This 1869 MIT Maths Entrance Exam Has Been Considered... Hard? [ Improvised Session + Solutions! ]
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- Опубліковано 16 чер 2024
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The Exam: docdro.id/CLXm5hc
Improvised Session Playlist: • Improvised Sessions
Today we take a look at the Algebra Section of a 1869 Massachusetts Institute of Technology Exam :) I don't really consider this one to be "hard", but it'll still go into the playlist, just because it's an interesting piece of university history! The Exam covers basic algebra questions, ranging from handling square roots, over to reducing fractions and simplifying expressions. Also, I attempt on solving it without any preparation improvised, let's see how it turns out :p Enjoy :) @Flammable Maths Two
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0:00 Introduction and Background Information
4:05 Solving Exercise 1
5:50 Solving Exercise 2
6:37 Solving Exercise 3
10:30 Solving Exercise 4
11:53 Solving Exercise 5
14:22 Solving Exercise 6
16:13 Solving Exercise 7
18:18 Conclusion and Outro
![This is What a 1869 MIT Geometry Entrance Exam looks like! [ Improvised Session + Solutions! ]](http://i.ytimg.com/vi/kes8_g_NrEI/mqdefault.jpg)
![This is What a 1869 MIT Geometry Entrance Exam looks like! [ Improvised Session + Solutions! ]](/img/tr.png)
Physicists: e is e
Engineers: e is 3
1869 entrance exam: *e is 8.*
Note that: e-definition-equal to, or e==8
Assuming "e" is a variable with a value of 8.
well... for physicists e = -1.6*10^(-19) C
_rip_
@@hamsterdam1942 Also correct. Unless you use different (better) units.
Imagine what the future math entrance exam would be in a hundred years
dem boi
Putnam exam
If the reimann hypothesis exist, then prove it........rigorously (2 Marks)
@@theemeraldempire5073 prove any 4 of Hilbert's problems(if any of them remain unsolved then)...(4 marks)
“Prove the Riemann hypothesis”
Just remember, high schoolers back then didn't have Khan Academy.
true lmfao
but they had fewer people to compete with
@@a_spire also most people didn't really have an education.
@@a_spire fewer*
I never use khan academy
Should've applied to MIT back in 1869 so I wouldn't have been rejected like I was this year :(
fucc ;_;
gang gang
A little late for the party
Same Bro
Gang gang
If this was my entrance exam I could have gotten into mit as a 12 year old
Born in 1857? 😉
@@peterbrough2461 wouldn't be too bad
@@zarifahmed8549 thats around a third of your life expectancy in 1850 lmao.
@@awerawer0708 ahahahahahah
Yeah, legit
I enjoyed that 8 - 5 + 12 was the problem that took you the longest
Nein
@@ThatBrubakerFellow I agree - it is wrong.
Nein
I feel so stupid. But wouldn't pemdas make 5+12 go first?
@@Bravo_L pemdas goes left to right so 8-5 goes first
the best prime number that has two factors..
It's the only one as well
And neither of them are 1
He said 57 was prime in a video that was probably over a year ago. He's memeing himself.
uberless1 are you trying to imply that 57 isn’t a prime number just because it has two factors that are not 1? 😤
@Zi Kun Zeng I think it was the Extended Ligma Axiom
Imagine being a current day engineering student and travelling back to 1869 and accidentally using Kruskal's algorithm in a computational mathematics class and being hailed as an engineering genius or introducing distributors to internal combustion engines and lithium-in batteries by accidental mention and rapidly accelerating society 50-100 years
Or just travelling back and dying from a preventable disease
@@shawn5809 That's why you'd also know some basic medical knowledge like disinfecting medical equipment and using alcohol to bandage wounds
@@shawn5809 your comment made me laugh lmao
@tyler t tbh I don't think most people did
At first I thought this would be really cool/funny. But then I realized I'd probably get arrested or possibly killed for being so "well educated" lol
Math is scary when written in that font.
For real tho
Can't tellll youuu how relatable thattt isss
But all the best physics textbooks are written in that font...
