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⭐️Terry Tao's generals: web.math.princeton.edu/general...
^I have included this content onscreen in its original form, including typos (e.g the spelling of Klainerman)
⭐️The general exams of other Princeton students: web.math.princeton.edu/generals/
⭐️A Close Call: How a Near Failure Propelled Me to Succeed: www.ams.org/journals/notices/...
^This article written by Tao is where I got my info about his study habits and relfections.
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This video was sponsored by MEL Science.
So he nearly failed? I bet I could totally fail it.
😂
What is failure before start called? That would be me 😂? StartFuck? 🤣🤣🤣
You'd still have to get there, to even get to be able to fail it.
If Terence Tao almost failed it, I think it’s safe to say that we all have pretty much no shot
Think big.
He passed Princeton's qualifier at 18... Mind-boggling.
It took me three years in High School to pass Algebra lol
@@fred290eif you didn't work hard then it's not something to be proud of. Please stop with this trend of belittling yourselves and praising others, it's destroying our generation.
He passed the SAT at 8 years old obvi
Studies and discipline are for men....not Gods!
@@chinesejesuschrist Stats doesn't say that. Last 20 years, Princeton Alumni (formed within it) have won the most Fields Medals. Just facts.
This is why I'm better than Terence. He was unable to fail. So close but couldnt do it. I, on the other hand, can fail it, without any effort.
Lmao
XD😂
Reverse better
I went to an engineering school and saw a lot of this, though at a much lower level. Smart kid coasts through high school and is never challenged enough that they have to developer study skills. Then they crash and burn in the first term at university because it's the first time they've encountered something that's genuinely hard for them. It can be a tough lesson.
In my experience with engineering school, it's over as soon as you think of yourself as smart because you start to slack off on studying. I liked to think of myself as an idiot and because of that I would spend weeks prepping for exams. Your success in engineering school (or anything difficult) is all about your motivation to succeed, not how smart you are.
experiencing that now
@@badconversation956 if you buckle down and grind you'll get through it and by your third year you will have developed those skills. Same happened to me coming out of HS
@@badconversation956good luck
@@badconversation956 The only advice I have is that most schools have some sort of tutoring available, including how-to-study workshops. Find out what's available and take advantage of it.
I remember my oral exam in analysis. It was 2 hours in length as well. Two professors (one of them known to be harsh!) summoned me to a class room. They started to ask me about what do I know about the norms L^1, L^2 and L^\infity. I gave definitions and how L^2 is special as it's Hilbert space. After several minutes one of them asked me to state and prove a fundamental result in measure theory. I stated it well but struggled to prove it (one direction was easy, but the converse was hard). One of the professors was telling me to try and consider a simpler case. I couldn't see it. I stalled for 2-3 minutes, but seemed an eternity. My head felt hot and I was sweating, anxious and I thought it was all over. Tears were sliding down my eyes. I concealed them while looking at the black board. Then, totally unexpectedly, before they said to move on the next question, I remembered a definition involving absolutely continuous functions and used the Radon-Nikodym theorem and I proved it! The next and final question was, to me, a standard Holder inequality result. I passed!
Thank you for sharing. So interesting to hear about people's experiences😊
Uffff great experience. Thanks for sharing. I need to study more....
I like your funny words magic-man
That sounds terrifying, but congratulations!
Had a near identical experience at Berkeley in 1977. Absolute Hell.
Hi Tibees, thanks for this wonderful video, it makes me think about my failures, which should make me stronger. I used to think failures make me weak, but this is a really good paradigm shift.
lol i actually had a pretty awkward encounter with professor tao in my first year of college. i’m a psych major but one day i was exploring campus and ended up near the pure math building. i saw professor tao talking to a student as he exited the building and i didn’t know what to do lol. kinda wanted to say hi or something. i was thinking back to my high school calculus teacher who always raved about tao. he really wanted me to become a math major and told me to say hi for him. so i did and instantly wanted to disappear forever. i don’t even know why. maybe i just felt so out of place being in that part of campus with the amazing terence tao. i just wanted to run away at that point but luckily dr. tao was really chill and said hello back. i haven’t been back there since but i do think about that interaction a lot.
