[主持人按:彭加勒说过“数学的真理是用一连串无懈可击的推理,从少数一目了然的命题推演出来的”.数学家们的喜好是要把这样的推演和谐地一直扩展到极致,数学史反映的发展历程可以为证.和谐扩展也是数学学科知识展开的主要方式与准则,常见的有三种类型:由特殊扩展到一般;由一般 [Moderator: According to Poincare, “The truth of mathematics is a series of impeccable inferences, drawn from a handful of obvious propositions.” The preference of mathematicians is to consistently extend this deduction to the extreme, mathematics. The history of development reflected by history can be used as evidence. The extension of harmony is also the main method and criterion for the development of knowledge in mathematics. There are three common types: expansion from special to general, and general