@@saritshull3909 ikrr that's sad
Sheeit🤣
Idk why some people are genuinely surprised how easy it is. Like come on, if u expected it to be hard then you’re basically saying that human’s comprehension of mathematics have not change for over 150 years
I blame the internet. But as someone who studies education and school administration etc...
These tests are designed to filter interest via competence. Aka, if you knew this stuff in 1869 you are probably genuinely interested in math and an environment where only passionate people go to enriches discussion
Plus the shady part where they also use applications to filter people from rich families but hey... Technology is expensive plus higher chances of entrepreneurialship for propaganda.
I don't know math, I just research education
I think people are underestimating how good schooling is now and how rampant illiteracy was over 100 years ago.
@@Mhurilo10 Yea, I told that to a feminist who thought there weren't any girls there because people forbid them from entering. Truth is they weren't interested especially when most men also weren't interested. Then I showed her even in today's world women choose not to participate in the study of physics and advanced maths.
@@howardlam6181 Its really weird trying to point at the past and use our societal standards to try and poke holes in it. The entire 50s ideal US household didnt force women to be slaves to their husband, most women WANTED to be the household caretaker and it was a nearly full time job too. In fact, many women still do today. Nothing is inherently wrong with that, and its really aggravating to see those attempting to empower women to do what they want to turn around and try to stop these women for doing exactly what they enjoy
@@aidanquiett668 Yea weird and then most of them would come back at me it's because of the social propaganda of women standards and men laughing at them not being able to do maths that discourage them from pursuing it. Seriously, I don't think any sane men seeking mates would want to belittle the women. At least I had not seen it during the entire high school, undergrad, and the time as a college tutor or maybe I'm just ignorant and they were all doing it in secret like taking them back to an alley without people not to do anything sexual but criticize them for their lack of math skills. As for the first point, I think we have been pushing STEM really hard on women already and even give them free extra tutoring and there is still hardly any increase. I think that should tell them something, right?
I'm an SAT tutor, these questions are basically on par with the hardest algebra SAT problems. Which is to say, they're pretty easy.
ye ^^'
Bart Barker well if you’ve got any specific examples, I’m happy to give you a quick answer for em.
Some SAT problems seem hard but are actually easy.
Engineers: Let e=8
then sqr(e) = pi
Mathematics hell:
e = 3
Pi = 3 = e
Lmao
"If you're from 1869...."
Yes, I'm also waiting for someone who outlived great Physicists and Mathematicians......
:^)
Dude, the first problem gave me a stroke when I failed to see that e isn't the mathematical constant.
Exactly😂
For physicists e ist the constant for electrical charge
e is a unit vector in linear algebra lol
People didn´t know anithing about e in 1869
1777 e=e
1869 e= 8
1900( When the fundamental theorem of engineering was discovered) e=3
1950 e= 2 or 3
2000 e= 2,7whatever
2020 e= 2,3 or 8, who cares
2.7levtolstoylevtolstoyisoscelesrighttriangle
Question 8. Prove that all zeros of the zeta-function lie only on the line in the complex plane Re{s}=1/2 for all 0
Riemann Hypothesis??
@@budiadjiwijaya9946 yes
Someone in the future is gonna look back at the stuff we struggling with and think "Damn, they had it easy"
Einstein had his doctor's degree in his early twenties.
Physics back then was essentially only Newton's mechanics.
So in my first two semesters we did pretty much all the physics which were known back then.
yeye
Nah mate you forgot electromagnetism, analytical mechanics, optics, wave mechanics, fluid dynamics, thermodynamics... And they are not that easy. Also back then a physics degree came with a mathematics degree. So he also had to go through advaced mathematics.
@@Shadow05eth Well Maxwell's equations were published in those years. so I would exclude that. Analytical mechanics is not that hard if it's part of a standard curriculum (and you wouldn't do Arnold in those times because you lack the math). I guess you could have done more special functions and cool coordinate systems, but that's pretty much it. There really wasn't a lot of advanced math to learn imo
@@emanueletroiani8153 Learning E&M without vector calculus sounds like absolute hell.
@@bilalhussein9730 Learning E&M -without vector calculus- sounds like absolute hell.
