Just a very small point indeed but I loved the instruction at the start of the 2022 paper "Write legibly; otherwise you place yourself at a grave disadvantage."
They should make it an exam question: If each student must sit 12 papers, 2 papers per day, how many days would each student take to sit all assigned papers? [Note: do not use differential calculus in your answer.]
I can get from my house to senate house without a map. But after that it would all be down hill. Fortunately they don’t make you sit the maths tripos in order to work at the university! You’ll be glad to know I have nothing to do with numbers.
@@graememorrison333 Ha ha, same here. Started reading old maths text books from the beginning, at my own pace, at the start of the pandemic, and suddenly it's all starting to make sense.
I'm not from maths, but I've supervised some chemical engineering modules for undergrads as a PhD student. The tripos exam questions can appear overwhelming but, with enough practice, are certainly manageable. The trouble is, students have so much going on in their course -- supervisions, courseworks, computing classes, etc. -- that it can be really difficult for them to find a good learning pace.
I have no comprehension of literally anything that's being spoken of here. But the way Tibees explains it is hypnotic as hell. I love it, even if it makes me feel like the dunce in the room lol
I just did Part III last year. I came from another university and joined in the 4th year. It was honestly the most stressful thing I've ever done in my life. My average dropped from 95 percent to 70 percent.
I already knew that I was at my mathematical limit when I started Part III... As I had decided not to continue to a PhD, all the stress melted for me, though. It's a really interesting course going through current research topics - basically a shop front for picking your research area. I did pass the exam (probably I was a 40 percent student though!), but if I was under the pressure of wanting to continuing on to research, it probably would have broken me.
Thank you very much 🙏 You are making the world smaller and providing access to various knowledge which many(including me) wouldn't even know available.
That was a really nice video, thanks. My 2p worth (my background is that I took the Tripos and have taught undergraduates at Cambridge) is that the exam is actually pretty good now, and probably very unlike what it was 100 years ago in Hardy's time, or earlier, when you had to "put your mathematical life on hold" to do extensive speed training for a narrow form of questioning. IMHO the exam today does incentivise you to actually learn the syllabus material, which I think is the main merit of an exam - more important than classifying people at the end. And the syllabus material is good: if you understand it then you should have a good grasp of the subject. Most Tripos exam questions are of a certain form. They will first get you to state some piece of theory and maybe do something relatively straightforward with it, then they will ask you a more problem-solving-type question that relates to it to see if you've understood it more fully.
It's the toughest undergraduate Mathematics course in the World, not just in UK. The arguments against it are cogent and reasonable, but the bottom line is that many, many Cambridge Mathematicians consistently win the Fields medal and are usually in the top 1-5% greatest mathematicians of their respective generations. The Mathematics dept' at Cambs must be getting something right?
I think Michael Atiyah might have come first on his.
ปีที่แล้ว +15
@Tibees, at 0:14 you mention that the tripos comes in three parts. Those parts (for the mathematical tripos) would be Part I, II and III. Part I is split into IA and IB as you say and each run over one year. Thus Parts I and II run over three years and constitute a Bachelor's degree. Part III is optional and comes as the fourth year of the mathematical tripos, which constitutes a Master's degree. Different subjects may have a different partial structure to their corresponding triposes. This is clarified on the Wikipedia pages for Tripos and Mathematical Tripos.
Love the content. Thank you. Just shows how competitive old schooling system was. And the one and only goal for a successful candidate was a university professor.
Did my final year computer science exams June 2022. I spent the grueling revision months leading up to it in the library with a few friends, one of whom did maths. They hated their tripos for the exact reasons Hardy described: no time for genuine exploration of ideas, and a horribly gameified marking structure. (Compsci was similarly not great, but not as bad as maths.)
As an example of marking: questions are marked out of 20, if you get 15 or more then you get an 'alpha', netting you about 30 marks extra iirc. What this means is you can slightly mess up on a question, getting 14 marks, and miss out on more than tripling your marks. This crazy discontinuity is unnecessarily stressful and can be the difference between failing and getting a first for a very small incremental effort.
@@benmandrew I'm still in first year of the maths tripos, but I already have a feeling that alpha and beta marks are gonna become the bane of my existence. Our DOS was trying to explain them at the matriculation dinner, and eating a fancy meal, dressed up in gowns, while discussing the technicalities of maths examinations is still the most 'Cambridge' thing that's happened to me so far this year lol
@@malignusvonbottershnike563 There are proposals to smooth out the sharp transition between an alpha quality solution and a beta one. I think that proposal has a lot of support. Reform of Part II more generally is under discussion though there are some disagreements on the best way to proceed.
@@benmandrew I got a first in Lit Hum at Oxford - I am sure I would not have got one at Cambridge. One of my papers is even had a γ grade (my expertise in latin and greek i think actually declined while i was at oxford). It was just fortunate that I wrote one of the two best papers that year in schools in what I really loved studying- that was philosophy of language, semantics of natural language, the debate between realist and intuitionistic mathematics etc. (One of my teachers said that I was a monomaniac!)
I graduated fourth year in computer science last year, can agree Compsci wasn’t completely awful but still very tough! However looking at my mathmo friends’ papers gave me minor heart attacks each time I’d go in to chat!
Thank you for another fascinating video!!! I was particularly impressed by how meticulously you have researched this topic and not succumbing to the plethora of myths that exist, and how you have presented everything in the most intriguing way!!! Looking forward to more of your videos in the new year!!!
in maths it’s customary to denote things like sets and some vector spaces and the expected value function with blackboard font (the letters with doubles lines) and other objects to be written in cursive, so i hope that explains the font styles
Having recently played around with Bezier curves for the first time, I felt very clever when Tibees asked "What is a convex hull?" Granted my answer would most probably be deemed inadequate, but still!
Another interesting thing about the current tripos is the way that the marks are calculated (it involves 3 kinds of marks and different inequalities for different grade boundaries)
Toby's Video features some of the wealthiest colleges in the world. Trinity college is said to have been UK's largest land owner only after the government and the church. At one time you could travel from Cambridge to Oxford solely on land owned by Trinity college Cambridge.
