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Israel's birthday is May 14, 1948 because that's the day it was declared a country.
Birthdays were not customarily recognized or celebrated in the Old Testament so Jacob/Israel's birthday is unknown. If you are referring to the modern Nation-state of Israel, then it was declared 14 May 1948 and recognized by the U.N. on 15 May 1948.
Israel Dagg was born on June 6, 1988.
Israel Folau was born on April 3, 1989.
Israel Kamakawiwo'ole was born on May 20, 1959.
Israel Putnam was born on January 7, 1718.
Elizabeth Israel was born on January 27, 1875.
Israel Regardie was born on November 17, 1907.
Märt Israel was born on September 23, 1983.
Israel Gelfand was born on September 2, 1913.
Israel Falou was born on April 3, 1989.