Psyche major psyched himself out.
@@apophenic_ true
@@apophenic_ that's mental
For real, I met Dr. Dave Amos, professor of City and Regional Planning at Cal Poly San Luis Obispo and I was starstruck.
I was a physics major in ucla. During my junior year (2021-2022) I saw Tao walking his bike outside a coffeeshop, Elysee (for the ones familiar with the area). I said "hello, I am a physics student and I am struggling with a problem of analytic functions in my Mathematical Methods in Physics class". He told me to wait and keep an eye on his bike. He grabbed a coffee takeaway, and went on to explain in the simplest way possible the problem I had trouble with before running off back to his office to get work done. lol At that moment I realised mathematicians are super nice to be around, unlike most physicists.
Wow! What a terrific mathematical story. Great for Terrence. You're wonderful Toby.
One of my favorite videos you've ever put out.
Great and thoroughly well explained - Thank you! Also, your voice is very calming and well articulated :)
thank you tibees. Your video gave me courage to continue my studies.
Great video. Thank you. I am truly humbled when I encounter most graduate level mathematics. It's like a foreign language to me, and I have a undergrad degree in math. It's not easy even for the brightest minds.
What an awful and ridiculous oral exam, I'm glad I didn't have to go through nonsense like to be accepted for PhD. It measured nothing other than the ability to have memorized a whole lot of stuff including proofs, which is all irrelevant to the ability to do research.
I think this format is amazing as 3 people can balance skills and fairness, but also having very wide ranging items it's going to mean you have to know your stuff flawlessly. This would bypass the many different ways to cheat.
@@jaybestnz The whole thing is completely irrelevant to the candidate's ability to do a PhD.
@@jaybestnzi think the commenters issue lies specifically in the emphasis put into memorisation, which does not really show understanding - it would make more sense if he (tao) was asked questions about what something is rather than derivations and proofs
@@M.athematech Says the random person on KZhead. Ugh
@@Keralasha444Says someone who actually has a PhD in Mathematics but had a sensible supervisor and referees who were more interested in what new results could be developed not how many texts could be learned by rote.
Another day of learning. Thanks Toby, always a joy to watch and learn.
This guy is the best mathematician alive. Absolute genius. Lots of interesting stuff, thanks. PS Loved the fact that the topic he was apparently inadequate at, went in to win maths highest prize. PPS You have a very soothing voice.
What a beautiful video. I love your ending that having a high IQ is not the most important thing, but how you nurture your creativity to accomplish great things!
Or just normal things..normal things and normal people make the world go round and are the foundation of great things and feeders or so called great people. Great is in the eye of the beholder. ❤*normcore*❤
Nice video as always Toby! Haha Enjoyed this much👍👍👍
Keep up the great videos, Toby!
I literally just found this channel - by way of a Quanta Magazine video(The High Schooler Who Solved a Prime Number Theorem) - earlier tonight after clicking on a previous Terence Tao video by you(The Test That Terrence Tao Aced at Age 7). After looking through some of your other videos, I noticed that it had been a couple months since you'd uploaded anything; so I was kind of shocked when I just noticed this new submission ten to twelve minutes ago(now more than twenty probably) AND it also had to do with Terence Tao... So shook. Anyways, that prompted the decision for me to do something I hardly ever do on any platforms which is to leave a comment: Informative with such a soothing voice and style to the vids. Especially loved that pencil hovering over text action. Great content!
In the end, it was humility that saved him.
Hi Tibees. I’m a long time fan. I love math. I’m about to graduate with my bachelors. I’d thought about earning a PhD since I was younger, but now that I’m here, I don’t think it would make me happy. It’s incredibly uplifting hearing you state “I don’t really know what these questions are asking” because I also don’t understand. Math is intimidating, and it’s a subject I’m passionate about, but I think it has the capacity to drain the life from my soul. I think I’ll be much happier working in software, exploring other hobbies with my friends and family, and learning math at my own pace.
Hey Tibees!! Missed you ♡
I used to watch your videos back in 2018-19. Seeing you again is amazing. Nostalgic.
