[foldr]

What I don't understand about this comparison is that there's actually an awful lot of "knowing what" involved in math and science too. You won't get far in solving math problems if you try to derive everything from first principles. You could make fun of historians for learning lists of dates, but you could also make fun of mathematicians for learning lists of trigonometric identities.

[kmill]

It is true that you need to remember a lot of things to do math effectively, but a big difference between knowing dates and knowing theorems is that you can re-derive the theorems by yourself given enough time. A not-insignificant reason I got into mathematics was that I have difficulty remembering specifics, so I could lean on reinvention.

I frequently forget the trig identities, but I know the basic definitions of trigonometry and that there ought to be certain identities, so I know I can re-derive them or look them up. But, I only need to do this when I teach calculus.

[foldr]

You can also re-discover the dates by doing your own historical research, if you want to. And of course, historians don't really spend much time literally learning lists of dates. More realistically, there are lots of causal and logical connections between historical events that enable a historian who knows the details of a particular period to infer certain facts that they've forgotten from facts they remember.

[kmill]

Don't worry, I'm not completely ignorant about the work historians do.

> You can also re-discover the dates by doing your own historical research

My point was that you can put a mathematician in a closed room with only pencil and paper, and they could redevelop an entire theory if needed. A historian in the same position would be unable to do any work -- they need primary sources. I went with your "learning lists of dates" as a stand-in, since, like primary sources, you can't derive dates from scratch.

Sure, history has a "how" of research methods, but the research products must rest on the "what." Mathematics is almost entirely "how." The "what" for a mathematician is mainly knowing what's been done and what needs doing, for the purposes of directing research and giving attribution.

Also, I am pretty sure G.C. Rota was being somewhat facetious in quite a lot of the article. These are "lessons of an MIT education." Lessons aren't necessarily truth.

[foldr]

That's just to say that history is an empirical discipline whereas math, to a large extent, isn't. There are also limits to the amount of useful work that, say, an astronomer or biologist can do with just a pen and paper.

[skybrian]

It seems like a mathematician should be able to derive a trig identity if asked? Otherwise you don't know it very well.

Often mathematicians will make informal arguments but the idea is that you should be able to add rigor when needed.

[foldr]

Sure, and a historian who knows a particular period should be able to explain what evidence is available that event X happened on date Y.