非歐幾何的發現解决了幾何学中兩千多年的一个基本問題,大大地擴展了幾何学研究的对象,在根本上改变了人們对幾何学的看法,開創了幾何学的一个新時代,第一个發現非歐幾何的罗巴切夫斯基非常恰当地被称为幾何学中的哥白尼。非歐幾何的創立在整个數学的發展上,特别是在數学基礎的問題上起着深远的决定性作用。但是,單从幾何学和數学本身去說明非歐幾何的歷史意义是很不够的。因为,非歐幾何的影响远不限於幾何学和數学。非歐幾何的問題,虽然是从幾何学中提出的,实际上却牽涉到哲学的基本問題。非歐幾何的創立打破了兩千多年的唯心的形而上学的空間观念,把幾何学从傳統的哲学束縛下解放出來,因而有着非常重要的認識論上的意义,非歐幾何的歷史是唯物主义和唯心主义在幾何学中的一段鬥爭 The discovery of non-Euclidean geometry solves a basic problem of more than two thousand years in geometry, greatly expands the object of geometric research, fundamentally changes people’s view of geometry and opens up a new era of geometry, The first one that discovered non-Euclidean geometry, Lobachevsky, was aptly called Copernicus in geometry. The founding of non-Euclidean geometry plays a profound and decisive role in the development of mathematics as a whole, especially on the basis of mathematics. However, it is not enough to illustrate the historical significance of non-Euclidean geometry solely from geometry and mathematics. Because the influence of non-Euclidean geometry is far from being limited to geometry and mathematics. The problem of non-Euclidean geometry, though raised from geometry, actually involves the basic philosophical problems. The establishment of non-Euclidean geometry breaks the 2,000 years of idealistic metaphysical space concept and liberates geometry from the traditional philosophy. Therefore, it has very important epistemological significance. The history of non-Euclidean geometry is materialism and Idealism in the geometry of a fight