As Round as a Pearl and as Polished as Jade
Prologue. There are some gaps and loopholes in [Wat1, p.455, l.22-l.32;
p.484, l.1-l.29]. I am disappointed with the authors’ writing. In contrast,
[Sak1, chap. VIII, §11, §12 & §13] gives an excellent presentation on the
modular function J(t) and amends the above
shortcomings: [Sak1, chap. VIII, §11] provides clear definitions of automorphic
functions and modular functions; [Sak1, p.397, 2°]
fills the gap in [Wat1, p.484, §21.712]; [Sak1, p.398, l.1-p.399, l.4] closes
the loopholes of the argument given in [Wat1, p.484, §21.712]. [Sak1, chap.
VIII, §11, §12 & §13] is outstanding indeed. I would like to write a poem using
it as an example to encourage authors of mathematical books to improve their
It is a pity if one has good ideas,
But others have difficulty understanding them.
Guo-fan Zeng 1 wrote to his son,
"Essay writing and calligraphy should be as round as a pearl
And as polished as jade."
The same principle applies to book writing in mathematics.
The goal of book writing is to help readers master the subject.
An author should not use a terminology before its meaning is defined,
Should not give a vague proof with gaps and loopholes,
And should not use a reference unless it is necessary.
Quoting many references does not prove
That the author has digested all the material in them.
Readers do not like to run around searching for references.
Even if they find the reference books,
They may have a hard time jumping into the middle of a book.
Readers would be appreciative
If the author can layout key ideas systematically and effectively,
Formulate the statements in his or her own words,
And organize the material in his or her own style.
Guo-fan Zeng (1811-1872)
Zi-cheng, Bo-han, and Di-sheng were Guo-fan Zeng’s other first names. He was
a native of Xiang-xiang City in Hunan Province during the Qing dynasty. In 1838,
he passed the Advanced Exam. Later, he was appointed a member of the Royal
Academy. In 1849, he was made Senior Deputy Secretary of the Board of Rites. In
1851, he returned home to attend his mother’s funeral. At this time the Tai-ping
Rebellion [Peaceful and Heavenly Kingdom] captured many cities in Hunan
Province. In the capacity of Military Examiner, Zeng helped the Governor of
Hunan to raise the Xiang [Hunan] Army to fight against the rebellion. He learned
military affairs quickly and appointed many talented generals. He military
strategy was to be cautious and certain. He enforced his rules strictly. In
1860, he was made Joint Governor of Jiangxi, Anhui, and Jiangsu Provinces. In
1864, Zeng’s troops crushed the rebellion by capturing their headquarters, Nan-jing
City. At the peak of his career, he was Yi (persevering)-yong (brave) Count of
the First Class. Guo-fan Zeng died in 1872. Due to his achievements in integrity
and literature, Emperor Mu-zong gave him posthumous name, Wen (literature)-zheng
Guo-fan Zeng was humble, honest, and diligent. He earnestly practiced
applying Confucian ideals to his daily life. He was wise, but appeared dumb.
These noble characteristics greatly increased his chances of success. His
literary legacy was his letters to his extended family. The Letters that Guo-fan
Zeng Wrote to His Extended Family (4 volumes, Beijing: The Contemporary
World Press, 2008) collects 1,460 of his letters.