Fixed
It’s really interesting how things have changed, I learned how to do a lot of this my freshman year. Great video!
e=8
Astronomer: Yeah, this seems to be right.
xD
No joke my astronomy teacher literally said e/π=1. I mean it basically does the massive distances and we only had a single sig fig anyway but lol. It was still funny
@@micayahritchie7158 wtf
why am I imagining a weird shape?
*Am I... an Astronomer?*
Similar thing happened with my physics professor, he simplified a 4 with a 5.
He's an astrophysicist
One thing you have to remember is that in 1869, even finishing the 8th grade was a big deal. A lot of people never even went to high school. Illiteracy was pretty high too.
2100 kids seeing our quantum mechanics exam:
*Is it really that hard?*
It's great to think that the math level in 200 years has gone so far !
:)
I mean SAT math isn't much harder. There's no calc on it, but they ask questions about more things like graphs and patterns.
No kidding, this is literally a class 8 level examination in India
Cool man, cool...
Dhikshith Gajulapalli don't ever say kumon holy every single instructor at mine was hell. only good thing from there was the trophies u got if u completed the highest level. and the clock at least at ours
Bro I took an exam like this in 5th grade
Hi friends, in France we're doing that at the 10th grade !
Are you illiterate? This is stuff we Indians are born with, barely worth recapping in 1st grade
Man, the first second of this video is pure perfection. I've been replaying for the last 3 minutes. Haven't even watched the whole thing yet hahah
:'D
Math majors in 1869 seeing this exam: Wow, this is too difficult
7th graders now: Homework?
I was waiting for your take on this one! A really interesting Exam for sure!
=)
@@PapaFlammy69 :)
I am from 1869 and I can say for a fact that we 69ers thought this was hard back in the days. No Wolfram Alpha, only 69
:^)
Hello, I’m from the 1869 I’m almost 152 year olds and no this is actually meant for 1st grade students, i think it was a misunderstanding.
Don’t mind the pic on my profile it’s my Enormous great grand son.
Have a nice day
tf lol
... seems legit
...
Yea, I can believe it.
Bro...you made me feel so welcome just by saying "fellow mathematicians"👌🔥
Man, this was interesting. Thank you for showing us
"Pretty good and standart algebra questions that each and every High Schooler should know how to solve."
Yeah... well... there's me.
:D
Same
(2)SAME
You are an inspiration to me , love your work
Papa Flammy having a flashback to that "diagonaizabilty" problem in the intro.
xD
How cool is that tho? People are knowing a lot more than they did before. Even my parents learned much easier stuff in school that I did. I'm just wondering what kind of stuff high schoolers will be learning 100 years into the future
I think theres a limit in average intelligence for it to get too much higher in general.
@@apexking6794 That's true, but I think we underestimate how deep the average person could get into math before it gets too abstract for them. Math builds upon itself, so once something is understood, it basically becomes simple as addiition
I think high school math classes are terrible and could go into at least linear agebra by the end of senior, if maths were taught more efficiently
@@simonzakeyh6515 IDK about you but we did vectors in my senior year
@@rlpn6710 in senior year, you only do 2 and 3 dimensional vectors, correct? Idk if that counts as linear algebra
I can now travel back in time and pass the MIT..as a 15 year old.
So, all I have to do to get into MIT is create a time machine and take the entrance exam in 1869.
ye, it's as ez as this
e=8 is some next level engineering ngl
I’m from 1869 and yes this exam was fkn hard for us
xD
Love these kinds of videos
:)
Wie Deutsch soll dein Akzent klingen?
Flammable Maths: yes
DER IST N DEUTSCHER
Ich dachte Schwede
Man merkt das aber sehr schnell
ne dachte gleich der klingt deutsch, profil .. aha deutsch xD
ja er hat einen starken deutschen Akzent
@@reinoldi1097
Und humor
Serious question: why are entrance exams not a thing anymore? At least somewhere like MIT or Caltech you'd think that's the way to go. Then there's no more bullshit in the admissions process and no bad feelings after. If you didn't get in you know why and if you did, you know you earned it.
Standardized exams in general are not very useful at all. Right now, high school kids spend huge amounts of time studying for the SAT which is pretty pointless and unnecessary if you really think about it. If schools had entrance exams, then kids would have to grind practice for SATs and a dozen different entrance exams which takes away from time spent on school work and just living life and having meaningful experiences. Plus, why is an exam the indicator of the best student? Studies show that higher MCAT scores don't correlate with better future doctors, and same with LSATs. Really, standardized exams are pretty damn pointless.
