
MIT Entrance exam (1869) - anemecek
http://libraries.mit.edu/archives/exhibits/exam/algebra.html
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DanielN
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.

[http://en.wikipedia.org/wiki/History_of_the_Massachusetts_In...](http://en.wikipedia.org/wiki/History_of_the_Massachusetts_Institute_of_Technology)

~~~
cma
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).

~~~
DanielN
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.

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spc476
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.

~~~
michael_dorfman
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.

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prat
link to IIT joint entrance exam (JEE)
[http://www.wiziq.com/tutorial/98820-IIT-JEE-Mathematics-
Pape...](http://www.wiziq.com/tutorial/98820-IIT-JEE-Mathematics-Paper)

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

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iuytgfrtyuik
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?

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kwantam
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.

~~~
amelim
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...](http://www.ted.com/talks/conrad_wolfram_teaching_kids_real_math_with_computers.html)

~~~
redthrowaway
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.

~~~
varjag
The Greeks got by fine without it.

~~~
redthrowaway
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.

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

~~~
redthrowaway
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.

~~~
varjag
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.

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

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

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chr15
Answers: [http://libraries.mit.edu/archives/exhibits/exam/algebra-
answ...](http://libraries.mit.edu/archives/exhibits/exam/algebra-answers.html)

~~~
etfb
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.

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

~~~
sid0
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.

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trurl123
It's usual exercises for school in Russia. I don't find any difficult
problems. I mean all except English.

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

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

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

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

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ashot
the geometry section is much harder:

[http://libraries.mit.edu/archives/exhibits/exam/geometry.htm...](http://libraries.mit.edu/archives/exhibits/exam/geometry.html)

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verroq
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.

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

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tjarratt
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.

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

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bm98
Am I the only one who was struck by how much that exam looks like something
produced by LaTeX?

<http://bm98.posterous.com/did-they-have-latex-in-1869>

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nopinsight
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.

~~~
jan_g
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.

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

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nutjob123
anyone have a more recent copy? took me 15 min.

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pshirishreddy
I already feel like a MIT Graduate :D :D

