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The Russian mathematician P.S. Novikov had announced42 that the 'word problem' for groups was indeed unsolvable by any definite method;
俄国数学家诺维科夫曾经宣布，群的字问题不存在任何确定的解法。
Alan's article explained this and tied it in with some questions in topology, showing that the problem of deciding whether some knot was the same as some other knot was essentially a 'word problem' of this kind.
图灵在文章中详细地解释了这个结论，并把它和拓扑学联系起来，表明某些拓扑学问题本质上就是群的字问题。
It was up to date, and looked forward to the complete proof of the Russian result becoming available.
图灵的这篇文章，使俄国数学家的结论得到了完整证明。
He was interested in solving problems up to the end。
这是一项重要进步，图灵总是喜欢把问题解决到底。
A last letter of May 1954 to Robin discussed certain ideas of Robin's for 'getting round the Godel argument' but ended with:
1954年5月，在图灵写给罗宾的最后一封信中，图灵评论了罗宾的一些关于哥德尔定理的想法，并在结尾写道：
'Looked at the rainbow problem again. Can do it rather successfully for sound, but total failure for electricity. Love, Alan.'
“再想想那道彩虹吧，用声学可以解释，用电学却不行。爱着你的，图灵。”
When out walking together in Charnwood Forest, near Leicester, they had seen an unusual double rainbow, a phenomenon that Alan insisted on analysing. There had to be a reason for it.
有一次，他们在莱斯特附近的树林里散步，遇到了一道不同寻常的双层彩虹。图灵后来花了很多时间分析这道彩虹，他一定要找到其中的原因。
