Business guru Peter Drucker called management "the most important innovation of the 20th century." It was well-justified praise. Techniques for running large corporations, pioneered by men like Alfred Sloan of General Motors and refined at a bevy of elite business schools, helped fuel a century of unprecedented global prosperity.

But can this great 20th century innovation survive and thrive in the 21st? Evidence suggests: Probably not. "Modern" management is nearing its existential moment.

Corporations,...