The mechanical sciences (aka engineering) tripos in 1970 had 10 3 hour papers over five days - Monday to Friday. 6 hours of exams every day for five days in a row was quite tiring.
That doesn't happen these days (when I took the maths tripos, I would have four 3 hr papers over two days). With some students being allowed extra time, it has become impossible to schedule exams in the same way that you and I were used to.
@@0cgw Massive respect for someone who passed the maths tripos. At Trinity the maths guys were considered to have superior brains. I did double maths and physics at A level. I started to find maths difficult at third order PDEs. Until then it had been something like "that's obvious. What else could it be?" We got practise at taking exams. Starting in first year, we had two sets of exams every year - one before Christmas and one before the summer break. Each one had multiple 3 hour exams. I think that it was 10 * 3 hours each time. Fail one paper and you were out. Gone. As in don't come back next term.
This still happens, at least in my subject (Natural Sciences), depending on what combination of modules you pick. That one week of exams determined the vast majority of our final grade for each year, so there was a lot of pressure.
Ah, this takes me back. Interesting to see how the syllabus has changed since the 1980s. I remember grades being read out in the Senate House (it only happened in maths, not other subjects, where the class lists were pinned to a noticeboard). I'm not certain, but I believe tghat tradition is no more because of GDPR data legislation. I think nowadays, you only find out your own class, and not everyone else's - you only fid out someone else's grade if they tell you. So the reading in the Senate House, I believe, no longer happens. Part III, the optional 4th year, is a huge step up from Part II. I passed it, and that was a minor miracle!
ENS entrance exam is at the level of a 3rd year undergraduate not that of a high schooler (17+). French system is weird and confusing and it falls into the same Hardy's argument of a game rather than deep understanding.
Would be quite interesting to study history at a university like this, you're very much surrounded by it and the the research you could do would be endless.
In theory, yes. Cambridge is a sea of tranquility surrounded on all sides by history. Sadly, it’s also one of the wokest universities in Britain, which means the choice of permissible research topics is heavily circumscribed. Not as bad as most Ivy League colleges in the USA, however.
I solved section 1 To compute the continued fraction expansion of V29, we can use the following algorithm: 1. Set a_0 = floor(sqrt(29)) = 5. 2. Let x_0 = 29 and y_0 = 5. 3. For each integer k >= 1, compute a_k = floor((sqrt(x_{k-1}) + y_{k-1}) / (x_{k-1} - y_{k-1}^2)). 4. Compute x_k = (x_{k-1} - y_{k-1}^2) / a_k and y_k = a_k * x_k - y_{k-1}. 5. Repeat steps 3 and 4 until x_k = 1. The resulting continued fraction expansion of sqrt(29) is [5; 2, 1, 1, 2, 10]. To find integers z and y satisfying a^2 - 29y^2 = -1, we can use the theory of Pell equations. The fundamental solution to this equation is (a, y) = (5, 2). The general solution is given by: a_n + y_n sqrt(29) = (5 + 2sqrt(29))^n, where n is an integer. Therefore, we can find z and y by computing: a_n = (5 + 2sqrt(29))^n + (5 - 2sqrt(29))^n / 2, y_n = (5 + 2sqrt(29))^n - (5 - 2sqrt(29))^n / 2sqrt(29). For example, if we take n = 2, we get: a_2 = 169, y_2 = 39. Therefore, the integers z and y satisfying a^2 - 29y^2 = -1 are z = 169 and y = 39.
Dear Tibees All the Work you have done Has Transcended Math and Physics You are an Angel on this Earth Thank you for your Magnificent Effort I Hope you will Always have A Happiness in your Life Take Care my Friend
I am but a med school student, but exams are destroying my life continuously due to the enormous stress they impose, as well as the fact that they really do stagnate any path to personal growth. When you are faced with an exam as difficult as Tripos, you are NOT thinking about learning things or showing your mettle, you are thinking about just passing that exam. I would argue that G. H. Hardy had hit the cigar with his opinion on Tripos.
At least for medicine, fact-retention is significantly more relevant than in more creative/theoretical degrees, so examinations (I feel) are more relevant to the actual requirements of the job. I'm currently studying Engineering and the exams feel completely irrelevant to the work. I understand the necessity for knowing the maths/physics/chemistry fundamentals, but the questions are always phrased from the perspective of maths/physics/chemistry rather than engineering. i.e. "Use laplace transformations to solve the following second-order resonant ODEs" It's a maths question that's relevant to my overall understanding, but it isn't applied to any real world situation, so if I encounter a future situation in my future job where I may need to use a laplace transform then the exam questions haven't tested me on making the connection between problem->laplace. It's not a very good example, but I feel like this is probably a shared situation with a lot of different degrees. Now that google exists and software can and will do the majority of heavy lifting in calculations, surely the ability to identify the process of solving an overall problem is far more important than the ability to just solve individual equations. Yet exam questions seem to focus primarily on the latter. Anyway, rant over. I've just finished my exams so I'm angry 😂
@@caryoulwhitty - My hat’s off to you either way. A very difficult job. Remember the stress of uni exams acutely. Always thought, surely there’s a better way…
I took this in 1993. Hardest thing I've ever done, to this day. Interestingly, the "describe the ... method" or "prove the ... theorem" are, in my opinion, easier, as you can memorise the answers in advance!
Just practice and take your time, I hope you get the support you need. University mathematics is not like secondary school/college mathematics, it can quickly become a beast and you need to tame the beast. I recommend looking into useful textbooks/research papers and just grind problems, keep on writing a proof/theorem until it makes sense and find real world applications of those proofs/theorems to see why it works and how it can be applied. Another thing that helped me is using a programming language to do maths and investigating numerical methods. I didn’t go to Cambridge, but I know your frustrations and can relate to you. You will pull through, all your hard work will be worth it I believe in you.
You can take a look at the hardest french maths exam : Maths D ENS ULM. I think It's the hardest maths exam in the world for people with just two years of post-highschool studies. It's a special exam to enter ENS ULM in Paris (école normale supérieure), a very little university which has produced thirteen Fields Medals.
