are all the same. Since the end of the 19th century, therefore, various schools of idealism have emerged in the philosophy of mathematics: logicism, intuitionism, formalism, and others. No one in the mathematics community in our country has made it clear that he belongs to any of the above factions, and few mathematicians