Illui (Hebrew: עילוי or עלוי also ilui; pronounced [ʔiˈluj] plural: illuim) is a noun (meaning "above," "elevation," "going up," or "best" from the root על meaning "on top" or "above" ) derived from the Hebrew and Yiddish, meaning a young Torah and Talmudic prodigy or genius.
The Hebrew term and title is applied to exceptional Talmudic scholars among Orthodox Jews. It is used among English speaking and Yiddish speaking Orthodox Jews to identify, as a type of mark of honor, those who have been blessed with greater mental and intellectual capabilities than the average intelligent Torah scholar.
It is considered a mark of honor and excellence for a Talmudic scholar to be recognized as an illui and to be described and called as such by his peers. It indicates that he is regarded as having extraordinary intelligence and mental capacity, necessary for the most serious, advanced and complex Talmudic learning and Torah study.
In common terminology, an illui would be someone who has an extraordinarily high "IQ" as recognized from early childhood as a child prodigy by rabbis and Torah scholars who have a keen eye to recognize the qualities of excellence in budding young Torah scholars.
Haredi and Hasidic Jews are very familiar with this term, and if a scholar that they are familiar with has been known to have been called an illui they will regard it as a great honor for that individual as well as for his family, teachers and those with whom he associates. In Orthodox, Haredi and Hasidic circles, the term illui is applied to males only, as women are not obligated in Torah study to the same degree that men are required to devote much of their early life to serious and intense Torah studies, also referred to as Torah learning.