ho.history overview - Great mathematicians born 1850-1920 (ET Bell's book ≲ x ≲ Fields Medalists)

Motivated by an e-mail from grshutt, I looked myself at the Princeton Companion to Mathematics. I discovered that the editors of the PCM answered the same question as the one that I posed here. Part VI is a collection of biographies of 95 mathematicians, plus one for Bourbaki, and the fact that the Bernoullis share a slot. They chose 37 mathematicians born between 1850 and 1920, exactly in the middle of the range that I suggested. See the table contents to see who they picked. They also wrote nice biographies, although they are much shorter and more sedate than E.T. Bell's single-author work.

It is a little embarrassing that we had this whole discussion without noticing that the PCM, with Timothy Gowers as the chief editor, had already done the same work. But it is also useful. It seems that when informed people carefully make lists of influential mathematicians of comparable length, they'll arrive at roughly the same list. Typically the intersection is about 1/2 if the lists are exactly the same length. PCM's list is longer than Bell (in the corresponding period) and mine, and shorter than Pete's, so we can look at who I (or Harrison) included but they did not, or who they included but Pete did not.

PCM minus Pete: Fredholm, Vallée-Poussin, Russell, Sierpinski*, Littlewood*, Skolem, Ramanujan*, Courant, Kolmogorov*, Church, Hodge* (* = honorable mention in Pete's list)

me minus PCM: Picard, Hurwitz, Lefschetz, Siegel, Chevalley, Gelfand

Harrison minus PCM: Henri Cartan, MacLane, Erdos, Feynman

Bell minus PCM: Zeno, Eudoxus, Poncelet, Monge

PCM $cap$ Pete $cap$ Harrison $cap$ me: Hilbert, Minkowski, Hausdorff, Cartan, Noether, Weyl, Banach, von Neumann, Godel, Weil

Some of the differences can be explained as a somewhat different emphasis. In listing Russell and Church, the PCM gave more credit to the philosophical end of logic. (This is also grshutt's point in in his answer posted here and in his letter.) Whether Feynman should "count" is another question with two different reasonable answers. (As I said in a comment, the argument for Feynman is that he is an architect of quantum field theory, and quantum field theory is arguably a fundamental mathematical theory, even though parts of it haven't been made rigorous.)

And I suppose that some of the differences indicate the ill-defined side of the question, or they are just random fluctuations, and aren't really worth arguing over.