I could never be a genius, having people examining how and why I failed a test 😭😭😭
It just goes to show that even the most talented among us become complacent and overconfident at their own peril. Terrence may be brilliant, but he is also human and susceptible to the same pitfalls we all are. To his credit he processed this rebuke in a constructive way by gaining a deeper appreciation for the importance of focus and discipline.
Among us sussssssssss
His thesis advisor Elias Stein is the coauthor of the complex analysis textbook my course used back in undergrad!
Big fan from Brazil here, awesome videos you make!
You make the incomprehensible interesting. Which in turn motives further study.
I can relate tbh. Not to the genius prodigy part obviously, but I did breeze through HS and through my first two years of law school. My classmates studied pretty much every day while I read the contents of the test one or two days before and spent pretty much most of my time playing games or reading other things. That ended when I went through third year, I started missing classes, thinking that it didn't matter as I could just read a book on the subject and do well anyway, but because I was quite arrogant I took classes with hard teachers, and I failed the semester because I didn't prepare for the oral exams. After that I lost my scholarship that covered like 90% of the cost of my studies, and I had to repeat the year. Now, I can't say that I completely changed after that, I continued to study less than my other classmates, and I'm still quite confident in doing so, but I took care of having enough time to prepare for every test, I managed to come back from that one bad year and this year I passed the final exams (an exam that covers most of what one studies in law school) and finished my studies. I think that if I hadn't taken classes with those strict teachers and hadn't failed that year I wouldn't have been able to pass this exam, because I would've overestimated my abillities, so, in a way, I'm thankfull that I failed.
i think this is going to be my 2nd year of college. I breezed through the first year and became top 3 of my peers. Now my grades are going lower than expected and are very dangerous for my scholarship (which also covers 90-100% of my tuition). Hoping I don't jinx it 💀
haha, just like me, i'm 39 now, but had the same exact experience. Took two hard majors and a softer one (math and engineering and economics=not so hard), rocked out freshman year in top 10 school, started partying to extreme levels like 6 days a week, missing class, kept taking harder classes, got DESTROYED when i saw my first term grades. HUGE wakeup call, never again. Humility and work ethic is key and sometimes youngins must learn the hard way.@@kusa4837
Story sounds similar to what I had to experience when I tried studying for the first time at university. The bad thing is: Cutting down on gaming or other interests is a matter of resolve. But there are many things in life one does not have any power over to change or improve them. No money, no stipendium, working every night to finance food and social life, being terrorized by neighbor, construction workers and parents and many other things are what can break a person and bring one to fail no matter how hard one tries. In week long university projects professors had to tell me to lean back and let others have a chance at trying to solve it in more than a few minutes. But all the skill and IQ in the world can not help against massive sleep deprivation and starvation. I may have been one of a low fraction of cases, but the social system in germany exists only in theory. When you really encounter problems, the bureaucrats and institutions are rather trying every trick to save on costs and make you leave frustrated without getting what is rightfully yours by law. I ended up with no room of my own, no money, taking care of sick parents and a lot of other problems, while at the same time everyone demanded me to give it my all at university. I did each weeks practice homework just an hour before the deadline (mostly in my car while driving to university) or quickly in class, while others required several days to solve the math problems. I simply did not have enough time, otherwise I would had to cut back on my 3-5 hours of sleep. It ended up in me failing university and having to retry another time. Second time did not work without any money either, so I worked 6 years, saved up money and finished studying on my third try.
why didn't you just wait to go through university and just work instead?
Thank you for sharing your experience
Deutschland ist hard, das stimmt. Ich bin verheiratet und studiere. Es ist sehr anstrengend.
Thanks for sharing content! Any more resources for systematic study habits?
Thanks Toby. Before the exam semester, one needs to credit or seriously audit courses. Most questions are asked from relevant courses. I would have liked FORTRAN anytime.
Okay, I finally understand that Tibees has a passion for maths and review of interesting history from primary resource documents relating to specific persons. Her maths knowledge is way beyond my own.
Your voice is soo soothing ✨
Someone described a statistics qualifying at one of the top universities as the worst week of their life. They were given 5 problems, each by a different faculty member and 5 days to complete. So there were both theoretical problems and complex data fitting requiring the method to be programmed from first principles.
