From six degrees of separation to six degrees of Kevin Bacon, we are fascinated and delighted by how small the world can feel. Six degrees of separation is, of course, that all people are on average six or less social connections away. Six degrees of Kevin Bacon is the same game but for actors and their connections via costarring with Kevin Bacon.
Mathematicians like to play a similar game. The Erdős number of a mathematician measures the degree of closeness they share, measured by co-authorship of mathematical papers, with the eccentric and astoundingly prolific twentieth century mathematician Paul Erdős.
This brings us to North Dakota State University’s Mathematics Genealogy Project. The project is a collection of nearly 260,000 mathematicians, each of which is cataloged with their doctoral advisor(s) and the doctoral students they themselves have advised. In the ‘family tree’ of mathematics a mathematician’s advisor(s) are their parents and the students they advise their children.
Mathematicians can use the project to trace back their mathematical lineage back to history’s greatest mathematicians including not just Paul Erdős, but David Hilbert, Emmy Noether, Carl Friedrich Gauss and Leonhard Euler. Most are surprised by how closely they are descended from some of humanities brightest minds. Daniel Ullman, Professor of Mathematics at George Washington University, for example, is five degrees of separation from David Hilbert.
The Mathematics Genealogy Project is more than just a parlor game though. The project allows us to reflect on not only the history of mathematics and mathematical progress, but for us as a civilization as a whole to connect with our intellectual heritage. One may recall the ubiquitous quote from Isaac Newton, a groundbreaking mathematician himself, that is:
“If I have seen further than others, it is by standing on the shoulders of giants.”
