The n-Category Café

Mikael said

I was actually up in the database.

You’re actually up in the database as my first cousin once removed, I see.

Here’s my relation to the other people in this thread: Tom is an eighth cousin once removed; John and Scott are both seventh cousins twice removed; Bruce is not related to me as he has not been yet been born; and Jamie is of indeterminate lineage, his forebears being of another denomination and so not registered in the parish records.

Note 1 If $x$ and $y$ have a lowest common ancestor $z$ where $z$ is the great$^n$-grandparent of $x$ and is the great$^m$-grandparent of $y$ then, $x$ and $y$ are $(min(n,m)+1)^{{th}}$ cousins $|n-m|$-times removed (for $n,m\ge 0$ and $z\ne x$ and $z\ne y$).

Note 2 I have a big family tree sitting in front of me, so I didn’t have to trawl through the database to figure this out.

They don’t call me the Wizard for nothing!

If the base would be complete, wouldn’t everyone trace back to one of those monster mathematicians … ?

It seems that fails to happen more than you’d guess, and not just because of incompleteness in the database. Well, depending on how narrowly you define “monster mathematician”. There certainly are modern giants who turned out to be much more famous than their own advisors (and advisors’ advisors, etc.). They end up with lots of descendants who don’t necessarily trace back to the 18th and 19th century monsters.

There are other issues, too. The database will trace my lineage back to plenty of monsters, but only if you believe their claim that Banach’s advisor was Steinhaus. Even granting that the concept of the student/advisor relationship has evolved over time, from this biography it seems more accurate to say that Banach didn’t actually have an advisor; or else his advisor was Lomnicki, who doesn’t appear in the database.

See the algorithm that Simon Willerton gave higher up. The way I get it, Gauß is your 8th grandparent (9 clicks up in the database), and he’s my 9th grandparent, so you’d be my 9th cousin, once removed.

I haven’t yet checked rigorously that Gauß is our earliest intersection, but it illustrates the theory.

Dan said

Gauss is one of my ancestors too, but I suspect that half the people in the database have that privilege.

A good proportion of the people I know either go back to Gauss or else to Euler and Lagrange. (At least to judge by the big departmental family tree, due to Andrew Stacey, which we have in the corridor.)

John and Dan go back to Gauss; Bob, Tom, and Scott go back to Euler; however, Mikael and I go back to both of them via Klein who had both Plucker (Gauss) and Lipschitz (Euler) as supervisors.

Dan wrote:

Gauss is one of my ancestors too, but I suspect that half the people in the database have that privilege.

Indeed — I enjoy showing off, but it’s absurd that Wikipedia has a chart of my genealogy going back to Gauss, as if that were something special. If I were a normal person I’d be quite embarrassed.