Thank you Tibee!!
What a great study trick, i never thought about conversational testing.
Your voice is so relaxing
the *Tebees' theorem!* btw comic Terence's tan is very orange
It is even more ironic given Eli Stein's stature in harmonic analysis!! And there is even more irony. When Terry was 12 in Adelaide he was take under the wing but Professor Garth Gaudry who - wait for it -specialised in harmonic analysis. Garth also introduced Terry to Alan McIntosh at Macquarie University and Alan was - wait for it - an expert in harmonic analysis who solved Kato's square root problem and along the way publishd with Abel Prize winner Yves Meyer of wavelet fame and other heavy hitters like Ron Coifman. Both Garth and Alan are dead now (I was a student of Alan in the early 1970s) . Eli was a student of Zygmund (who was instrumental in gettng Calderon to Chicago university) and proved many major things in the subject. The approach he followed in his undergrad Fourier theory and functional analysis courses (which form 2 of the 4 volumes of his Princeton Series) was to do those subjects "properly" and if you have mastered that material the questions are understandable. Eli used to say things like "This morally has to be true" and when I look at how Terry explains stuff I see a lot of Eli. I did an oral undergrad exam in analysis in 1973 and even though it only counted about 20% I still remember my interrogator saying "Mmmm..that is a novel approach....but what can you tell me about Riesz's Theorem on compact perturbations of the identity?"
people should remember that terence tao had far more hours in this subject matter than most people instead of comparing where you were in these subjects at his age, compare to where you were after spending the amount of hours he had (even most college graduates haven't spent as much time doing math as terence tao did by middle school) this is the same for things like drawing, playing piano, and any other skill. it is a little insulting the amount of work the human would have spent honing their skills to just be told it is the result of genetics and nothing more, when there are millions of people with similar genetic capability who just didn't have the privilege to succeed in our world's broken educational systems, and do not reach this level of mastery
The video literally says he cramped his way through his exams. This is the difference between iq not time spent and effort. You can spend the same amount of time on phsyics as Einstein, but you can never reach his level. Time spent is one factor, but natural born talent weighs so much more. Especially on super complex problems.
cope. IQ matters more than effort, discipline, hard work anything
You just changed my life with what you said
this is true. i've had discussions about this with friends where i'd ask them what is more impressive, a child prodigy pianist who after 10 years of playing can play listz's la campanella perfectly or someone who has been playing for only 2 years but started at 20 years old and can play it perfectly. to me, the latter is an indication of far faster learning than the former.
Who did the animation for this video Tibbs? It's really impressive and funny
I want to know as well!!
@@dubsas Me too!! @Tibees ! (worth a shot) Is it WallaceAndGrommitGPT? XD
I love your videos!
great vid tibs. on your sponsor. in the 70"s we had a toy, spirogragh I think it was called. Wow if I knew it was science I would have done better in third year science lol
Love this channel
I guess he named the T(b) function in your honor. Congratulations!
I actually saw Terrace Tao in person recently. I did not talk to him but it was cool to see him in his office.
This reminds me when I had an idea of building a house with a secret room which has four paths underneath one lead to the beach the second lead to the volcano the third lead to the cemetery and the third to the snowy mountains 😂 but there was like really fast cars to get to the places😅there was also a secret door that lead to these roads.😢 and I also had a house in the forest❤
Great video thank you T
We are all imperfect beings. That being said, can you imagine how intelligent and skillful each of us would be with a perfect mind and body? Something to ponder over.
Studies and preparations are for men...not Gods!
@@zhoubaidinh403 No one is a god, and this video proves even Terrence needs to study. I don't know what you're on about, seems like you've never seriously studied for anything if you're spouting this nonsense.
If each of us had a perfect mind and body, no one would stick out and be exceptional. Actually everyone would be average.
@@dekippiesip On the contrary, we each have our own personalities and attributes that separate us from one another so that we are recognizable by them. On the other hand, we are not robots either.
@@SacredSecret Perfection is seriously overrated! I mean what do we even means by perfection??? It's because we don't know everything and cannot ever know everything is what makes life worthwhile. Imagine a world where everyone is born a genius. It would be such a sad world because no one would ever dream of working towards something. There would be no difference of opinion and everything would be monotonous and mundane. It's our imperfections that makes us strive to be better and think outside the box!
