, ▁the ▁math ematic ian ▁Leon id ▁Kant or ov ich ▁developed ▁economic ▁models ▁in ▁partially ▁ordered ▁vector ▁spaces , ▁that ▁emphas ized ▁the ▁du ality ▁between ▁quantities ▁and ▁prices . ▁Kant or ov ich ▁renamed ▁prices ▁as ▁" object ively ▁determined ▁valu ations " ▁ ▁which ▁were ▁abbre vi ated ▁in ▁Russian ▁as ▁" o .   o .   o .", ▁all ud ing ▁to ▁the ▁difficulty ▁of ▁discuss ing ▁prices ▁in ▁the ▁Soviet ▁Union . ▁ ▁Even ▁in ▁finite ▁dimensions , ▁the ▁concepts ▁of ▁functional ▁analysis ▁have ▁ill umin ated ▁economic ▁theory , ▁particularly ▁in ▁clar ifying ▁the ▁role ▁of ▁prices ▁as ▁normal ▁vectors ▁to ▁a ▁hyper plane ▁supporting ▁a ▁convex ▁set , ▁representing ▁production ▁or ▁consumption ▁possibilities . ▁However , ▁problems ▁of ▁describing ▁optimization ▁over ▁time ▁or ▁under ▁uncertainty ▁require ▁the ▁use ▁of ▁infinite – dimensional ▁function ▁spaces , ▁because ▁agents ▁are ▁choosing ▁among ▁functions ▁or ▁st ochastic ▁processes . ▁ ▁D iffer ential ▁decl ine ▁and ▁rise ▁ ▁John ▁von ▁Ne umann ' s ▁work ▁on ▁functional ▁analysis ▁and ▁topology ▁broke ▁new ▁ground ▁in ▁mathematics ▁and ▁economic ▁theory . ▁It ▁also ▁left ▁advanced ▁mathematical ▁econom ics ▁with ▁fewer ▁applications ▁of ▁differential ▁calculus . ▁In ▁particular , ▁general ▁equilibrium ▁the or ists ▁used ▁general ▁topology , ▁convex ▁geometry , ▁and ▁optimization ▁theory ▁more ▁than ▁differential ▁calculus , ▁because ▁the ▁approach ▁of ▁differential ▁calculus ▁had ▁failed ▁to ▁establish ▁the ▁existence ▁of ▁an ▁equilibrium . ▁ ▁However , ▁the ▁decl ine ▁of ▁differential ▁calculus ▁should ▁not ▁be ▁ex agger ated ,