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MIT Entrance exam (1869) (mit.edu)
135 points by anemecek on Dec 2, 2010 | hide | past | web | favorite | 66 comments

It's worth noting that MIT didn't really become an academically prestigious institution until the 1940-50's. Before the second world war it was largely a Engineering and technical college and certainly wasn't one of the top 10 institutions in the country.

More specifically, at the time of this exam the school was only ~8 years old and engineering wasn't considered the prestigious career it is today.

The round up of federal funding in the 1940's and 50's is really interesting to read about as it completely transformed the school and in a broader sense transformed higher education in the US as a whole.


Along with the funding, prior to the 30's/40's guys like Norbert Weiner were excluded from places like Harvard due to their race, and ended up turning MIT into a powerhouse (on top of the federal funding).

This is a really good point. They talk about this in "A Beautiful Mind". It was a big divider between places like Harvard and Princeton, and places like MIT and Carnegie Mellon. The latter would take in Jews and other immigrant populations. This pissed off Nash (an undergrad from CM and a Phd at Princeton) to no end.

Interestingly enough, many students there currently are all about 'keeping tradition' and are very adverse against change. There's an uproar currently over potentially required purchase of dining hall plans. In the not too distant past, they had such as well from what I understand, but now students want to keep things as they were.

As a current MIT undergraduate, I would say that this isn't the whole story. The reason that people are in an uproar about the new dining hall plan is not that we dislike change. It is because the new plan will cost incoming students an additional $3,000 per semester (students already enrolled will only have to pay $2,500). Also, our administration was dishonest in drawing up these plans (releasing them for student input during finals week, blatantly ignoring the input we are currently providing).

EDIT: well, maybe not blatantly ignoring our current input, but the concessions that they are making are too little too late in my opinion

Yea, you're right. It isn't just about the action, but the way the administration isn't listening. It's probably a poor example of the way I've seen students want to keep traditions.

I've often heard, "Oh, the (parties|hacks|accomplishments|steer roast) was better years ago, and now all the incoming students don't do it the same anymore". There's a weird looking back on things, and today is never as good as yesterday to some students. I hope that this is due to a missampling on my part in talking to people, because that's a really depressing view of the institution

Is it just me, or would one expect the dining hall system to be open to use for anyone who is a student (and their facebook friends)?

Odd. One of the English questions asks "Who is Count Bismark?" The answer given is, "Count (Otto von) Bismark (1815-1898) was creator and first chancellor of the German Empire (1871-1890)." But this is the MIT Entrance Exam of 1869-70, one year before Count Bismark became the first chancellor. Either the year of the exam is wrong, or it was expected that Bismark was going to become the next ruler of Germany.

More likely, the answers provided are not from an original answer sheet, but were researched by someone more recently.

(Note that they are not scanned in from an original document like the questions.)

Bismarck was already a world-historical personage by 1869, and anybody applying to MIT would have likely been able to identify him.

This is from IIT JEE 1999. If i remember this was one of the most difficult Math paper in those years.check out question 11 at the end , nice one. Trivia: Check out JEE 1998 paper on physics & try out subjective questions at the end.Boy was that paper hard.

Some questions have more than one answers right and all answers have to be marked to get credit =)

from what i remember 1987's jee maths was the toughest. with the cutoff's in the lower teens or something....

what's considered a good score on the iit?

in 1998, we used to aim for 50-60% on all 3 (P,C,M) to get in top 500 out of total ~2500 seats - all india topper that year scored himself at 85% (they just tell you the rank you have to score yourself later).

Isn't that kind of high school level algebra?

I thought we were all supposed to have been dumbed down compared to our illustrious forefathers?

Depends on how far back you go. For a Roman, mental multiplication was exceedingly difficult. Clearly this implies that there was a period of upward trend. If we believe that we're dumber than some of our forefathers, then there must have been a peak at some point in the past (or perhaps even multiple peaks, but we don't have enough evidence to suspect more than one, so let's assume it's an approximately parabolic trajectory).

Obviously, it was the men and women of the 1950s, who built computers and airplanes from nothing with little more than their wit, a grease pencil, and some twine, who were of the utmost in mental capacity and grit.

Since we're only 60 years from 1950, whereas 1869 is 81, we must be smarter than them. In fact, we're about as smart as people were in 1890. Ten years ago, we were as smart as people in 1900, but sadly such intelligence is ten years gone.

