What do Hilary Putnam and Natalie Portman have in common?
Why, of course, they share talents in common. They are among the very, very few to have Erdos-Bacon numbers--indeed, these two have the same Erdos-Bacon number of 6.
An Erdos number of 1 refers to coauthorship with the mathematician Paul Erdos, (an Erdos number of 2 belongs to those who have coauthored with an Erdos coauther, and so on).
Degrees of separation from Kevin Bacon are calculated by appearing in a performance or film in which Kevin Bacon also appeared.
Hilary Putnam has an Erdos number of 3 (and if anyone can show the coauthorship path in comments, I'd be interested), and a Bacon number of 3 from having appeared as himself in the documentary film Julia Robinson and Hilbert's Tenth Problem.
Natalie Portman has a Bacon number of 1. As an undergraduate at Harvard, she co-authored a paper in neuroscience, giving her an Erdos number of 6. She also won a Westinghouse Prize (Intel Science Talent Search)--making a unique combination with her Oscar for Best Actress.
Not surprisingly, xkcd has illustrated the Erdos-Bacon dream.