It takes character to study things even though you don't like them. I'm specifically talking about his quantum physics exam. Things which we may not think are important for learning a subject, may still be emphasized in a course and grinding through them takes tremendous character, especially if it's a subject one may like. "I'm talented in other fields so this one doesn't matter" is a naïve thought process.
me who didnt understand a single thing he said: "yes i totally agree with you"
Happy New Year
Very inspiring, thanks for sharing.
I love ur videos ❤
I have no idea what you talking about but can listen to you all day and night.
Thank you very much!
Please make a video on the first rubik's cube, and how it got solved
I got a C on an exam once. I thought I was going to die.
First in harmonic resonance any factor of resonance that come in to mass may bounce of said medium if density is such not to increase or amplify said resonance.
Thank you : D. It helps.
I wonder: "How did they find three other people, besides Terence, who even began to understand these concepts?"
You have to remember he was a grad student. Any researcher in harmonic analysis would know more than he did at the time.
It's the basics of Harmonic Analysis so it's not too crazy. It sounds weird and foreign to someone who's not a specialist in HA specifically, but that's just math outside your field in general. With the necessary foundations, anybody could learn this stuff relatively quickly. Plus, specialists in HA aren't hard to find, it's a very popular field considering its relevance to physicists and electrical engineers.
Please do a comparison between the Botswana General Certificate of Secondary Education (BGCSE) and IGCSE to see which is harder
Great video. But weird, though, when the animated examiners lip-synch with Terence's words.
I know this is offtopic but can check the indian exam that you have to give for being a charted accountant. Apparently that is also a nightmare
Tests are not always accurate measurements of intelligence. Terence Tao is a monster even if he failed all these tests ten times over.
i gave up the math of korea SAT test your contents is interesting to me 😅
😅
@@ShooterFPS i am no brain person
Tibee‘s have you submitted your Thesis other than video?
If he had failed, it wouldn't have derailed his career. He would've had a successful career no matter what
Yass Tibees!
Terence Tao is so relatable
I was a lecturer and this solves so many issues that we had regarding being as thorough and fair as possible. The dynamic nature means that the exam migrates to all the items that someone is weaker on and needs students to study as many areas as possible.
this is the only asmr channel i like
Alliterative titles hook me in better than clickbait thumbnails
Ill communication
I don't know what you're talking about but you have a very soothing voice
The biggest surprise to me the entire video was learning that Terence Tao played video games.
He is a player of civilization 😂
I could not even tell you what my masters thesis was about, except that it dealt with A Portrait of An Artist As A Young Man. I also have no idea about my Masters examination questions. I certainly have never referred to it after it was finished. My undergrad thesis was a book about Conrad’s Nostromo. Supposedly it’s still in the library of the college. 🤣
new Toby video PogChamp
Nice topic❤️
Wow those animations!
He went to the same high school I went to. Probably the most famous alma mater.
I thought for a moment it may have been a Turing test. I always have trouble with those.
DO NOT HALT
Never heard of Turing but when I took the test, I aced it...and gave a few suggestions on how to improve on the questions...true story.
omg! did u do that animation?
and Einstein claimed to have said, "Does the moon seize in existence" maybe he meant that to be the error correction code to the moon with the Reihmann zeta function and it's algebraic Pythagorean expression with Parallelism in abstraction to quantum chaos. Purely Abstract as Serial in forward direction 1 track mind. And Einstein only put it into words the way gravity, deficit, Newtonian freewill had during Issac newtons discovery of supposed Constructs of determinations for calculus extractions of who is God who does not roll dice.
@Tibees What did you use to create these animated characters?
Oh hey tibbs. Thx
I LOOVE YOUR VİDEOS 🤩🤩🤙
Wow, those sure are words.
I wonder how many prodigys failed in exams that had changed their careers into a total catastrophy
Who knows? Though this is a pretty good exam format.
Probably a lot. Being a prodigy requires opportunity alongside intelligence.
Learning from Terence Tao's carelessness and never to take things for granted. Noel from NIGERIA!
