In a letter to President Harry S. Truman, Albert Einstein wrote "I know not with what weapons World War III will be fought, but World War IV will be fought with sticks and stones." I tend to agree, but really hope there is no WWIII.
In other writings he believed about 2/3 of mankind would be wiped out. Of course, much has changed since then. I do think some people would survive, somewhere, and probably not the people we think it would be.