▁group ▁over ▁the ▁rational ▁numbers ). ▁B aily ▁and ▁Bor el ▁built ▁on ▁the ▁work ▁of ▁Ich ir ō ▁S ata ke ▁and ▁others . ▁ ▁B aily ▁was ▁a ▁winner ▁of ▁the ▁ 1 9 5 2 ▁Put nam ▁Mathemat ics ▁Compet ition . ▁He ▁studied ▁at ▁the ▁Massachusetts ▁Institute ▁of ▁Technology ▁( MIT ), ▁receiving ▁a ▁Bach elor ▁of ▁Science ▁in ▁Mathemat ics ▁in ▁ 1 9 5 2 , ▁after ▁which ▁he ▁attended ▁Pr inc eton ▁University , ▁receiving ▁a ▁Masters ▁in ▁ 1 9 5 3 ▁and ▁a ▁Ph . D . ▁in ▁Mathemat ics ▁in ▁ 1 9 5 5 ▁under ▁the ▁direction ▁of ▁his ▁th esis ▁ad visor ▁K uni h iko ▁K od ai ra ▁( On ▁the ▁Qu ot ient ▁of ▁a ▁Complex ▁Anal yt ic ▁Man if old ▁by ▁a ▁Dis continu ous ▁Group ▁of ▁Complex ▁Anal yt ic ▁Self - Hom omorph isms ). ▁Sub sequently , ▁he ▁was ▁an ▁instruct or ▁at ▁Pr inc eton ▁and ▁then ▁M IT . ▁In ▁ 1 9 5 7 ▁he ▁worked ▁as ▁a ▁math ematic ian ▁at ▁Bell ▁Labor ator ies . ▁In ▁ 1 9 5 7 , ▁he ▁was ▁appointed ▁Ass istant ▁Professor ▁and ▁subsequently ▁promoted ▁to ▁Professor ▁in ▁ 1 9 6 3 ▁at ▁the ▁University ▁of ▁Chicago . ▁He ▁became ▁a ▁Professor ▁Emer it us ▁at ▁the ▁University ▁of ▁Chicago ▁in ▁ 2 0 0 5 . ▁ ▁He ▁was ▁a ▁member ▁of ▁the ▁American ▁Mathemat ical ▁Society ▁and ▁the ▁Mathemat