Funny to see the philosopher Saul Kripke's face pop up since I am so familiar with him. He is certainly one of the actual geniuses on the list.
Among the things that Kripke did as a child was read the entire works of Shakespeare in the fourth grade (at age 9), as well as teach himself geometry, algebra, and calculus. He said that if analytic geometry hadn't existed when he was a kid he would have invented it.
The story about Harvard offering him a job at 18 is true. He produced an incompleteness proof for modal logic when he was 17, and Harvard did not know he was a teenager. When they encouraged him to apply for a job he wrote back and said he would like to but his mom wanted him to finish high school first.
He was teaching graduate courses in logic at MIT while still an undergrad at Harvard. He graduated summa cum laude as a math major and said that he wished he had never had to go to college because, although he met some nice people, he never learned anything.
His bachelor's degree was the only non-honorary degree he ever received. He gave three lectures at Princeton in January of 1970 which revolutionized contemporary work in the philosophy of language and metaphysics. Among his most famous claims is that there can be necessary a posteriori truths, that is, truths which cannot possibly be false but which nevertheless can only be known on the basis of experience.
