I am indebted for many valuable criticisms to Professor C. D. Broad and Dr C. P. Snow, each of whom read my original manuscript. I have incorporated the substance of nearly all of their suggestions in my text, and have so removed a good many crudities and obscurities.

In one case I have dealt with them differently. My §28 is based on a short article which I contributed to Eureka (the journal of the Cambridge Archimedean Society) early in the year, and I found it impossible to remodel what I had written so recently and with so much care. Also, if I had tried to meet such important criticisms seriously, I should have had to expand this section so much as to destroy the whole balance of my essay. I have therefore left it unaltered, but have added a short statement of the chief points made by my critics in a note at the end.

G. H. H

18 July 1940

我非常感谢查理 • 布罗德 1 教授和查尔斯 • 斯诺 2 博士对本书提出了许多有价值的批评意见,他们都读过我的手稿。他们提出的几乎所有建议的精髓都已被我采纳,我借此改正了书中许多经不起推敲或是令人费解的地方。

1Charlie Dunbar Broad(1887.12.30—1971.03.11),英国科学哲学家、作家。

2Charles Percy Snow(1905.10.15—1980.07.01),英国物理化学家、小说家,哈代的朋友。

在处理那些建议时,我对书中的第 28 节采取了不同的做法,它是基于我年初发表在《顿悟》杂志(剑桥阿基米德协会的期刊)上的一篇短文 3 写成的。我发现自己几乎没有办法去改写这篇文章,它是我精心写就的新作。倘若我认真回复那些重要批评,就会把那一节无限扩写,乃至于会破坏随笔的总体平衡。因此,我保留了第 28 节的原貌,只在注记中补充了一小段文字,探讨他们提出的主要观点。

3指《战争时代的数学》(Mathematics in war-time)。


戈弗雷 • 哈代

1940 年 7 月 18 日