▁too ▁incomplete ▁to ▁qual ify ▁as ▁a ▁doctor al ▁dis sert ation . ▁He ▁was ▁told ▁that ▁he ▁could ▁submit ▁one ▁of ▁his ▁published ▁papers ▁to ▁the ▁Y ale ▁fac ulty ▁as ▁a ▁dis sert ation , ▁but ▁ins isted ▁on ▁doing ▁a ▁new ▁research ▁project ▁instead . ▁His ▁dis sert ation , ▁entitled , ▁" Sol utions ▁of ▁the ▁Math ieu ▁equation ▁of ▁period ▁ 4 ▁pi ▁and ▁certain ▁related ▁functions ", ▁was ▁beyond ▁the ▁compreh ension ▁of ▁the ▁chem istry ▁and ▁physics ▁fac ulty , ▁and ▁only ▁when ▁some ▁members ▁of ▁the ▁mathematics ▁department , ▁including ▁the ▁chairman , ▁ins isted ▁that ▁the ▁work ▁was ▁good ▁enough ▁that ▁they ▁would ▁grant ▁the ▁doctor ate ▁if ▁the ▁chem istry ▁department ▁would ▁not , ▁was ▁he ▁granted ▁a ▁Ph . D . ▁in ▁chem istry ▁in ▁ 1 9 3 5 . ▁Even ▁before ▁the ▁dis sert ation ▁was ▁finished , ▁he ▁was ▁appointed ▁assistant ▁professor ▁in ▁ 1 9 3 4 , ▁and ▁promoted ▁to ▁associate ▁professor ▁in ▁ 1 9 4 0 . ▁He ▁quickly ▁showed ▁at ▁Y ale ▁the ▁same ▁tra its ▁he ▁had ▁at ▁J H U ▁and ▁Brown : ▁he ▁produced ▁brilliant ▁theoretical ▁research , ▁but ▁was ▁in cap able ▁of ▁giving ▁a ▁lecture ▁at ▁a ▁level ▁that ▁a ▁student ▁( even ▁a ▁gradu ate ▁student ) ▁could ▁compreh end . ▁He ▁was ▁also ▁unable ▁to ▁direct ▁the ▁research ▁of ▁gradu ate ▁students , ▁except ▁for ▁the ▁occas ional ▁out standing ▁one . ▁ ▁During ▁the ▁late ▁