So earlier today I was walking along, listening to the Math/Maths Podcast. They mentioned Erdös numbers, as math people are wont to do occasionally. It occurred to me that nobody can get an Erdös number of 1 now — of course — and that at some point in the future, all of Erdös’s collaborators will have died, so it will be impossible to get an Erdös number of 2. So how old, I wondered, is the youngest of Erdös’s collaborators?
The latest birthdate I could find on the Internet for an Erdos collaborator was Csaba Sandor, May 10, 1972.
(This Christian Mauduit, born 6/9/75, is not the Erdos collaborator.) Information about dates of PhDs and such is easier to find, and yields two potential younger collaborators. Gergely Harcos is one: he started primary school in ’79, university in ’91, and got his PhD in ’03. Laszlo Koczy got his PhD in ’03; he’s an economist but has some discrete-math interests, so may be the Erdos collaborator. To find these people I took the list of Erdos collaborators by date of first collaboration and started googling names from the bottom until I got tired. This happened pretty quickly, so I can’t guarantee that I’ve found Erdös’s youngest collaborator.
Of course then I got home and came across a similar question for baseball players at sports nation divided. Here the nodes are baseball players, and two players are linked if they faced each other in Major League Baseball play, one as a batter and the other as a pitcher. It’s possible to get from the 19th century to the present day in six steps. This seems about right — twenty years is a rough upper bound for the length of an MLB career, and a regular batter/pitcher will face most pitchers/batters in their league in a given season, so it should be possible to do this in six steps.
Uncovering Ramanujan’s “Lost” Notebook: An Oral History, by Robert Schneider from interviews with George Andrews, Bruce Berndt, and Ken Ono.
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God plays dice 
I would have thought Erik Demaine, but his Erdos number is 2. He would be likely to be youngest, if his number was 1.
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Searching through all the links on the wikipedia pages for people with Erdos number 1 (found here https://en.wikipedia.org/wiki/List_of_people_by_Erd%C5%91s_number), it seems that the youngest is either Florian Luca (born in 1969) or Gábor Sárközy (birth year not given, but he obtained a Bachelor’s degree in 1990, so was probably born around 1969 or 1970).
I asked Professor Harcos today after an exam and he believes he is the youngest Erdos collaborator.
Actually I believe now that László Á. Kóczy (born on 11 March 1976) is the youngest person with Erdős number 1.