▁imp lication , ▁to ▁a ▁thought ▁process . ▁M ental ▁experience ▁and ▁its ▁relation ▁to ▁the ▁physical ▁brain ▁form ▁an ▁area ▁of ▁philosoph ical ▁debate : ▁some ▁identity ▁the or ists ▁originally ▁argued ▁that ▁the ▁identity ▁of ▁brain ▁and ▁mental ▁states ▁held ▁only ▁for ▁a ▁few ▁sens ations . ▁Most ▁the or ists , ▁however , ▁generalized ▁the ▁view ▁to ▁cover ▁all ▁mental ▁experience . ▁ ▁Mathemat icians ▁can ▁exempl ify ▁cum ulative ▁mental ▁experience ▁in ▁the ▁approaches ▁and ▁skills ▁with ▁which ▁they ▁work . ▁Mathemat ical ▁real ism , ▁like ▁real ism ▁in ▁general , ▁holds ▁that ▁mathematical ▁entities ▁exist ▁independently ▁of ▁the ▁human ▁mind . ▁Thus ▁humans ▁do ▁not ▁invent ▁mathematics , ▁but ▁rather ▁discover ▁and ▁experience ▁it , ▁and ▁any ▁other ▁intellig ent ▁be ings ▁in ▁the ▁universe ▁would ▁pres umably ▁do ▁the ▁same . ▁This ▁point ▁of ▁view ▁regards ▁only ▁one ▁sort ▁of ▁mathematics ▁as ▁discover able ; ▁it ▁sees ▁tri angles , ▁right ▁angles , ▁and ▁curves , ▁for ▁example , ▁as ▁real ▁entities , ▁not ▁just ▁the ▁cre ations ▁of ▁the ▁human ▁mind . ▁Some ▁working ▁mathemat icians ▁have ▁esp oused ▁mathematical ▁real ism ▁as ▁they ▁see ▁themselves ▁experien cing ▁naturally ▁occurr ing ▁objects . ▁Ex amples ▁include ▁Paul ▁Erd ős ▁and ▁Kurt ▁Gö del . ▁Gö del ▁believed ▁in ▁an ▁objective ▁mathematical ▁reality ▁that ▁could ▁be ▁perce ived ▁in ▁a ▁manner ▁analog ous ▁to ▁sense ▁per ception . ▁C ertain ▁principles ▁( for ▁example : ▁for ▁any ▁two ▁objects , ▁there ▁is ▁a ▁collection ▁of ▁objects