The importance of math in the study of history

I'm currently reading William Shirer's The Rise and Fall of the Third Reich.  Several times during the course of his narrative, he mentioned the hundreds of tons of Nazi documents seized at the end of the war.  This just seems like such a vast amount of paper that I was having trouble wrapping my mind about it.

So I set out to try to translate it into something I can relate to.  Based on my experiences with the US postal system, I know that 5 sheets of paper is about an ounce*.  Multiplying this through by ounces per pound, pounds per ton, etc., yields the result that 100 tons of paper is approximately 16 million sheets.  A quick search at Google turns up the factoid that a sheet of 20-lb paper is 0.004 inches thick.  Multiplied through by 16 million sheets yields 64,000 inches, or 5,333 feet.  So a hundred tons of paper would require a little over a mile of filing cabinet spaces (at this scale, I feel pretty comfortable ignoring the thickness of the folders).  A quick search of an office supply shopping site turns up a 4-drawer, 26-1/2" deep filing cabinet for $170**.  Crunch the numbers and you'll need about 600 filing cabinets (at a total cost of just over $100,000) to store 100 tons of documents.  And the Allies had multiple hundreds of tons of Nazi documents to deal with - it's really kind of amazing.

Things like this are why I'm glad I had science-level training in math before switching over to history:  There's so much history that can be inadvertently glossed over if one doesn't know how to deal with the numbers, and one's experience of history is really the poorer for it.

*  I'm making the assumption here that any differences in the weight of a single sheet of paper between standard US office paper of today and German office paper of the 1930s and 1940s will be negligible enough over the course of hundreds to tons that I can still get a meaningful approximation.
**  Not necessarily the best deal, but it got 4.4 stars in customer reviews so should be adequate for our purposes here.