viii FOREWOR D
turns ou t t o b e th e sam e a s a gam e playe d wit h a singl e paw n o n a chessboard .
This become s a lesso n fo r sevent h grader s i n restatin g problems , the n offer s a n
introduction t o the nature o f isomorphism fo r th e hig h school student. Th e Pigeo n
Hole Principle , amon g th e simples t ye t mos t profoun d mathematic s ha s t o offer ,
becomes a tooi fo r proo f i n number theor y an d geometry .
Yet the tone of the work remains light. Th e chapter o n combinatorics doe s no t
require a n understandin g o f generating function s o r mathematica l induction . Th e
problems i n grap h theory , too , remai n o n th e surfac e o f thi s importan t branc h o f
mathematics. Th e approac h t o eac h topi c lend s itsel f t o min d play , no t weight y
reflection. An d ye t th e wor k manage s t o strik e som e deep notes .
It i s thi s qualit y o f th e wor k whic h th e mathematician s o f th e forme r Sovie t
Union develope d t o a hig h art . Th e expositio n o f mathematics , an d no t jus t it s
development, becam e a par t o f th e Russia n mathematician' s work . Thi s boo k i s
thus par t o f a literar y genr e whic h remain s largel y undevelope d i n th e Englis h
language.
Mark Saul , Ph.D .
Bronxville School s
Bronxville, Ne w Yor k
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