西南联大数学名师的“治学经验之谈”及启示

Some Enlightening Remarks on Mathematics-Studying Talked by Eminent Teachers of SWAU in 1940's

西南联大是一所名师云集的高等学府,为我国培育出了许多英才,被海内外人士喻为“藏龙卧虎”之地.西南联大数学系的“数学三杰”——华罗庚、许宝禄、陈省身3位教授,以及后起之秀钟开莱先生均在海内外享有盛誉.华罗庚先生讲课的主要特点是,他总是尽力把题材化繁为简,化难为易;强调搞学问必须有“看家工夫”;强调“读书要从薄到厚,再从厚到薄”.陈省身先生强调“数学为的是简单性”.许宝禄和钟开莱先生在教学中特别强调要“直观地理解数学”,主张要把数学定理及其证明的“原始思想”告知学生.所获得的教益:认识到追求简单规律的重要性,并以此作为研究数学的目标和兴趣出发点;学会使用直观、联想去理解数学并籍此去发现问题,提出可以研究的题材;学会了重视“特例分析”、数学概括和抽象方法;向华罗庚、许宝禄先生学到了“不怕计算”和“乐于计算”的习惯并乐于从计算中发现规律和提炼一般性公式.

The South-West Associated University (SWAU) was a union of Peking University, Tsing-Hua University and Nankai University established in Kunming during the years 1938-1946. Here expounded by the author (an old student of SWAU with his recalling) were several instructive and enlightening view-points concerning mathematics learning and research that had been talked and stressed by the learned professors and teachers Hua Loo-Keng (1910—1985), Hsu Pao-Lu (1910—1970), Chern Shiing-Shen (1911—) and Chung Kai-Lai (1917—). A remarkable view-point in common was that 'mathematics is for simplicity'.