There is no end to the conundrums involved in defining what it means to be a Jew. Must a Jew be someone who believes in the Jewish religion, in the way a Christian believes in Christianity or a Muslim in Islam? That can't be the case, since many devoted Jews are atheists. Is a Jew necessarily someone who acknowledges membership in a Jewish ethnic group, people, or nation? That definition would exclude people who believe in Judaism but feel little kinship with other believers, and it would read out Jews who are anti-Zionist. Should "Jewish" be seen as a cultural identity? If so, it would cover people who are stirred to their souls by Fiddler on the Roof, live on the Upper West Side of Manhattan, enjoy Jewish food, appreciate Jewish humor, and believe—like the woman who once told me she was Jewish because she subscribed to the New Republic—that Judaism mandates liberal politics. But there are certainly non-Jews who meet all these criteria and significant numbers of Jews who don't.
Not only is there no satisfactory answer to this puzzle; there is a fundamental reason why not. The people who would come to be called Jews and the faith that would be known as Judaism are ancient in their origins. From their earliest history, Jews attributed those origins to a family founded by biblical patriarchs and guided by divine revelation. For centuries afterwards, Jewish religion, peoplehood, and culture were indistinguishably bound together. The people and faith thus predate by many centuries the emergence of such modern concepts as "religion," "nation," and "culture."