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CHAPTER 1. THE BASICS
1.1 Wha t I t I s Al l Abou t
In orde r t o writ e effectivel y an d well , you mus t hav e somethin g t o say .
This sounds trite, but it is the single most importan t fac t abou t writing .
In orde r t o writ e effectivel y an d well , yo u als o mus t hav e a n audience .
And yo u mus t know consciously wh o tha t audienc e is . Muc h o f th e
bad writin g tha t exist s i s performed b y th e autho r o f a researc h pape r
who thinks that al l his readers are Henri Poincare, or by the autho r o f a
textbook wh o does not see m to realize that hi s readers will be students .
Good writin g require s a certai n confidence . Yo u mus t b e confiden t
that yo u have something to say, and that thi s something is worth saying.
But yo u also must hav e the confidence t o kno w that "M y audience i s X
and I wil l writ e fo r X." Man y a write r o f a mathematica l pape r seem s
to b e writin g primaril y t o convinc e himsel f tha t hi s theorem i s correct ,
but no t a s a n effor t t o communicate . Suc h a n autho r i s embarrasse d
to explai n anything , an d hide s behin d th e details . Man y a textboo k
author seem s t o b e embarrasse d t o spea k t o th e studen t i n languag e
that th e studen t wil l apprehend . Suc h a n autho r instea d find s himsel f
making excuse s t o th e instructo r (wh o either wil l not rea d th e book , o r
will flip throug h i t impatientl y an d entirel y mis s th e author' s efforts) .
Imagine penning a poem to your one true love, all the while thinkin g
"What woul d m y Englis h teache r think? " o r "Wha t woul d m y pasto r
think?" o r "Wha t woul d m y mothe r think? " Hav e the courag e o f you r
convictions. Spea k t o tha t perso n o r t o thos e peopl e who m yo u ar e
genuinely tryin g t o reach . Kno w wha t i t i s tha t yo u wan t t o sa y an d
then sa y it .
For a mathematician , th e mos t importan t writin g i s th e writin g o f
a researc h paper . Yo u hav e prove d a nic e theorem , perhap s a grea t
theorem. Yo u certainl y hav e somethin g t o say . Yo u als o kno w exactl y
who your audience is: other research mathematicians who are intereste d
in you r fiel d o f study . Thu s tw o o f th e bigges t problem s fo r a write r
are alread y solved . Th e issu e that remain s i s how to sa y it . Remembe r
that i f you pen a love letter t o yourself, the n i t wil l have both th e goo d
features an d th e ba d feature s o f suc h a n exercise : i t wil l exhibi t bot h
passion an d fervor , bu t i t wil l ten d t o exclud e th e res t o f th e world .
What d o thes e remark s mea n i n practice ? I n particular , the y mea n
that a s yo u writ e yo u mus t thin k o f you r reader—no t yourself . Yo u
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