The exercise was harder than I thought, probably because I never worked out what “Influence” meant. (I see that JohnT has offered a pretty fair presentation though.) Partly, I used the counterfactual approach: I asked what would have happened if you took the individual out of history. But mostly I shuffled the goalposts around as necessary.
Here they are:
1 Mohammad
2 St Paul
Religious types deserve top ranking, if only because of their overwhelming share of the human mind-space. Mohammad beats Christianity because his genius was literary, religious and political. I judge St. Paul to be necessary for Christianity to take hold: Jesus of Nazareth was merely born into the role, as it were. Alternatively, I ascribe a substantial share of his teachings to those who came before and after him.
3 Johann Gutenberg
See above. The printshop is prerequisite for the Reformation, the Enlightenment, the Scientific Revolution. It was a precursor to the Industrial Revolution, an application of interchangeable parts and the American system of manufacture. Lose communication and you lose modernity.
4 Aristotle
The first methodical thinker. A precursor to empiricism. Unfortunately, his philosophical work pushed deduction.
5 Francis Bacon
The father of empiricism, the scientific method, the advocate of induction. Or anyway, this would be his ranking, if I could actually claim that. But Bacon was born in 1561, 100 years after Copernicus. His contemporary Galileo did fine without being overly influenced by him, to my knowledge. So consider this false entry to be a marker of sorts.
5 Confucius
6 Alexander
Confucius also possesses a lot of mindshare, as does Tao. Alexander wins the conqueror contest because he pushed Greek ideas deep into the Asian continent while the most successful invader (Genghis Khan) didn’t have a comparable cultural influence. Nor did Caesar, I would argue.
7 Jesus Christ
8 Nicolaus Copernicus
Well I had to put the Man from Nazareth somewhere! Copernicus was the first scientist to base a major counter-intuitive result from empirical observation, thus permitting the idea of science.
9 Isaac Newton
10 Buddha
11 Shakespeare?
12 Darwin?
Newton loses to Copernicus because the idea of Science was firmly established by the time he was born. But Newton showed the possibilities of successful science, as well as being an intellectual champion of the highest order.
The Buddha secures this ranking because he is a) a religious figure who b) influenced Hinduism. Buddhism itself is a once major religion that is now a noteworthy religion.
That was my first cut anyway. Debate is welcome!