Preface
The pas t fifty year s hav e no t see n a s much emphasi s o n th e qualit y
of mathematical writin g as perhaps on e would wish. Becaus e of compe-
tition fo r grants an d othe r accolades , we hasten ou r work into print. A n
obituary fo r Han s Heilbron n (1908-1975 ) asserte d that , afte r h e wrot e
(by hand ) a draf t o f a paper , h e woul d pu t i t o n th e shel f fo r on e year .
Then h e woul d com e bac k t o i t wit h fres h eyes , rea d i t critically , an d
rewrite it . I n effect , afte r a year's time , Heilbron n wa s readin g hi s ow n
work a s though h e were unfamilia r wit h i t an d ha d t o understan d eac h
point fro m first principles . I t i s perhaps wort h dwellin g on this exercis e
to se e wha t w e might lear n fro m it .
There is no feeling quite like that whic h comes after yo u have proved
a goo d theorem , o r solve d a proble m tha t yo u hav e worke d o n fo r a
long time . Drive n b y th e hea t o f passion , th e word s burs t fort h fro m
your pen , th e definition s ge t punche d int o shape , th e proof s ar e buil t
and ben t an d patche d an d shore d up , an d ou t goe s tha t preprin t t o
an appreciativ e audience . Th e whol e pape r sparkles—bot h th e correc t
parts an d th e incorrec t parts . A frien d o f mine , wh o solve d a proble m
after workin g o n i t t o th e exclusio n o f al l els e fo r ove r fifteen years ,
used t o ris e u p i n th e middl e o f th e nigh t jus t t o cares s hi s manuscrip t
lovingly.
In circumstance s lik e these , yo u find i t virtuall y impossibl e t o dis -
tance yoursel f fro m th e material . Everythin g i s emblazone d i n you r
own min d an d i s crysta l clear ; yo u ar e unabl e t o tak e th e par t o f th e
uninitiated reader . Yo u ar e tor n betwee n th e desir e (expeditiously ) t o
record an d validat e you r ideas , an d th e desir e t o communicate .
In today' s competitiv e world , yo u probabl y d o no t fee l tha t yo u
have th e luxur y o f settin g a ne w pape r asid e fo r a year . Th e pape r
could b e scooped ; th e subjec t coul d tak e a differen t directio n an d leav e
your grea t advanc e i n th e dust ; th e NS F migh t cance l you r grant ; th e
XI
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