▁connection ▁between ▁quantum ▁physics ▁and ▁Mont gom ery ' s ▁pair ▁correlation ▁conject ure ▁about ▁the ▁zeros ▁of ▁the ▁Z eta ▁function . ▁The ▁pr imes ▁ 2 , ▁ 3 , ▁ 5 , ▁ 7 , ▁ 1 1 , ▁ 1 3 , ▁ 1 7 , ▁ 1 9 ,   ... ▁are ▁described ▁by ▁the ▁Riemann ▁Z eta ▁function , ▁and ▁D ys on ▁had ▁previously ▁developed ▁a ▁description ▁of ▁quantum ▁physics ▁based ▁on ▁m ▁by ▁m ▁arrays ▁of ▁totally ▁random ▁numbers . ▁Mont gom ery ▁and ▁D ys on ▁discovered ▁that ▁the ▁eigenvalues ▁of ▁these ▁matrices ▁are ▁spac ed ▁apart ▁in ▁exactly ▁the ▁same ▁manner ▁as ▁Mont gom ery ▁conject ured ▁for ▁the ▁n ont rivial ▁zeros ▁of ▁the ▁Z eta ▁function . ▁Andrew ▁Od ly z ko ▁has ▁verified ▁the ▁conject ure ▁on ▁a ▁computer , ▁using ▁his ▁Od ly z ko – Sch ön h age ▁algorithm ▁to ▁calculate ▁many ▁zeros . ▁ ▁There ▁are ▁in ▁nature ▁one , ▁two , ▁and ▁three ▁dimensional ▁qu as ic ry st als . ▁Mathemat icians ▁define ▁a ▁qu as ic ry stal ▁as ▁a ▁set ▁of ▁discrete ▁points ▁whose ▁Fourier ▁transform ▁is ▁also ▁a ▁set ▁of ▁discrete ▁points . ▁Od ly z ko ▁has ▁done ▁extensive ▁comput ations ▁of ▁the ▁Fourier ▁transform ▁of ▁the ▁n ont rivial ▁zeros ▁of ▁the ▁Z eta ▁function , ▁and ▁they ▁seem ▁to ▁form ▁a ▁one - dimensional ▁qu as ic ry stal . ▁This ▁would ▁in ▁fact ▁follow ▁from ▁the ▁Riemann