@@tb8183 A levels started covering less material, and so people were not entering with such a high standard. The tripos therefore contained more basic material at the sacrifice of more difficult content. That's one reason.
Hardy sums up exams nicely. Also bear in mind that a good examiner can test understanding over rote by clever question design. Alas, many examiners are stuck in a one time mindset and set the same style year after year and, in my experience with English maths papers, they keep those posts for decades .. groan. If you want to see questions that are a little more probing but far more fun, look at the UKMT challenge papers.
There was a tale about a history professor who was criticised for setting the same question every year, and his response was that it didn't matter, because they changed the answers.
James Maxwell was Secoind Wrangler in the Tripos, beaten by Peter Guthrie Tait who went on to be a professor of mathematics but no-one outside a small group has ever heard of him. Hardy wanted to do away with the Tripos. There has been a little industry in coaching for the Tripos going back to the 19th century.
Oh yeah I had to use the Navier-Stokes fluid mecanics equation in my exam this year. Funny to find the Stokes name in this video indeed. This channel looks great by the way.
It's a mathematics olympiad in essence. And Hardy was right: pursuing the Tripos allows no time for a person to develop as a mathematician. Only later does that come.
Such exams are useful for testing what knowledge was gained, and to check understanding of principles, topics, and mathematical rigour by asking for proofs to be derived, but beyond that it does not help the student to necessarily THINK independently, form new and interesting concepts, apply what they learned to new problems, or even challenge the status quo. One thing I found as a student of mathematics is it helped me to think analytically about problems and problem-solving, but it didn't turn me into a mathematical genius. I wouldn't even consider myself average, and studied as a "mature student" for my own interest/benefit rather than for the purpose of obtaining a job requiring heavy use of advanced mathematical concepts. IMHO, the people who go on to be the "heavy weights" in such disciplines were already destined to do so, regardless of their academic background.
One of the arguments against a high-pressure exam like this which students take a year or two to prepare for is that it uses up the best years of their lives when they could be getting to grips with the growing points in their field. It seems that no one discovers (or invents) anything really ground-breaking in pure maths much after the age of 25: so a Senior Wrangler has limited time to do his stuff. Other countries have this sort of exam, calling for expertise in quickly answering trick questions, placed at the entry point to engineering courses in India and China and for the Grandes Écoles in France. As most candidates fail to get through, it's a great waste of time and effort for them. Unfortunately academics gain prestige from keeping people out, which is not what we need them to do.
Hardy war right. Competitiveness is the human feature that should be transferred to the whole sphere of education, not everyone is interested in the competition, and not everyone is motivated by it. for many, this simply prevents them from understanding the subject in their own way.
Ranked above the Senior Wrangler, but not awarded the title? That's some advanced misogyny right there. I hope the official awardee was teased as the Senior Male Wrangler for all of his days.
All through school, college and university I felt that examinations were not a good measure of understanding or intelligence. I much preferred coursework and my dissertation as I think the time pressure of an exam creates anxiety that negatively affects performance.
they are to a certain point I would say from 20% to 70% scores you can find out understanding but beyond that it isn't about understanding but preforming, computations, and memorization (though I would except proofs and some harder logic problems than it is just iq/not being a genius)
My prof criticized me for gaming past exam papers, then went on to put in questions we never talked about in the course into the exams. Testing for originality is intrinsically oxymoronic, don’t you think?
I checked out the 2022 Tripos Part 2 paper. The only things I understood were 1) what the questions in Section 1I Number Theory were asking for (expand sqrt(29) into fractions, and solve for x and y in x^2 - 29y^2 = -1); and 2) come up with the mathematical equation that produced the results displayed by the two questions with the R code. Everything else is Greek to me.
Competitive unreasonably hard exams are really games as Hardy said. It tests one's ability to cram, endure and digest before one's knowledge and ability to level up in one's studies. They are for me gates and obstacles meant to filter out and not to evaluate and open the next door. Slow learners, those who cant keep up with the race, those who need breaks, have mental health issues, some sort of instability are discarded actually. Those traditions hardy talked about are rooted in elitism, and the desire to pick the bright and throw away those who didnt perform. Education should be about helping everyone improve and evolve and not sorting and discarding. In my country we are still obsessed with ranking and being the best. I have always felt and seen the system pushing out any struggling student instead of helping them. Those who cant play the game are punished and their chances of a good education are put in jeopardy. I feel it stems from elistim, scarcity, maybe capitalism and the obsession with productivity. And ofc socio-economic conditions and the ability to afford tutoring play a determining role in ranking well.
Can you please make a video about the Romanian graduation exam in Maths? In 2012, more than half of the graduates failed to pass that exam. I'm curious what you think about it.
5:12 - Reminds me of the time when I got my only D... Which was when the class averaged an F per the "usual" cutoffs. Wonder if it's kinda standard for higher math exams?
It looks like a much longer, and somewhat more academic, version of the Putnam Exam (which was probably modeled on it). Certainly there isn't a strong correlation between being a Putnam winner and being a first-rate mathematician - all the people I knew, even as undergrads, recognized it was a game which was irrelevant to your career in math. However, the Putnam is entirely optional and isn't given by your school, so you can do it or not without being judged (several of the best mathematicians I know never took it). At least this exam appeared to be aimed at a curriculum, which would encourage people to learn a subject instead of a bag 'techniques' (which is a weakness of the Putnam). It wasn't clear if the current Tripos is the same endurance test as the older ones, but if you're trying to sort people, which is one of the goals of a competitive exam, you have to do it somehow, and making it impossible to finish it the easiest way. The trouble with this approach is you measure speed, which isn't the most important quality in the real world.
Your social media posts are so very interesting. Thank you for your efforts. I think it would be great to be friends with you socially. Keep up the good work!