Hello How can i study abroad in a foreign university? How can i have a student's loan to pay the expensive university fees ? How can have the material and study it with myself without getting a certificate?
This woman is the definition of idk a word a what she said but I like it!
How long can this exam be? It must have been several hours right?
2
This is the motivation not footballers or rappers, not to say they don’t work hard, and get lucky, most of us can aim to work hard work in education as an Asian
the first 5 words all start with 't'
I'm studying calculus in my computer science degree and I can say that after completing calculus 1 I could get maybe 1% of the terms used in this video. I could see how each subject of study like the prime numbers theorum could be interesting to study. And made sense conceptually. But I had bo idea what it actually entailed beyond what was showed. Harmonics sounds very interesting too. Number theorum sounds more elementary than it probably is, like the sort of thing that would inlclude base mathematical expressions proofs such as 1+ 1 = 2. I like mathematics, but especially when it's applied in practice and when it's utility is clear. If it sounds engeniously fitting like pusle peaces snaping in place perfectly it makes it even better. Math is awesome, tho it isn't easy it is fasinating. I think i'll take the rest of calculus even tho it's optative in my university version of computer science. I actually got the highest score in my first calculus exam. I could not believe it when i saw it but I did ask 1001 questions to the teacher in class, so it makes sense. I love math...
Haha that's ok because you have never gone through real analysis, algebra (theory of groups, rings and fields) and functional analysis. Calculus is generally taught in high school nowadays and you can even get college credits by passing AP exams and continue to take multivariable calculus in college (normally vector analysis at this point) just to finish up the rest of the calculus topics. If you are doing computer science then you don't need much advanced math but just linear algebra, differential equations, discrete math (combinatorics, graph theory and such) possibly numerical analysis as well (scientific computing at this point) or linear and non-linear optimization. No rigorous math for you at all like real analysis, complex analysis, topology, differential geometry and stuff.
@@pashaw8380 Yeah I've been studying linear algebra on my own as my degree don't include calc 2 and 3 even as optional things to take, so it looks like I'll learn it as self taught as well. I've managed to project a 3d cube on the screen using nothing but python and pygame, I made my own line and triangle drawing algorithm, along with matrix rotation and projection to project and rotate the cube on screen. I've been reading up some resources online about computer graphics so it's not reinventing the wheel but more recreating the wheel following the steps the people who made it optimal did. It's hell a fun to figure this stuff out and make ur own instead of using premade graphics API(such as opengl). I hope to get a fully fledged software renderer for simple geometry in python soon enough and have it as one of my many personal projects to show off my skills in a job interview. It's not about the practicality of selling such a thing but more about learning the inner workings of such functions instead of just treating them like black boxes. I might switch to software engineering instead of CS, as it would work more with game engine creation than regular computer science would, which involves the sort of stuff I've been learning on my own, which is of great interest to me. I also plan on making a procedural terrain generator with different terrain regions being modified by sin waves of different frequency in order to have biome terrain variation instead of the usual look that perling noise gives. As u might be able to see I love creating complex systems that produce complex and organic behaviour using math to achieve it. I'm also autistic asperge which might explain why I love complicated complex topics so much, and breaking them down, recreating them on my own. If I could live forever I would take all exact science subjects on university, from math to astrophysics, to artificial intelligence and finance, I just don't have enough time to live as a regular human being in the 21 century to learn all I would want to, so I'll focus on programming for now and learn all other subjects as a hobby. I just love using my brain to think about and learn complicated subjects. It's hell a fun!
If you are a real genius, it'll come naturally, a priori...
@@pashaw8380 all of that comment was a snarky pat on the back to yourself (if that), and a kick in the balls to actual talent.
@@pashaw8380 integral transforms from complex analysis come in handy
Terrance accidentally insulted anyone who uses the class number theorem... lmao
Did you intentionally give three of your characters exophthalmus?
Isnt... the fact that a single potential "fail" of a given test could ruin your career a sign that your system is broken? I mean, it took the brightest guy in generations to simply keep his career in math? Yall need to fix this.
Would love to know the parental support/structural system he had.
I think it was good. -- doesn't say a lot, I know