A corollary: in another 21 years, people will look back at this exam and just barely understand it. A few years after that, all hope is lost.

>A few years after that, all hope is lost.

I loved how you wrapped it up! humor at its best.

Another issue to consider, though, is specialization. 100 years ago, even 50 years ago, people could master all the breadth of their subjects (in math/sciences). Who is the current Gauss or Einstein? Hard to tell, possibly no one can now have that effect alone.

Even 20-30 years ago, when Woz singlehandedly invented the personal computer, it was very different. (he says he had it all in his head at once, really amazing). You can read a beautiful interview here: http://www.foundersatwork.com/steve-wozniak.html

I'm sorry, but being able to perform arithmetic does not equate to higher intelligence or mental capacity. As society begins to perform more calculations via computer, it will allow us to begin address more abstract and higher level mathematics, problems which would be near impossible to address had we been required to do the math with grease pencils.

Conrad Wolfram recently gave a wonder TED talk on the subject. http://www.ted.com/talks/conrad_wolfram_teaching_kids_real_m...

If you can't do arithmetic in your head, the other problems are considerably more involved. I can't see a time where the ability to do mental multiplication is not a prerequisite for higher maths.

The Greeks got by fine without it.

If by "fine", you mean, "with Bronze Age math", then sure. The Greeks figured some great things out in their time, but your average math undergrad would school their best in most things. We've done more with math in the last 20 years than they did in their entire 600 year history.

They didn't need to multiply in their heads to lay out the foundations of geometry and discover irrational numbers. Every generation of math grads from then on begins studies from their achievements.

> We've done more with math in the last 20 years than they did in their entire 600 year history.

What Greeks did with advancing the math profoundly affected technology and sciences. What was done in the last 20 years does not even begin to compare in impact.

Depends what you mean. Some would say that we haven't gotten past pythagoras even with all we have accomplished.

They would be wrong. Calculus is huge. Linear algebra is huge. Boolean logic is insanely huge. The things we can do with numbers now make possible our modern world, something that members of HN don't need me to tell them.

All of the fields you mentioned get by mostly with modes of mathematic proof introduced by Greeks. In that sense there wasn't much new since Pythagoras until the infamous proof of map coloring theorem recently.

Performing math in your head requires concentration and a working memory. These improve with practice and are useful for more than just math (like following complex writing or multiparty discussions).

With computers, people won't perform the basic calculations in their head. But their strategy-forming about what, of the gigantic possibility space, they could or should ask the computer next will still require the same old concentration and working memory... and more.

> As society begins to perform more calculations via computer, it will allow us to begin address more abstract and higher level mathematics, problems which would be near impossible to address had we been required to do the math with grease pencils.

This is quite likely true, especially for scientists and mathematicians. An interesting question for me though is whether the average citizenry is becoming better or worse at mathematics over generations.

I think there's a point where further mathematical prowess no longer holds any sort of competitive advantage for the average person. That point is probably grade 6.

The average person will do just fine in their lives without needing to factorize a quadratic equation. They will do swimmingly without knowing the relation between ln and e. The average person will, after high school, never again have to utter the word "pi" in a non desert-related setting. Similarly, "'x' equals" will become nought but a forgotten dream.

Modern life makes no mathematical demands of 98% of humanity. The only mathematical skill beyond basic arithmetic that most people need to know is compound interest, and most people don't know that.

Knowledge is driven by need, and there's simply no need for most people to be anything but marginally proficient in math.

Those roman numerals don't help with the multiplication at all.

They weren't meant to. The purpose of Roman numerals was to be a convenient notation that you would read on and off of an abacus. All actual calculations were done on an abacus.

Right. That's why "for a Roman, mental multiplication was exceedingly difficult". The representation didn't lend itself to mental calculation.

You bring up good points, but mental multiplication is a bad example. That's certainly more related to an inadequate notation for the task than any trend in human intellect.


Well, since the entrance exam would likely be geared toward people graduating high school, wouldn't the entrance questions have to be at that level of educational experience?

For a normal university, yes. Not for one of the foremost technical institutions in the entire world.

Considering construction finished just 3 years before this exam was published, and the charter was formalized just 10 years before, I would say that MIT (known as Boston Tech from 1866-1916) was not among the foremost technical institutions. At the time.