I am a Mathematics Director of Studies for the Tripos, and supervise (i.e., teach) many over 20 courses in the Tripos. The tripos has be reformed many times since Hardy's day, but Part III remains one of the hardest courses of its type in the word. Part II exams now have section I and section II questions. Section I questions are designed to be answerable by any student that has diligently studied the material, whereas section II include more demanding questions. Section I questions should take roughly 15 minutes and section II ones twice that time. Your information about the reading out of class is outdated. Due to a campaign lead by the student union (but seemingly without much support from mathematics students), the reading of class lists on the Thursday of May week has been discontinued. The argument is that the students results are private information not to be seen by other members of the university (or those outside). It is a sad development, as the public recognition of the students' hard work is now not recognized.
Excellent report. Could you say a few things about probability theory and maybe discuss the central limit theorem, and why didn't the central limit theorem appear earlier, and when had mathematics progressed far enough for the central limit theorem to have appeared. Also, do you have a Germanic relative in your heritage ? Your voice is very soothing.
Some of the questions were quite difficult, but at least the one on Automata and Formal Languages (at 1:13) was pretty straight-forward. The first questions are just basic definitions, and as for G1 and G2, they produce almost the same languages, except that G1 can produce an empty word, whereas G2 cannot. You can see the equivalence by noting that in G2, X and Y just produce single letters, so you can replace the X's and Y's with a's and b's. Then, replace Z by Ta, and you get S -> aTa | bTa, T -> Ta | Tb | c, which is nearly the same as G1, except for the e (empty).
That question’s from the first section which are meant to take 10 mins or less. The second section’s where the harder questions and most of the marks are.
Tobi, I hope you'll talk aboutf the notoriously difficult Lev Landau's "Theoretical Minimum" test for young theoretical physicists. I believe they had to pass this test to start a doctorate in his department. And also take an exam at one of the elite french institutions the Ecole Normale Supérieure and the Ecole Polytechnique.
No it shouldn't be abolished. Human beings are naturally competitive and will always find a way to rank themselves against their peers. If you take away the exam people will either find another way to compete and prove themselves the best, or else lose direction, motivation and interest and move to a different area of study which provides that competitive thrill.
![[LIVE] : ONE ลุมพินี 88 | คู่เอก "ป้อมเพชร vs อัสลามจอน"](http://i.ytimg.com/vi/1ZqTVVbMgbo/mqdefault.jpg)
Just a very small point indeed but I loved the instruction at the start of the 2022 paper "Write legibly; otherwise you place yourself at a grave disadvantage."
Very British humour.
@@shastasilverchairsg I know it's taken as humour today, but back then the author might have meant it with no humour.
@@oatmongen4263 "Back then" was last year. The instruction is on the 2022 paper 🙂
@@prh47bridge Oh.
That was a bit silly of me.
@@shastasilverchairsg Why is it humour? It's just good advice.
4:32 "There are 12 papers to be taken, 2 a day, for 6 days"
That part I could just about follow
They should make it an exam question:
If each student must sit 12 papers, 2 papers per day, how many days would each student take to sit all assigned papers? [Note: do not use differential calculus in your answer.]
I can get from my house to senate house without a map. But after that it would all be down hill. Fortunately they don’t make you sit the maths tripos in order to work at the university! You’ll be glad to know I have nothing to do with numbers.
2 by 6 equals 12 ?.
@@liamhickey359 That's one of the exam questions. 😊
@@vk2ig did I get that right?
Hardy's comments really resonated.
I used to joke that it was only after I had graduated that I finally had the chance to build any understanding!
Me: still revisiting stuff I really only half understood in my physics from thirty five years ago!
yup, i'm planning on consolidating my understanding only after graduation
@@graememorrison333 Ha ha, same here. Started reading old maths text books from the beginning, at my own pace, at the start of the pandemic, and suddenly it's all starting to make sense.
I'm not from maths, but I've supervised some chemical engineering modules for undergrads as a PhD student. The tripos exam questions can appear overwhelming but, with enough practice, are certainly manageable. The trouble is, students have so much going on in their course -- supervisions, courseworks, computing classes, etc. -- that it can be really difficult for them to find a good learning pace.
I have no comprehension of literally anything that's being spoken of here. But the way Tibees explains it is hypnotic as hell. I love it, even if it makes me feel like the dunce in the room lol
At least you don't have to pose with a giant wooden spoon. 😆
It's called ASMwhatRyoutalkingabout?
@@astewartau he looks so proud and so would I be lol. He still passed the exam, and got some decent banter out of it
👍🏻 I agree
You are all overthinking it , she is just explaining basic mathematics concepts. Nothing more , nothing less.
I just did Part III last year. I came from another university and joined in the 4th year. It was honestly the most stressful thing I've ever done in my life. My average dropped from 95 percent to 70 percent.
well done, I think that's still a distinction! I wasn't good enough for part III. I went on to do the now defunct diploma in computer science.
Dude, that’s so good! Congrats, pal!!
Hey Jarah, it was rough for me too, but a 70 is still fantastic. It's an achievement to have just made it through in one piece.
You've got a big brain, most people couldn't even hack a bottom tier maths undergraduate degree.
I already knew that I was at my mathematical limit when I started Part III... As I had decided not to continue to a PhD, all the stress melted for me, though. It's a really interesting course going through current research topics - basically a shop front for picking your research area. I did pass the exam (probably I was a 40 percent student though!), but if I was under the pressure of wanting to continuing on to research, it probably would have broken me.
Thank you very much 🙏
You are making the world smaller and providing access to various knowledge which many(including me) wouldn't even know available.
That was a really nice video, thanks. My 2p worth (my background is that I took the Tripos and have taught undergraduates at Cambridge) is that the exam is actually pretty good now, and probably very unlike what it was 100 years ago in Hardy's time, or earlier, when you had to "put your mathematical life on hold" to do extensive speed training for a narrow form of questioning.
IMHO the exam today does incentivise you to actually learn the syllabus material, which I think is the main merit of an exam - more important than classifying people at the end. And the syllabus material is good: if you understand it then you should have a good grasp of the subject.
