, ▁Ram an uj am ▁wrote ▁up ▁in ▁his ▁first ▁year , ▁the ▁notes ▁of ▁Max ▁De uring ' s ▁lect ures ▁on ▁Al gebra ic ▁functions ▁of ▁one ▁variable . ▁It ▁was ▁a ▁n ont rivial ▁effort ▁and ▁the ▁notes ▁were ▁written ▁clearly ▁and ▁were ▁well ▁received . ▁The ▁analyt ical ▁mind ▁was ▁much ▁in ▁evidence ▁in ▁this ▁effort ▁as ▁he ▁could ▁simplify ▁and ▁extend ▁the ▁notes ▁within ▁a ▁short ▁time ▁period . ▁" He ▁could ▁reduce ▁difficult ▁solutions ▁to ▁be ▁simple ▁and ▁elegant ▁due ▁to ▁his ▁deep ▁knowledge ▁of ▁the ▁subject ▁matter " ▁states ▁Ram an an . ▁" Max ▁De uring ' s ▁lect ures ▁gave ▁him ▁a ▁taste ▁for ▁algebraic ▁number ▁theory . ▁He ▁studied ▁not ▁only ▁algebraic ▁geometry ▁and ▁analyt ic ▁number ▁theory ▁of ▁which ▁he ▁displayed ▁a ▁deep ▁knowledge ▁but ▁he ▁became ▁an ▁expert ▁in ▁several ▁other ▁al lied ▁subjects ▁as ▁well ". ▁ ▁On ▁the ▁suggestion ▁of ▁his ▁doctor al ▁ad visor , ▁K . ▁G . ▁Ram an athan , ▁he ▁began ▁working ▁on ▁a ▁problem ▁rel ating ▁to ▁the ▁work ▁of ▁the ▁German ▁number ▁the or ist ▁Carl ▁Ludwig ▁Sie gel . ▁In ▁the ▁course ▁of ▁prov ing ▁the ▁main ▁result ▁to ▁the ▁effect ▁that ▁every ▁cub ic ▁form ▁in ▁ 5 4 ▁variables ▁over ▁any ▁algebraic ▁number ▁field ▁K ▁had ▁a ▁non - t rivial ▁zero ▁over ▁that ▁field , ▁he ▁had ▁also ▁simplified ▁the ▁earlier ▁method ▁of ▁Sie gel . ▁He ▁took ▁up ▁War ing ' s ▁problem ▁in ▁algebraic ▁number ▁fields