Science. 1966 Oct 21;154(3747):357-62. doi: 10.1126/science.154.3747.357.
Let me emphasize the point I have been trying to make. The mathematician's playing with the roots of equations, a play which had no practical motivations and almost no possibilities of practical application, led to the recognition of the importance of symmetry and groups. The study of theory of groups led to mathematical discoveries in geometry and differential equations, and finally to prediction of the existence of a new elementary particle. Surely a surprising outcome for the ivory-tower speculations of an impractical mathematician! Despite my professional bias, I must acknowledge that the importance of symmetry was recognized before mathematicians invented the theory of groups. In 1794 William Blake wrote: Tiger, Tiger, burning bright In the forests of the night, What immortal hand or eye Could frame thy fearful symmetry? However, to the mathematicians must be given the credit of recognizing that, to understand symmetry, you must study the theory of groups. I can now answer my original question, What are mathematicians doing? They are trying to make precise the intuitions of poets.
让我再次强调一下我一直在试图说明的观点。数学家对方程根的把玩——这种纯粹出于理论动机、几乎没有任何实际应用可能的游戏，导致了人们对对称性和群的重要性的认识。群论的研究导致了几何学和微分方程领域的数学发现，并最终预测到了一种新基本粒子的存在。对于一个不切实际的数学家在象牙塔里的推测来说，这无疑是一个令人惊讶的结果！尽管我有职业偏见，但我必须承认，对称性的重要性在数学家发明群论之前就已经被认识到了。1794 年，威廉·布莱克写道：“老虎！老虎！火一样辉煌，在黑夜的森林中，什么样的不朽的手或眼睛，能制定你的可怕的匀称？”然而，我们必须承认，正是数学家们认识到，要理解对称性，你必须研究群论。我现在可以回答我最初的问题了，“数学家们在做什么？”他们试图使诗人的直觉精确化。