Most Tripos exam questions are of a certain form. They will first get you to state some piece of theory and maybe do something relatively straightforward with it, then they will ask you a more problem-solving-type question that relates to it to see if you've understood it more fully.
Your videos never fail to intrigue me. They are so well made a thought out. Thanks for the great content and keep up the amazing work!
Si. Esattamente come Karrie ldd 88 . It's a coaching.
I love that you're exploring different countries' tests. Will you look into french exams in the future?
It's the toughest undergraduate Mathematics course in the World, not just in UK. The arguments against it are cogent and reasonable, but the bottom line is that many, many Cambridge Mathematicians consistently win the Fields medal and are usually in the top 1-5% greatest mathematicians of their respective generations. The Mathematics dept' at Cambs must be getting something right?
That's impressive
I think Michael Atiyah might have come first on his.
@Tibees, at 0:14 you mention that the tripos comes in three parts. Those parts (for the mathematical tripos) would be Part I, II and III. Part I is split into IA and IB as you say and each run over one year. Thus Parts I and II run over three years and constitute a Bachelor's degree. Part III is optional and comes as the fourth year of the mathematical tripos, which constitutes a Master's degree. Different subjects may have a different partial structure to their corresponding triposes. This is clarified on the Wikipedia pages for Tripos and Mathematical Tripos.
ISTR that, originally, the term "tripos" is a reference the three-legged stools on which students traditionally sat.
Love the content. Thank you. Just shows how competitive old schooling system was. And the one and only goal for a successful candidate was a university professor.
Everything she says goes above my level of comprehension by far, but her voice and speaking is so soothing!
Lol!!!!!
Did my final year computer science exams June 2022. I spent the grueling revision months leading up to it in the library with a few friends, one of whom did maths. They hated their tripos for the exact reasons Hardy described: no time for genuine exploration of ideas, and a horribly gameified marking structure. (Compsci was similarly not great, but not as bad as maths.)
As an example of marking: questions are marked out of 20, if you get 15 or more then you get an 'alpha', netting you about 30 marks extra iirc. What this means is you can slightly mess up on a question, getting 14 marks, and miss out on more than tripling your marks. This crazy discontinuity is unnecessarily stressful and can be the difference between failing and getting a first for a very small incremental effort.
@@benmandrew I'm still in first year of the maths tripos, but I already have a feeling that alpha and beta marks are gonna become the bane of my existence. Our DOS was trying to explain them at the matriculation dinner, and eating a fancy meal, dressed up in gowns, while discussing the technicalities of maths examinations is still the most 'Cambridge' thing that's happened to me so far this year lol
@@malignusvonbottershnike563 There are proposals to smooth out the sharp transition between an alpha quality solution and a beta one. I think that proposal has a lot of support. Reform of Part II more generally is under discussion though there are some disagreements on the best way to proceed.
@@benmandrew I got a first in Lit Hum at Oxford - I am sure I would not have got one at Cambridge. One of my papers is even had a γ grade (my expertise in latin and greek i think actually declined while i was at oxford). It was just fortunate that I wrote one of the two best papers that year in schools in what I really loved studying- that was philosophy of language, semantics of natural language, the debate between realist and intuitionistic mathematics etc. (One of my teachers said that I was a monomaniac!)
I graduated fourth year in computer science last year, can agree Compsci wasn’t completely awful but still very tough! However looking at my mathmo friends’ papers gave me minor heart attacks each time I’d go in to chat!
Happy New Year Toby. Your videos are terrific. Makes one's mind think. Thank you. 👍
Thank you for another fascinating video!!! I was particularly impressed by how meticulously you have researched this topic and not succumbing to the plethora of myths that exist, and how you have presented everything in the most intriguing way!!! Looking forward to more of your videos in the new year!!!
Why do they use so many different font styles in sentences? And the paragraphs make it even harder to read. Just my opinion.
in maths it’s customary to denote things like sets and some vector spaces and the expected value function with blackboard font (the letters with doubles lines) and other objects to be written in cursive, so i hope that explains the font styles
Having recently played around with Bezier curves for the first time, I felt very clever when Tibees asked "What is a convex hull?"
Granted my answer would most probably be deemed inadequate, but still!
Another interesting thing about the current tripos is the way that the marks are calculated (it involves 3 kinds of marks and different inequalities for different grade boundaries)
Toby's Video features some of the wealthiest colleges in the world. Trinity college is said to have been UK's largest land owner only after the government and the church. At one time you could travel from Cambridge to Oxford solely on land owned by Trinity college Cambridge.
The mechanical sciences (aka engineering) tripos in 1970 had 10 3 hour papers over five days - Monday to Friday. 6 hours of exams every day for five days in a row was quite tiring.
That doesn't happen these days (when I took the maths tripos, I would have four 3 hr papers over two days). With some students being allowed extra time, it has become impossible to schedule exams in the same way that you and I were used to.
@@0cgw Massive respect for someone who passed the maths tripos. At Trinity the maths guys were considered to have superior brains. I did double maths and physics at A level. I started to find maths difficult at third order PDEs. Until then it had been something like "that's obvious. What else could it be?"
We got practise at taking exams. Starting in first year, we had two sets of exams every year - one before Christmas and one before the summer break. Each one had multiple 3 hour exams. I think that it was 10 * 3 hours each time. Fail one paper and you were out. Gone. As in don't come back next term.
This still happens, at least in my subject (Natural Sciences), depending on what combination of modules you pick. That one week of exams determined the vast majority of our final grade for each year, so there was a lot of pressure.
This exam is not letting you memorise math but prove the formulas you claim to know.Difficult but immaculate.
Ah, this takes me back. Interesting to see how the syllabus has changed since the 1980s. I remember grades being read out in the Senate House (it only happened in maths, not other subjects, where the class lists were pinned to a noticeboard). I'm not certain, but I believe tghat tradition is no more because of GDPR data legislation. I think nowadays, you only find out your own class, and not everyone else's - you only fid out someone else's grade if they tell you. So the reading in the Senate House, I believe, no longer happens. Part III, the optional 4th year, is a huge step up from Part II. I passed it, and that was a minor miracle!