From the wiki page, it seems like it was actually one of the first technical unis around: "a new form of higher education to address the challenges posed by rapid advances in science and technology in the mid-19th century that classic institutions were ill-prepared to deal with." (http://en.wikipedia.org/wiki/History_of_the_Massachusetts_In...)

In 1869, was MIT a normal university, or one of the foremost technical institutions in the entire world?

Weird. It was apparently easier to get into MIT in the late 19th century than it was to pass the eighth grade.

Hahahahaha. This cracked me up. That 8th grade exam was difficult, no?

Their answer to the first one is wrong. Square root of a positive number gives two results, plus and minus. I haven't checked my working, but I believe the correct answers are 15, -9, 21 and -3. Rather disappointed that I caught the trick question and the questioners, apparently, didn't.

Any positive number has two square roots, but the (present-day) notational convention is always to take the positive square root.

Indeed, and I think the reason it's done is simply to make square-root an easy-to-deal-with single-valued function rather than a multifunction. Remember the quadratic formula: the ┬▒ in it is in addition to the square root, not part of it.

Sometimes square root is assumed to refer to the positive one. I assume that was the case here.

On every notable standardized math test in the US, and on any commonly used calculator, a square root is non-negative. Another example: http://www.wolframalpha.com/input/?i=sqrt(x)

It's usual exercises for school in Russia. I don't find any difficult problems. I mean all except English.

True, but it wasn't typical Russian school level in 1868.

check this out http://upload.wikimedia.org/wikipedia/commons/a/a7/BogdanovB... this is a painting from 1895 pupils were supposed to do calculations like the one on the blackboard in their heads, without any writing

It's not algebra, you wouldn't have gotten to MIT with that even back then.

I would love to see G├Âttingen's or Cambridge's entrance exams of the early 20th century, if there was an exam for these institutions.

Not really

1. Construct a triangle ABC. Construct a line parellel to AB through C. Alternate angles and angle sum of triangle shows it is 180 degrees

2. Use congruent triangles

3. A number of ways doing this. I would cut it into two triangles

4. 360/6 = 60 degrees. Thus each sector is a equilateral triangle.

5. 100 pi

6. Basic algebra, let x be the length of the perpendicular. x = 12, solve for sides using Pythagoras. 20 and 15

7. x : x^2

Would expect to be year 7 or year 8 level.

Yep, the algebra was frankly also elementary school level IMO.

Algebra isn't normally taught at the elementary school level. Now, I'd argue that it SHOULD be, so students can choose to study some interesting fields of mathematics after grade 5, but that's a different argument entirely.

If I remember correctly, my school district didn't offer true algebra until 8th grade, for honors students only, in a class that started an hour before any regular class. Hardly elementary.

I'll grant you my elementary school math was better than most, but I think the point that this isn't very advanced stands.

When I was in middle school (5 years ago), algebra was standard 8th grade math. Honor students got 2 years of algebra from 7th to 8th grade.

At least, my year was given two years of algebra.

The geometry section looks like something I could have passed after taking high school geometry. i.e. an American or Canadian 14-15 year-old could probably do it easily.

The English section is much harder.

It wouldn't be for a modern American high school student in an advanced English (wouldn't even have to be AP/IB) class. At least, I'm confident that 75% of the people in my AP English class would have known 85%+ of the answers. Dating myself slightly, that would've been back in '94.

Geometry is only harder to you because we teach more Algebra than Geometry in schools. They really are elementary.

Am I the only one who was struck by how much that exam looks like something produced by LaTeX?


The Math sections are about the level of high school entrance exam in many countries in Asia (for students who just finish grade 9 equivalents applying to high school).

It is only a bit harder than SAT I Math, in my opinion. I've always wondered why SAT I Math is so easy--a good middle school graduate in Asia would have aced it. If anyone here can comment/point to references on the matter, I will appreciate it.

I agree, geometry/algebra/arithmetic seem almost too easy. But then again, 1869 is not 2010. Maybe the expectations were different 130 years ago. Namely, if the tests were any harder, how many students would pass?

I am from central Europe and have gone to schools here as well.

Much easier than the 8th grade examination from 1895 posted the other day. http://news.ycombinator.com/item?id=1959690

anyone have a more recent copy? took me 15 min.

I already feel like a MIT Graduate :D :D

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