Joseph Epstein assesses the question in a review of Darrin M. McMahon’s Divine Fury:
[G]eniuses tend to emerge in those areas of life dominant in specific cultures at specific times. For the Greeks, the main games were philosophy and art. For the Romans, it was military exploits and administration, and the only two Romans up for genius whom McMahon mentions prominently are Julius and Augustus Caesar. During the Middle Ages, devotion and piety, with an emphasis on asceticism and personal sacrifice, won the genius laurels, and the genius that occupied the souls of men and women was thought to be imbued by angels. Augustine of Hippo and Thomas Aquinas were both made saints. (“Genius,” wrote the Russian philosopher Nikolai Berdyaev, “is another kind of sainthood.”) For the Renaissance, it was art, chiefly visual art, painting and sculpture and architecture, that rang the gong. For the modern age, beginning with the 18th century, scientific geniuses predominate.
For our own age, the main game, once thought to be invention—Thomas Edison and Henry Ford held genius status for a while—has yet to be determined, especially with so much science now being done not individually but in teams. Hence the paucity of agreed-upon geniuses in our day. Those master marketeers of the digital age, Bill Gates and Steve Jobs, need not apply.