4
CHAPTER 1. THE BASICS
explain. I t enable s yo u t o formulat e th e explanatio n o f a n idea , o r th e
clarification o f a difficul t point .
I cannot repea t to o often thi s fundamenta l dictum : hav e somethin g
to sa y an d kno w wha t i t is ; kno w why yo u ar e sayin g it ; finally, kno w
to who m yo u ar e sayin g it , an d kee p tha t audienc e alway s i n mind .
1.3 Writin g an d Though t
The ability to think clearl y and the ability to write clearly are inextrica -
bly linked . I f you canno t articulat e a thought, formulat e a n argument ,
marshal data , assimilat e ideas , organiz e a thesis , the n yo u wil l no t b e
an effectiv e writer . B y th e sam e token , yo u ca n us e you r writin g a s
a metho d o f developin g an d honin g you r thought s (se e [Hig ] fo r a n
insightful discussio n o f this concept) .
We al l kno w tha t on e wa y t o wor k ou t ou r thought s i s t o engag e
in a n animate d discussio n wit h someon e who m w e respect . Bu t yo u
can instead , a l a Descartes , hav e tha t discussio n wit h yourself . An d a
useful wa y to do so is by writing. Whe n I want t o work out m y thought s
on som e topic—teaching reform , o r th e fundin g o f mathematics, o r th e
directions tha t futur e researc h i n severa l comple x variable s ough t t o
take, o r m y ne w idea s abou t domain s wit h noncompac t automorphis m
group—I ofte n find i t usefu l t o writ e a littl e essa y o n th e subject . Fo r
writing forces m e to express my ideas clearly and i n the prope r order , t o
fill in logica l gaps , t o sor t ou t hypothese s fro m blin d assumption s fro m
conclusions, an d t o mak e m y poin t forcefull y an d clearly . Sometime s
I sho w th e resultin g essay t o friend s an d colleagues , an d sometime s I
try t o publis h it . But , jus t a s often , I file it awa y o n m y har d dis c an d
forget i t unti l I hav e futur e nee d t o refe r t o it .
The writin g o f researc h leve l mathematics i s a mor e forma l proces s
than tha t describe d i n th e las t paragraph , bu t i t ca n serv e yo u just a s
well. Whe n yo u writ e u p you r lates t idea s fo r disseminatio n an d pub -
lication, the n yo u mus t finally fac e th e music . Tha t "obviou s lemma "
must no w b e treated ; th e cas e that yo u di d no t reall y wan t t o conside r
must b e dispatched . Th e idea s mus t b e pu t i n logica l orde r an d th e
chain o f reasonin g forge d an d fixed. I t ca n b e a rea l pleasur e t o craf t
your lates t burs t o f creativit y int o a compellin g flood o f logi c an d cal -
Previous Page Next Page