An anonymous commenter linked to the 1869 Harvard entrance exam that was dug up by a NYTimes writer and made the rounds last year. It looks pretty intimidating at first glance, and the commenter used it as evidence that Billy Sidis's entrance into Harvard in 1909 was a pretty solid accomplishment in itself. Interestingly, the boy's getting in was probably even better than the exam would indicate. Harvard was no great shakes in 1869, but had improved considerably by 1909, and was one of the world's best by then. I will note that it was still not what we think of today. Competitive university admission is mostly a post WWII, or even post 1960 phenomenon. Many of the brightest did indeed go to the Ivies, the Little Ivies, or the Seven Sisters,* but you simply couldn't count on it. The rich and the alums got their kids in, and nationally, people stayed closer to home and many of the brightest went to other schools, far more than, say, in 1990.
The gap exactly covers the period of Charles William Eliot's presidency of Harvard, if you want more background than I will give here.
But the test. That Latin and Greek looks awfully impressive right out of the gate. If you are older, and/or a reader of history, and/or a traditionalist, you may still have Latin Envy, believing that a "proper" education must include it, and Greek! Why, that just seals it. A different alphabet and everything. Weren't they smart, then?
No, not especially. They had had six years of Latin and four of Greek by then, whether by tutor or at academy. If you took any languages at all in late 20th C, and make the mental comparison of what, exactly, they were being asked to do, it looks much less impressive. Note also, there was a standard set of works studied in those languages, which these questions are drawn from, plus frequent drill in grammar. Even if you had Latin yourself, you should note that the primary authors studied now are not quite the same as studied then, nor in quite the same way. These exam questions are essentially "Did you have proper teachers, are you reasonably bright, and did you make a moderate effort these last few years?"
Before I get into the math, let me note the major difference, then and now. Look at what is missing in this exam. There is no biology, no chemistry, no physics, and certainly no other sciences such as geology or economics. There are no questions on English Literature - no Shakespeare, Chaucer, Milton - and certainly no American literature (horrors! To even imagine such a thing!). No modern languages, no history other than ancient, no world events, no weather, no basic medicine. Even deeper, no methods of research, and no use of reference materials. Because these were not taught to young men. They were taught English Composition and Grammar, Latin and Greek, Ancient History, and the mathematics you see here. That's it.
Thus, their facility with L&G is dropping even farther down the list of impressiveness. Most of what 7th-12th graders have to learn today they did not have to even pretend to know. They were being trained to be gentlemen. The push for more useful arts was just beginning in this country.
The mathematics would look worrisome at first, but on closer examination, not so. The arithmetic is mostly just big numbers, and irritating, tedious working by hand. We forget mathematics that we don't use very quickly, but these students were still immersed.
Two stories: I was a math wizard, but I had to relearn a lot of it each time a son got beyond the first few weeks of algebra in HS. The terms and symbols were familiar, but I couldn't remember where they went. I could get it back, but I had to sit and stare, consult the index, and trial-and-error a bit. All year, for both algebra and geometry. (And as the first two seldom needed help, I was even less prepared for the others.) Story 2: There was a math magazine when I was in school, which posed problems each month. It printed the names of those who solved them the next month. I did a few months of that in 12th grade. Because of going to St Paul's for summer studies, I recognised the names of many of the other NH students who got problems right. One month, there was a problem where I was the only kid in the country to submit a right answer - something about rotating one parabola along another and describing where the focus went. Very cool. I pretended, in my conceit , that I was the only one able to get it, which was insane. How many students, even the nerdy math ones, read magazines and submitted problems? Fast forward one year. I was in a different type of math at college, but for some reason wanted to review my accomplishment from the year before. Narcissism, likely. I could not follow the solution I had myself written, only one year later.
We lose new abstract thoughts quickly, unless they are used. Look at the logarithms, trig, and plane geometry in the exam. Even if you can't even remember how to begin to solve it now, do you recognise the words and ideas? Do you have some recollection of solving problems sort of like that? Then in all likelihood, you could have done those problems when you were in 11th-12th grade. And especially, if you didn't have to study any Biochem, Shakespeare, or Intro to Psychology as well. If you had the same five subjects pretty much year after year, you'd know 'em quite well.
Also - there was some different emphasis in what maths were taught then. Trig was the top shelf, and you got two years of drill in it. No sets, calculus, or statistics for you.
Also - read the directions. See how few questions were required.
Also - it doesn't say what a passing score was, does it?
185 out of 215 applicants got into Harvard that year.
*Fun trivia test for you: name 'em. I got five on my first try, then a sixth popped into my head a year or so later (this was before internet). I never did get the seventh until I looked it up.