@@seandmello3793 i'd say it's not for all subjects, but for like physics math chemie and engeneering it is pretty reasonable, because for one: you have to praktise calculating, aritmetics and shit at some point if you don't want to be useless in those fields and on the other side, if you where into meaningful experiences and shit why would you studie such subjects in the first place? smoke weed and pray to jah=)
on the other hand, if the test is just remembering questions and not calculating and shit, i totally agree with you.....and shit
@@dulli41 lmao then whats the point of MIT if not to teach you math LOL. And for experiences, I meant like doing cool research and volunteer work and starting clubs and shit which is what unis look at now rather than exams
@@seandmello3793 there is a difference between learning math [lerning new technics for solving integrals,differntial equations or new consepts like manifolds etc.] and praktising aritmetics and basic calculation. the first is thaught in univerity. the secound you git on the way, but you get it by prctising, and it doesn't hurt to start early. and "cool research" as far as i know is like 50% reading papers 20% calculating your shit and 30% doing the actual eyperiment. where reading the papers also includes recalculating theire math so you understand it. i newer did volunteer work if i work i want to get payed. and i never witnessed this clubthing so yea.... but i am only physics and chemestrie so could be in other courses. but that's what i was saying in these naturescinces reliebly calculating stuff with relative ease is so fundamentel, that i'd say, you do peolple who are not able to do that a favor, by putting them off early with such a test.
East asian countries still have it and it works fine here. People don't get why exam exist. It's not 'just' for learning purpose. Exams are used for filtering large group of people. But the problem with entrance exams is only top 20% benefit from it. The rest of 80% starts crying about inequallity, which resulted to no collage entrance exam+a national test(SAT, ACT) that is way too easy for seniors who actually study for it.
Exercise 3, to know if one side is divisible by a+b, you just have to consider it modulo a+b.
That is, a=-b must lead the polynomial to vanish.
It is way faster than calculating directly as you did, but maybe a very little more abstract as to why it works. But still.
Well, if anyone wants to get into a MIT, just be on the lookout for an abandoned DeLorean and it should as easy as pie.
57 is NOT the only prime with two factors. the other two are 51 and 91. you may have confused it with 1001, the only prime with three factors
:^)
This man really asked a bunch of 150 year old corpses if this test was hard
Damn, those people died within one year after the exam. This exam must be really tough for them
lmao that manifold graphic at 0:19; I encountered the exact same one in a paper (short book?) on manifolds. IIRC it was trying to demonstrate the notion of compatibility between charts
At 17:35, a better way to do that was -3y = 11 - 4*17, but factor like -3y = (11 - 17) - 3*17, which gives you 17 + 6/3 = 19. This allows you to avoid having to end up with 57/3. While some might find that easy to divide by 3, it is also easy to screw that up.
I enjoyed this and learned something from your working #3. I wonder how hard the test was considered back in 1869. If we could find out the scores to get into MIT, that might help.
:)
What happened to you at 11:54?
Adderall kicked in.
Beste
nice.
The fact that e was picked speaks volumes about the breadth of their mathematical knowledge back then. It’s sole existence helped the advancement of understanding in multiple branches of mathematics and engineering.
Wowzers have we come a long way.
Here in Brazil we have ENEM (High-School National Exam) that is a 2-day, 180 multiple-choice questions + essay that you have to take to get into any public college. Out of the 180 multiple-choice questions, 45 of them are in the field of mathematics and most of them are not too difficult. It may have a few questions harder then the ones showed in this video, but for the most part they are just as hard, if not easier. Last time I took ENEM I got 41/45 in mathematics and the 4 I missed were because of silly mistakes due to the sheer amount of questions. Its important to note tho, that ENEM is a national exam, which means the same exam is applied all over Brazil, no matter where you're from, what college you wanna attend or what course you wanna take. That means getting the same questions, regardless if you wanna take Engineering, Mathematics, Law, Medicine or Gastronomy.
in the US we get too choose between the ACT in which you have 3 hours to do 215 questions, or you can also take the SAT which only gives 56 minutes for 52 questions.