At Oxford the noticeboard malarkey is still in place
Great job, guys 😂😂
Great piece of history. Nice work.
Keep up the informative videos, Toby 👍
Hello, you should take a look at the ENS Ulm maths entrance exam. Its difficulty would probably dwarf everything you've ever presented.
ENS entrance exam is at the level of a 3rd year undergraduate not that of a high schooler (17+). French system is weird and confusing and it falls into the same Hardy's argument of a game rather than deep understanding.
Would be quite interesting to study history at a university like this, you're very much surrounded by it and the the research you could do would be endless.
In theory, yes. Cambridge is a sea of tranquility surrounded on all sides by history. Sadly, it’s also one of the wokest universities in Britain, which means the choice of permissible research topics is heavily circumscribed. Not as bad as most Ivy League colleges in the USA, however.
@@sirrathersplendid4825 you sound goofy
@@vilteb4701 ??? My teeth are very straight.
@Retired Bore - Trinity College on its own has garnered 32 Nobel prizes, more than many European nations.
I solved section 1
To compute the continued fraction expansion of V29, we can use the following algorithm:
1. Set a_0 = floor(sqrt(29)) = 5.
2. Let x_0 = 29 and y_0 = 5.
3. For each integer k >= 1, compute a_k = floor((sqrt(x_{k-1}) + y_{k-1}) / (x_{k-1} - y_{k-1}^2)).
4. Compute x_k = (x_{k-1} - y_{k-1}^2) / a_k and y_k = a_k * x_k - y_{k-1}.
5. Repeat steps 3 and 4 until x_k = 1.
The resulting continued fraction expansion of sqrt(29) is [5; 2, 1, 1, 2, 10].
To find integers z and y satisfying a^2 - 29y^2 = -1, we can use the theory of Pell equations. The fundamental solution to this equation is (a, y) = (5, 2). The general solution is given by:
a_n + y_n sqrt(29) = (5 + 2sqrt(29))^n,
where n is an integer. Therefore, we can find z and y by computing:
a_n = (5 + 2sqrt(29))^n + (5 - 2sqrt(29))^n / 2,
y_n = (5 + 2sqrt(29))^n - (5 - 2sqrt(29))^n / 2sqrt(29).
For example, if we take n = 2, we get:
a_2 = 169, y_2 = 39.
Therefore, the integers z and y satisfying a^2 - 29y^2 = -1 are z = 169 and y = 39.
I'm sorry. But the correct answer was, yellow.
Dear Tibees
All the Work you have done
Has Transcended Math and Physics
You are an Angel on this Earth
Thank you for your Magnificent Effort
I Hope you will Always have
A Happiness in your Life
Take Care my Friend
Thank you
Take Care
I am but a med school student, but exams are destroying my life continuously due to the enormous stress they impose, as well as the fact that they really do stagnate any path to personal growth. When you are faced with an exam as difficult as Tripos, you are NOT thinking about learning things or showing your mettle, you are thinking about just passing that exam.
I would argue that G. H. Hardy had hit the cigar with his opinion on Tripos.
I think the stress is part of the point. If you can hack the exams you should manage pretty well in real life.
At least for medicine, fact-retention is significantly more relevant than in more creative/theoretical degrees, so examinations (I feel) are more relevant to the actual requirements of the job.
I'm currently studying Engineering and the exams feel completely irrelevant to the work. I understand the necessity for knowing the maths/physics/chemistry fundamentals, but the questions are always phrased from the perspective of maths/physics/chemistry rather than engineering.
i.e. "Use laplace transformations to solve the following second-order resonant ODEs"
It's a maths question that's relevant to my overall understanding, but it isn't applied to any real world situation, so if I encounter a future situation in my future job where I may need to use a laplace transform then the exam questions haven't tested me on making the connection between problem->laplace. It's not a very good example, but I feel like this is probably a shared situation with a lot of different degrees.
Now that google exists and software can and will do the majority of heavy lifting in calculations, surely the ability to identify the process of solving an overall problem is far more important than the ability to just solve individual equations. Yet exam questions seem to focus primarily on the latter.
Anyway, rant over. I've just finished my exams so I'm angry 😂
@@sirrathersplendid4825 False. Being responsible for a ward of patients is an entirely different type of stress
@@caryoulwhitty - My hat’s off to you either way. A very difficult job. Remember the stress of uni exams acutely. Always thought, surely there’s a better way…
I took this in 1993. Hardest thing I've ever done, to this day.
Interestingly, the "describe the ... method" or "prove the ... theorem" are, in my opinion, easier, as you can memorise the answers in advance!
Yes, those are questions that involve knowledge in your answers, so by studying the answers you will be advantaged
Thank you ma'am for the information 🙂🙂
I got as far as learning trigonometry before I reached my limit in math. This material is well beyond my comprehension.
Thanks for sharing ❤️❤️❤️
Terry Pratchett must've known about the Senior Wrangler title, given the same title at Unseen University in the Discworld books.
"Prestige" should not be used as the basis for any decision.
Did 1st year cambridge maths exams couple of months ago. Flopped it and felt like crying… most stressful moment of my life bar none
same same cam is way stressful :(( good luck this year!
we're friend
Just practice and take your time, I hope you get the support you need. University mathematics is not like secondary school/college mathematics, it can quickly become a beast and you need to tame the beast. I recommend looking into useful textbooks/research papers and just grind problems, keep on writing a proof/theorem until it makes sense and find real world applications of those proofs/theorems to see why it works and how it can be applied. Another thing that helped me is using a programming language to do maths and investigating numerical methods.
I didn’t go to Cambridge, but I know your frustrations and can relate to you. You will pull through, all your hard work will be worth it I believe in you.
@Thawne could u elaborate? i'm not sure i know what u mean
@Thawne just read over notes and do lots of past papers i guess :00 are you a first year? :))
You can take a look at the hardest french maths exam : Maths D ENS ULM. I think It's the hardest maths exam in the world for people with just two years of post-highschool studies. It's a special exam to enter ENS ULM in Paris (école normale supérieure), a very little university which has produced thirteen Fields Medals.
