直觉与潜意识（二） (6-1)

在15天的时间里，我努力证明不可能有任何类似于我后来称之为 Fuchsian 函数的函数。那时我很无知；每天我坐在工作桌前，待上一两个小时，尝试各种组合，但都没有结果。一天晚上，与我的平时习惯相反，我喝了黑咖啡，这让我无法入睡。想法成群涌现；我感觉到它们相互碰撞，直到成对地相互连锁，可以说，形成一个稳定的组合。到第二天早上，我已经确定了一类 Fuchsian 函数的存在性，它们来自超几何级数；我只需写出结果，这只花了几个小时。

Then I wanted to represent these functions by the quotient of two series; this idea was perfectly conscious and deliberate, the analogy with elliptic functions guided me. I asked myself what properties these series must have if they existed, and I succeeded without difficulty in forming the series I have called theta-Fuchsian.

随后，我想用两个级数的商来表示这些函数；这个想法是完全有意识，且深思熟虑的，与椭圆函数的类比指导着我。我问自己，如果这些级数存在，它们一定具有什么性质，我毫不费力地成功构造出了我称之为 theta-Fuchsian 的级数。

Just at this time I left Caen, where I was then living, to go on a geologic excursion under the auspices of the school of mines. The changes of travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus to go some place or other. At the moment when I put my foot on the step the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidean geometry. I did not verify the idea; I should not have had time, as, upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty. On my return to Caen, for conscience's sake I verified the result at my leisure.

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