Paul Erdos and Collaboration Distance

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Paul Erdos was a famous and prolific Hungarian mathematician. Erdos had collaborated with more than 500 other mathematicians. That is he has coauthored papers with that many mathematicians. His expertise was in the broad areas of Discrete Mathematics and Number Theory. 

I had met him once way back in 1982 or 1983 when Erdos visited the Math Department at Princeton University. I was introduced to him and shook hands with him. Soon afterwards I worked on one of Erdos' many many conjectures and thought I had solved it. I wrote up the "proof" and sent it to Ronald Graham at Bell Labs who was then the custodian of Erdos' conjectures. Ron Graham even offered a small prize for each one of the conjectures. So I was hoping to get a $100 check in the mail! Instead, several weeks later Ron Graham wrote back to me that he read my proof and didn't think it was right though he couldn't quite put his finger on why it was wrong. Days later I found the bug in my proof and poof went my dreams of the $100 check.

So what is the Erdos number? The inductive definition goes like this. If you had written a paper with Erdos your Erdos number is 1. If you had written a paper with someone who had written a paper with Erdos then your number is 2, and so on. You get the idea. In graph theory terms, your Erdos number is the shortest collaboration distance to Erdos. 

Since Erdos was a very prolific collaborator, pretty much every mathematician has a reasonably small Erdos number. 

My Erdos number is 2. 

You can generalize this collaboration number to any pair of authors. My collaboration distance to Albert Einstein is 4.

 https://mathscinet.ams.org/mathscinet/collaborationDistance.html

Click on the American Mathematical Society link above.

Type in my name as Vijayan, Gopalakrishnan in the First Author field. 

Select Use Erdos and hit Search. Voila!

Now try the search again keeping me as first author and typing Einstein, Albert as second author. Bingo!

Here is Erdos's obituary written by two famous mathematicians themselves Laszlo Babai and Joel Spencer.