Bruh..

So pi creatures aren't real ?

Real

​@@yashrawat5071They are. Luckily he found someone to go give the speech for him.

Glad 3blue1brown made a _rational_ decision

The place I went to for my undergrad didn't even _have_ a math department. You could get a math degree through the physics department or through the computer science department. But a graduate degree was out of the question.

My school had 3 graduation ceremonies to get through the entire math faculty!

How many mathematicians does Stanford hire each year tho?

It doesn't tend to matter with regard to private schools. Departmental graduations are pretty popular there.

@@Maou3 Same for europe. Hungary we only start degrees if they got their own department to begin with. You wanna study maths? You go to the university that offers a maths degree, and specialize within that. Maths are part of the Natural Sciences Institute. Think we go like Bsc 100 maths students 100 chemistry students 100 physics students 100 geology/geography students 100 biology students MSc 15 Materials Science students 15 Chemistry students 15 physics students 15 Geology students 15 biology students 15 maths students. Each year. (ELTE)

That's wonderful!

Miles my man, is your work related to the logistic map? What makes it interesting or useful (genuinely curious)?

@@agentdarkboote the logistic map is just one of the iterators I care about. Specifically I care about iterators which are rational polynomials of two variables. I’m interested in the properties of the bifurcation points they generate. For example, is the limit of bifurcation points always transcendental?

I can see that few of the professors evaluate themselves internally, like any other people in society. But it is not bothersome for their work, because it is the norm and deviating from norms can push you through the exit (because of you not liking the environment which is less adapted to you, or because of others don't liking you).

I'm not even sure it's necessarily a bad thing. Maybe an infatuation with intrinsic hardness is necessary to develop the pieces of math with unexpected later utility. Or maybe hardness for its own sake is what forces us to keep finding new ideas, analogous to the value of going to the moon. What does seem problematic is to have an evaluation function that works this way without ever having reflected on whether that's desirable.

​@@GrantSandersonI get the sense that a purely difficult mathematical problem only really has cryptographic applications. I think usually we want to show a kind of 'computational reducibility' in math.

🙂 Hi Pat! I think part of this may be that if a problem is harder, it is likely that more people have attempted it. So interest can be generated by people investing their time. What do you think? Also, I would love to hear what drives your evaluation function.

(Hi Elijah!) Without a doubt, my "internal" evaluation function was given to me externally. Starting out in math, I liked most things I learned about, and starting graduate school, I had no clue what I wanted to specialize in (let alone what problems were particularly "interesting" or "worthy of study"). At some point, I realized that I enjoy doing quiet puzzles that I think are fun, but I firmly believed (and still do) that those things aren't "sufficiently interesting" to impress the mathematical community at large. After understanding the game of which mathematicians are considered "good", I decided I had to choose between doing things that people perceived as interesting or doing things I really enjoy. I remember talking about this to folks outside of math, and I described it as "I need to play the game and do the stuff they care about until hopefully one day I'm hired in a nice job, and I can finally start doing the things I really enjoy." It's been 15 years since I started thinking like that, and I don't quite know how I feel about it now. Despite the fact that I still haven't been hired for a long term position, I feel somewhat more at peace finding things I genuinely enjoy regardless of whether or not others approve. But the quiet intrusive thoughts that my work is not "good enough" (and by extension, I'm not either) still don't seem to go away.

Same rn taking engineering degree. Doing really well but I'm starting to get humbled by rigorous real stuff.

This definitely describes me, but I’m also trying to change my mentality for the better. It’s nice to know that I’m not alone.

I wholly support this Buddhist view that doing something useful _for other sentient beings_ is the only meaningful thing in life, and trying to do it more, but... Keep in mind that caring about how other people perceive you is perfectly normal and even useful. In particular, if you don't want to look like a jerk, don't act like one. If you want to be perceived like honest and compassionate, be honest and show compassion through your words and actions. Totally reasonable thing to do if you ask me.

I think it's perfectly human and understandable. Admiration is a driver for everyone. You simply don't have the ropes of reality of standard brains like mine to keep you firmly on the ground. Yes, I believe this can also be seen as a deficiency, and it's good that you're trying to fix it. But don't ever refrain from pursuing your passion, a degree of self-complacency is normal, as long as you respect the ones less gifted than you... Arrogance and tendency to humiliate are the plagues of some very smart guys, and the ones to avoid...