That would be so nice if we got multiple days to work on them. sounds like it's easier but the question difficulty could be a lot different
it probably wasn´t "hard" per se, but it was what the student ABSOLUTELY needed to be capable of. University´s didn´t work like they do today, trying to be hard. No. sure you got a research job later, but it was very much about the Journey of those who could afford it. So such admission tests were set to see if you had the makings for the subject butr didn´t expect you to be a demigod before you even began to study. So they checked: what skills do the applicants HAVE to have or they are bound to fail. not "what can we expect from the best of the best?" (like if you want to Study IT in some German universities, you will not be taken with a perfect Abitur. Friend of mine was not taken because he did not skip a class. No joke. I mean it was Münster he applied at but still. A mentality like this did not exist in the late 19th century. )
There are many universitys that are not able to get enough people for the mint subjects so if your friend’s still searching he might have luck in another region. I will study IT too in some months and my grades were only average (3,1) so options exist. Not sure if im able to finisch it successfully though but it is worth a try
@@M..796 that was 8 years ago so he found something else xD
In Italy, this is precisely our 9th-grade program for algebra.
You have polynomials (both operations and decompositions), algebraic fractions, linear equations, and systems of equations.
If I could give my take on it, most exams usually tend to give you easier questions in the beginning stages, and harder ones once you get farther into it. For me, it just seems like these weren't ALL the questions that were on the original exam; but only a part of it. Haven't watched the rest of the video yet, but that's what would make sense for me
8:30 I would’ve just used long division but i cant do it in my head and i dont feel like writing it out😂
57 is a reference to the Grothendieck prime, right?
ayy :^)
polynomial devision is over kill.
a^2-2ab-3b^2 is the difference of two squares ((a-b)^2-4b^2)
This just shows how much better education has gotten over the years!!!
I think you could search for "coffin problems" which were problems on entrance exams at a university in Moscow. They look quite simple but when you dive into them they are really hard.
Also I have a challenge for you (idk if you take problems from yt comments) prove that on interval (-pi/2,pi/2) arctanx*tanx>=x^2
I gave this problem a shot, although my solution is very messy and time-consuming. Both functions are symmetric across the y-axis and both have values of 0 at x = 0. Both functions have a first derivative of 0 at 0 and second derivatives of 2 at 0, so all that is needed to prove the inequality is to show that d^3/dx^3 arctan(x)tan(x) >= 0 on [0,pi/2). This is obvious once you actually compute the third derivative, although computing it is a pain and takes a long time, but once you have it, since all the individual parts are greater than or equal to 0 their sum is as well.
@@ethanbottomley-mason8447 Yeah, I have done it that way too, but I think there should be an easier solution to this problem.
Correct me if I’m wrong, but derivatives do not preserve order. So you can’t derive on both sides and expect the inequality to remain..
@@igorvinicius8087 All you need to do is show that the third derivative is greater than 0 since the function shares the same first and second derivatives with x^2. If the third derivative is greater than 0, that means it eventually overtakes x^2. The function is symmetric so it works for negatives aswell.
Ah yes, I remember 1869, such a n I c e year to be alive. That exam was pretty damn hard if you ask me.
:^)
looks at the desk pics, okay thats it man of culture
In the future it would be something crazy like doing differential equations in like elementary school
Netflix:Are You Still Watching?
Someone’s Daughter: 11:53
But isn't |e+i|^2=e^2+1=8,3890......≈8
0:58
nah, e=2
but by fundamental theorem of engineering e=3=pi. An inconsistency i see
Re[(e+i)^2]=e^2-1
ayy
@@PapaFlammy69 |2e + i pi| = 5, they're a Pythagorean triplet
That was best video intro I've ever seen on UA-cam... 😂
:D
@@PapaFlammy69 I'm waiting for you to do a QnA video..
I did a bunch already, links to them are always in the description
@@PapaFlammy69 Have you answered questions like, (1) How old are you? (2) Favourite mathematician? (3) Favourite Physicists? (4) Favourite Pokemon? (6) Favourite star and planet? (7) favourite periodic element? (8) Data or Data? (9) Favourite movie and show? (10) Your sidekick hobbies other than maths?
