Its interesting to see some math papers written before high power computers were available readily. At the time, numerical solutions were all calculated by hand, so you'll see a hand drawn graph with just enough points filled in that the reader gets the picture. I think that's one of the ways computers have helped in teaching math; they've made it easy for students to visualize what a given function means. The down side, of course, being that they've become a huge crutch in place of real learning.
Hah. I can beat the shit out of that. I learned to build cars long before learning engineering. By the time I took my courses on steel I'd been welding for about six years (and taught the welding section of my class - because apparently, it's gauche for engineering professors to know how to weld). And I was getting my ass kicked by Mohr's Circle and psychometric charts and all these rootin' tootin' high falootin' engineering calcs and then we got to 495, capstone engineering, and you learn that a) to do real engineering work, you take the answer that you think is correct and you stack six "bullshit factor" coefficients in front of it to get your real answer b) more likely than not you skip those "bullshit factor" coefficients and just go with 1.6 for military hardware, 2 for racing, and between 5 and 10 for consumer gear and even then, the most successful designs are those that "look strong enough." I've pulled engines with seat belts - they work really goddamn well. Meanwhile, we had an engineering homework question where we were supposed to use our "FS=2" bullshit factor, our "FS=1.6" bullshit factor and our "FS=5" bullshit factor to determine how thick the chain on a playground swingset needed to be to support a drunken, overweight frat rat of 250 lbs. You won't be surprised to find out that playground swingsets are actually sized such that they can support a drunken, overweight Buick LeSabre. I decided I hated engineering when my Finite Element Analysis instructor docked us points if our answers weren't "heavy" enough (these were printouts from a server-based FORTRAN program and if your report didn't tip the scales at half a pound of paper, you didn't do enough work - something that would have been nice to have known before I imported it all into excel and truncated the last half of all my data tables because you know what? I like trees). Then I decided I loved engineering when I learned what dimensional analysis was.
That said, safety factors can be important, mainly because material defects exist so often. Its easier to over-design by a factor of 2-10 than it is to perform quality inspections constantly (not to mention the whole lawsuit protection game).
The amazing thing to me wasn't that mine was far and away the cheapest approach, but that mine was the only successful approach. Here's all these 4th-year engineering students, and exactly two of them are capable of building a fucking hoist.