Short answers, pulled from the story.
Thomas Carlyle stated clearly that The History of the world is but the Biography of great men. He published these ideas as On Heroes, Hero-Worship, & the Heroic in History shortly after the lectures concluded.
Carlyle identified the hero as divinity like Odin, the prophet such as Muhammad, the poet exemplified by William Shakespeare, the priest represented by Martin Luther, the man of letters including Jean-Jacques Rousseau, and the king modeled after Napoleon.
Herbert Spencer believed attributing historical events to individual decisions was an unscientific position because he argued that men labeled as great are merely products of their social environment. He insisted history results from broader social forces rather than isolated personal choices.
William James argued that genetic anomalies in the brains of great men serve as the decisive factor driving environmental change. He described how such instability tips a brain in a particular direction creating unique conclusions that function like new zoological species altering regional equilibrium.
Leo Tolstoy rejected the theory because he believed the significance of great individuals is imaginary since they are only history's slaves realizing Providence's decree. He viewed them as instruments of larger forces rather than independent drivers of history.
Ian Kershaw rejected the Great Men theory insisting it matters more to study wider political and social factors explaining Nazi Germany's history. He argued Hitler was an unremarkable person whose importance came from how people viewed him exemplifying Max Weber's concept of charismatic leadership.