So many ppl have commented on jre shorts about the bee lady's voice but Tibees has the MOST soothing voice I've ever heard.
Tibees or Eric Rosen are my go-to bedtime channels… If I fall asleep listening to them I somehow seem to wake up smarter 😅
@@rcnhsuailsnyfiue2 You actually will according to neuroscience. That in-between state is a great place to subconsciously program information 🧠
The undergraduate Tripos peaked in difficulty around 1970.
Why so?
@@tb8183 A levels started covering less material, and so people were not entering with such a high standard. The tripos therefore contained more basic material at the sacrifice of more difficult content. That's one reason.
Hardy sums up exams nicely. Also bear in mind that a good examiner can test understanding over rote by clever question design. Alas, many examiners are stuck in a one time mindset and set the same style year after year and, in my experience with English maths papers, they keep those posts for decades .. groan. If you want to see questions that are a little more probing but far more fun, look at the UKMT challenge papers.
There was a tale about a history professor who was criticised for setting the same question every year, and his response was that it didn't matter, because they changed the answers.
I did that in the early eighties. Great to find out more about it.
Thankyou TIBEES for such a amazing video
James Maxwell was Secoind Wrangler in the Tripos, beaten by Peter Guthrie Tait who went on to be a professor of mathematics but no-one outside a small group has ever heard of him. Hardy wanted to do away with the Tripos. There has been a little industry in coaching for the Tripos going back to the 19th century.
In 1841 all the Time is for Mathematics; today We Are poisoning by Phone, Tablet, >>> and many >>>>
At 7:41 Hardy is talking about Littlewood. Littlewood's strategy worked - he was Senior Wrangler and his career was not prejudiced.
These insanely obscure and difficult questions read by Tibees are perfect background noise while I do my Entry Level College Statistics homework :)
Oh yeah I had to use the Navier-Stokes fluid mecanics equation in my exam this year. Funny to find the Stokes name in this video indeed. This channel looks great by the way.
I love these vid's, hope your well Tobi and wishing you a great new year.
It's a mathematics olympiad in essence. And Hardy was right: pursuing the Tripos allows no time for a person to develop as a mathematician. Only later does that come.
I'm curious how this compares with the kind of exams you would encounter at places like Stanford or MIT.
And Caltech
American graduate level exams are totally rubbish.
@@electrocademyofficial893 Thanks...interesting.
@@electrocademyofficial893 But Harvard/MIT doesn't have Masters programmes as far as I know.
@@electrocademyofficial893 I see. Moreover, Oxford OMMS is also quite rigorous like Part III (I am not sure btw).
I have a few skills, which I'm rather proud of, but after watching this I've come to the conclusion that, good lord, I can barely human...
Such exams are useful for testing what knowledge was gained, and to check understanding of principles, topics, and mathematical rigour by asking for proofs to be derived, but beyond that it does not help the student to necessarily THINK independently, form new and interesting concepts, apply what they learned to new problems, or even challenge the status quo.
One thing I found as a student of mathematics is it helped me to think analytically about problems and problem-solving, but it didn't turn me into a mathematical genius. I wouldn't even consider myself average, and studied as a "mature student" for my own interest/benefit rather than for the purpose of obtaining a job requiring heavy use of advanced mathematical concepts.
IMHO, the people who go on to be the "heavy weights" in such disciplines were already destined to do so, regardless of their academic background.
Why will anyone take themselves through this....its like mental torture 😫
One of the arguments against a high-pressure exam like this which students take a year or two to prepare for is that it uses up the best years of their lives when they could be getting to grips with the growing points in their field. It seems that no one discovers (or invents) anything really ground-breaking in pure maths much after the age of 25: so a Senior Wrangler has limited time to do his stuff.
Other countries have this sort of exam, calling for expertise in quickly answering trick questions, placed at the entry point to engineering courses in India and China and for the Grandes Écoles in France. As most candidates fail to get through, it's a great waste of time and effort for them. Unfortunately academics gain prestige from keeping people out, which is not what we need them to do.
So now I know why there is a Philippa Fawcett Drive on the West Site in Cambridge. Thank you!
Hardy war right. Competitiveness is the human feature that should be transferred to the whole sphere of education, not everyone is interested in the competition, and not everyone is motivated by it. for many, this simply prevents them from understanding the subject in their own way.
Ranked above the Senior Wrangler, but not awarded the title? That's some advanced misogyny right there. I hope the official awardee was teased as the Senior Male Wrangler for all of his days.
All through school, college and university I felt that examinations were not a good measure of understanding or intelligence. I much preferred coursework and my dissertation as I think the time pressure of an exam creates anxiety that negatively affects performance.
they are to a certain point I would say from 20% to 70% scores you can find out understanding but beyond that it isn't about understanding but preforming, computations, and memorization (though I would except proofs and some harder logic problems than it is just iq/not being a genius)
Hey Tibees, Loved the video. Could you make a video about Scottish Exams especially the "Advanced Higher Maths" taken by highschool students 👍
Excellent video!
2:25 "Ruddy maker" 😂 sorry but that one got me for some reason.
that real analysis question was way harder than anything I had to do for my real analysis classes.
SAT-01/07/23@USA PACIFIC@701PM
DEARIO TOBIO,
THE UK TRIPOS IS FRIGHTENING,...
SAVED ONLY BY THE THRILLING
MUSICALITY OF YOUR VOICE...
BOWED
....wr...
Thanks!
My prof criticized me for gaming past exam papers, then went on to put in questions we never talked about in the course into the exams. Testing for originality is intrinsically oxymoronic, don’t you think?
Hardy's point was that no one could show be expected to show originality under exam conditions.
@Thawne If Hardy thought it couldn't be shown, it hardly matters what exactly it was that he meant wouldn't be there.
I checked out the 2022 Tripos Part 2 paper. The only things I understood were 1) what the questions in Section 1I Number Theory were asking for (expand sqrt(29) into fractions, and solve for x and y in x^2 - 29y^2 = -1); and 2) come up with the mathematical equation that produced the results displayed by the two questions with the R code. Everything else is Greek to me.