Oh I forgot number 5, (5) How tall are you?
@6:26 This is why you should always double check your exercises before handing in haha, great video tho!
In the future, gradeschool entrance exams will have Calculus.
they do now? lol
Me, who just found this via recommended:
I like your funny words magic man
If you see the exercice 3 and you considere a as X and b as a constant, basicly you're looking to prove that one of the 2 factors have -b as a solution to the equation in a, so if you see the right one and you replace a with -b you see it becomes 0 so you should only factor the right one and not the whole thing ;)
The fuck sollte das Intro ganz am Anfang? So nice 👌🏻😂 nices Video 😁
Interesting, so e =π^2-1
8 != 9
xD
@@nirorit well 10 is approximately EQUAL to 9, seems good to me
Was there a calculus section, or was this as hard as it got?
this was as hard as it got hehe^^
I’m currently doing very well in calculus.... and like 4 of these stumped me
oh that watch is so awesome
You can get it over on STEMerch :) stemerch.com/collections/clocks-watches-1
Just as I'm studying differential topology and geometry.
Meanwhile my entrance exam to engineering in Croatia gives me ptsd to this day xd
;_;
14:11 Faster method : pull a factorisation theorem and see if a=-b gives a 0
This trend continues...I studied at ETH Switzerland after the Bologna reform (which was a reform which switched to Bachelor / Master system) This meant we used former exams as an exercise..These could mostly be solved very easily, sometimes even in a few steps, whereas after Bologna reform exams in Math and Chemistry became incredibly difficult..
MIT: here is entrance exam
This guy: this is for elementary school
Me: 10th grade me probably would have failed
So when can i get that "ceil(e)-floor(pi) = 0" sweater? Lol
I can't find it on your merch website
Here you go my son
How about "ceil(phi)-floor(e) = 0"
Or about "sqrt(ceil(e)-floor(pi)-floor(phi)) = i"
Good video!!
Thanks Ryan! :3
Awesome reactions to 57!
Haahah! You don't know how many times I've thought 57 was a prime number before I realized 3×19, it looks so prime-number-ish
exactly!!!
It's the 7
I misswrote too, I thought I had to find the solutions of 7x-5y=24 and then 4x-3y=11 bruh...
:'D
1869 ..... wow. That is a long time ago. My late grandfather was born 14 years later, 1883, and my late father was born in 1921.
damn ^^'
i think there were fewer people that trying to get into MIT back then, so the test is kinda easy, because the amount of people they need to eliminate was such a small number
sheesh: necessity .neq. sufficiency - you're definitely not getting into MIT and take some remedial sentential logic.
"57! Aww it's the best prime number. It's the only prime number that has two factors."
LOL so hardcore
:D
Let's go bois we all made it into MIT
8:23 my algebra 2 teacher didn't know to add another variable to decompose an equation like this. She also didn't know logarithmic division rules. She did teach us a fun song for the trig functions though 😂
I had my algebra 1 teacher teach me algebra 2 after school that year
13:10 AUßEN MAL AUßEN DURCH INNEN MAL INNEN
I realized I was zoning out for like 10 minutes just listening to your voice lmaooo. Have you considered doing asmr?
nah xD
Now he did!
You still can further decompose the x^3/(x^3-a^2y)
4:52
I bet I'm being an idiot here but when you took the square root of 9, why wouldn't it be ±3?
Edit: got an answer, it's the principal root
Or was it just assuming the principal root? That's probably it
@@anuragthakur4341 yes the radical symbol refers to the principal root. 9 itself has 2 square roots, as you pointed out. But the radical symbol only asks for one of them.
If you're solving an equation like x²=4, the solution will be x=±2, because both values satisfy the equation. But when you have a square root (or an even root) then it's only the positive value.
√9 = 3 always
@@Haru_k4 oh ok so you just take the principal root. Ok, thanks
@@chessandmathguy alright, got it!
That's literally Year 8 maths lol
Remember, they didn't have good calculators which could solve System of Equations in Row-Echelon Form.
it's so mind blowing
11:52 when you see your ex
Haha how do you even do that?