Cédric Villani, one of the Fields Medal winners attending the Heidelberg Laureate Forum, studied with Pierre-Louis Lions, who was also a Fields Medal winner. Is it common for medalists to have students who go on to be medalists?

You might expect so, since it’s plausible that the best mathematicians would have the best students.

But you might also expect regression to the mean. As with physical genealogy, exceptional parents tend to have less exceptional children.

So which is it? How many academic “father-son” pairs have won the Fields Medal? While we’re at it, how many academic siblings have there been?

Fields medalist Michael Atiyah’s student Simon Donaldson is also a medalist. There has been one example of three academic generations of Fields medalists: Laurent Schwartz’s student Alexander Grothendieck was the advisor of Pierre Deligne. So the complete list of “father-son” Fields medalists is

• Schwartz / Grothendieck
• Grothendieck / Deligne
• Atiyah / Donaldson
• Lions / Villani.

There have been five pairs of medalists who studied under the same advisor:

• Jean-Pierre Serre and René Thom were students of Henri Cartan.
• Stephen Smale and Daniel Quillen were students of Raoul Bott.
• Heisuke Hironanka and David Mumford were students of Oscar Zariski.
• Charles Fefferman and Terence Tao were students of Elias Stein.
• Ngô Bảo Châu and Laurent Lafforgue were students of Gérard Laumon.

Not many people have won Fields Medals, 54 so far, and yet there has been a fair number of academic familial relationships.

The data for this post came from the Mathematical Genealogy Project.