Competitive unreasonably hard exams are really games as Hardy said. It tests one's ability to cram, endure and digest before one's knowledge and ability to level up in one's studies. They are for me gates and obstacles meant to filter out and not to evaluate and open the next door.
Slow learners, those who cant keep up with the race, those who need breaks, have mental health issues, some sort of instability are discarded actually.
Those traditions hardy talked about are rooted in elitism, and the desire to pick the bright and throw away those who didnt perform.
Education should be about helping everyone improve and evolve and not sorting and discarding.
In my country we are still obsessed with ranking and being the best. I have always felt and seen the system pushing out any struggling student instead of helping them.
Those who cant play the game are punished and their chances of a good education are put in jeopardy.
I feel it stems from elistim, scarcity, maybe capitalism and the obsession with productivity. And ofc socio-economic conditions and the ability to afford tutoring play a determining role in ranking well.
Your voice is so ridoncolously soothing 😴 and I mean it in a good way
You should also take a look at the defunct Cei part2 endineering papers. These were set at degree level but were set and assessed externally.
I like the way you speak, so calming….
All souls fellowship exam is considered the toughest exam in the world, not just the UK. It is the fellowship (entry) exam for all souls Oxford.
thanks for your way to put talent and performance in debatable perspective
I failed it...wait no, that was my highschool GCSEs
Can you please make a video about the Romanian graduation exam in Maths? In 2012, more than half of the graduates failed to pass that exam. I'm curious what you think about it.
1:40 “show that the closed universe cannot expand forever” 😂😂😂 aight yeah lemme just become a god real quick
6:14 i thought i recognized the name! i believed stokes shift in fluorescence spectroscopy is named after him as well.
5:12 - Reminds me of the time when I got my only D... Which was when the class averaged an F per the "usual" cutoffs. Wonder if it's kinda standard for higher math exams?
It looks like a much longer, and somewhat more academic, version of the Putnam Exam (which was probably modeled on it). Certainly there isn't a strong correlation between being a Putnam winner and being a first-rate mathematician - all the people I knew, even as undergrads, recognized it was a game which was irrelevant to your career in math. However, the Putnam is entirely optional and isn't given by your school, so you can do it or not without being judged (several of the best mathematicians I know never took it). At least this exam appeared to be aimed at a curriculum, which would encourage people to learn a subject instead of a bag 'techniques' (which is a weakness of the Putnam). It wasn't clear if the current Tripos is the same endurance test as the older ones, but if you're trying to sort people, which is one of the goals of a competitive exam, you have to do it somehow, and making it impossible to finish it the easiest way. The trouble with this approach is you measure speed, which isn't the most important quality in the real world.
Is a negative score possible because then I think I would find my score there.
Your social media posts are so very interesting. Thank you for your efforts. I think it would be great to be friends with you socially. Keep up the good work!
I am a Mathematics Director of Studies for the Tripos, and supervise (i.e., teach) many over 20 courses in the Tripos. The tripos has be reformed many times since Hardy's day, but Part III remains one of the hardest courses of its type in the word. Part II exams now have section I and section II questions. Section I questions are designed to be answerable by any student that has diligently studied the material, whereas section II include more demanding questions. Section I questions should take roughly 15 minutes and section II ones twice that time.
Your information about the reading out of class is outdated. Due to a campaign lead by the student union (but seemingly without much support from mathematics students), the reading of class lists on the Thursday of May week has been discontinued. The argument is that the students results are private information not to be seen by other members of the university (or those outside). It is a sad development, as the public recognition of the students' hard work is now not recognized.
Kind of silly. Surely they could read out the top ten, or at a minimum, the top three places along with their scores.
What is up with that maths of ML question? It seems like it's all bookwork and no rider - is that a thing now?
Gangster outro tibee 😎
Excellent report.
Could you say a few things about probability theory and maybe discuss the central limit theorem, and why didn't the central limit theorem appear earlier, and when had mathematics progressed far enough for the central limit theorem to have appeared.
Also, do you have a Germanic relative in your heritage ?
Your voice is very soothing.
Thank you...Good clip....
Some of the questions were quite difficult, but at least the one on Automata and Formal Languages (at 1:13) was pretty straight-forward. The first questions are just basic definitions, and as for G1 and G2, they produce almost the same languages, except that G1 can produce an empty word, whereas G2 cannot. You can see the equivalence by noting that in G2, X and Y just produce single letters, so you can replace the X's and Y's with a's and b's. Then, replace Z by Ta, and you get S -> aTa | bTa, T -> Ta | Tb | c, which is nearly the same as G1, except for the e (empty).
I understood some of these words
That question’s from the first section which are meant to take 10 mins or less. The second section’s where the harder questions and most of the marks are.
Very informative and nice channel
I have a tough question: how many ways can I map 5 equidistant points onto the 16 faces of a hypercube?
Your voice is impressively relaxing me.
Engineers/Mathematicians in the earlier times were something else.
Tobey is an angel )))
this really puts the asmr in smart.
Any tips for acoustic geometry? I've been counting vibrations per second and looking for patterns.
10 days until I find out if I have been offered for a place to do the mathematical tripos at cambridge :( perfect timing!
I remember writing cambridge primary checkpoint exams it was so difficult and tricky.
Tobi, I hope you'll talk aboutf the notoriously difficult Lev Landau's "Theoretical Minimum" test for young theoretical physicists. I believe they had to pass this test to start a doctorate in his department.
And also take an exam at one of the elite french institutions the Ecole Normale Supérieure and the Ecole Polytechnique.
Long time fan of yours..... when you decide to move on from math (or maybe never, lol), you should do voice-over work - just love listening to you.
No it shouldn't be abolished. Human beings are naturally competitive and will always find a way to rank themselves against their peers. If you take away the exam people will either find another way to compete and prove themselves the best, or else lose direction, motivation and interest and move to a different area of study which provides that competitive thrill.
Your voice is so soothing