Love this thread, very insightful

I decided to get a B.S. in Math for the opposite reason. I thought masochism was necessary for self-improvement and wanted to force myself to overcome my weaknesses through brute determination. I got the degree with a good GPA but I never reached that phase transition of mathematical maturity I sometimes hear talked about. I like to tell myself that I think about math in a way that's "slow but strong", with a more thorough and less artificial understanding than my peers, but I don't know if it's true.

Great quote, almost makes you wonder how he got himself to do it before he met littlewood and ramanujan.

I started a masters in math because I understood that every problem can be modeled and have a better understanding with this approach, at the end i learned much more than i could imagine and now i can think more generally about topics and identify patterns that can be translated from one field to another. Long story short I can read biology books to propose new algorithms for automotive industry

I know this is out of context, but this quote from GH Hardy is amazing: "1. To prove the Riemann hypothesis; 2. To make a brilliant play in a crucial cricket match; 3. To prove the nonexistence of God; 4. To be the first man atop Mount Everest; 5. To be proclaimed the first president of the U.S.S.R., Great Britain, and Germany. 6. To murder Mussolini -From a list of New Year's resolutions sent by Hardy to a friend in the 1940s"

@@markhall2414 Are you asking because he didn't include america in the countries he'd want to be first president? If so, I think it's possible that this quote was from a time where the USA was not yet involved in WW2, hence why he might have chosen not to include it

this is so beautifully said!! I’m wishing you all the best in your studies

I'm also 18, and this has been my experience too. I'm glad someone else gets it.🫶

"It makes me angry just thinking about it, but perhaps its my anger thats made me blind to the truth for so long. I see it now, i fought to push down others, you only fight to push yourself" -Vegeta

I would've thought that he would have to go *far* out of his way to *hide* his exceptionalism.

Having *no* ego is a very miserable way to live… a little bit is the perfect amount to have.

His ergo isn't too bad either.

​@@randomjunkohyeah1As someone who's suffered for decades wirh low self-esteem... yeah, the truth hurts.

You are describing a mathematician.

he has experience speaking like that from his videos, I guess. I’m sure he also practiced this speech a bit.

Ditto. Looking back, my time at uni - 4 years in Elec & E’nic Eng - was the most thought-filled and stimulating of my life. Finding good friends, great teachers (for the most part) and uncovering the “how” of things…Maths wasn’t my strongest subject, but became a familiar friend that described the rest of science, most elegantly.

@@daviddempsey8721 Awesome! My Dad also said to me "You'll never make it as a mathematician, but you could be a good engineer". Unfortunately, this was long after I'd graduated!

@@dylanparker130my dad too, he wants me to be an engineer (as he is an electrical one) but i am more interested in doing a math doctorat

lovely spirit

​@@apuapustaja2063whenever i see the word lovely i think of gordon ramsey

100%, that's the intent. I fear an unintended consequence of (some) existing educational trajectories is that students come out focussed more on their own outcome and perception than on being others-focussed, and seeking out who they can help the most with their newly gained knowledge.

Is that because educational institutions have an incentive to leverage the fundamental human instinct to want to be admired/perceived well… because it’s a simple and (historically the most?) effective/efficient strategy to drive up the output/results of their students? (It’s easier to get Johnny to want to crush his test if being showered in praise is the reward, vs trying to get him to understand deeper meanings of life and human connection in order to instill a motivation grounded in value-adding and fulfilment, right? …Especially for younger people). But this then has the unintended consequence that the kind of carrot they have ingrained in their students to chase produces a mentality that may not lead to them having the most fulfilling life/most use of their skills post-education? Loved this video, Grant.

Yeah I've realized that a lot of Physics phenomena that I found "interesting", were that way *mainly* because they were hard to understand, and I didn't understand them. And as soon as I did understand them, I of course felt accomplished, but also a bit hollow. The physics had "lost" some of its magic in my eyes. (I finished my Bachelor in Physics last year, for context)

​@@iveharzingkeep going with physics and you'll see that magic is still there :)

dude ROFL same

On the spectrum of educational entertainment, Mark Rober is almost completely entertainment while 3B1B leans heavily towards education.

@@Vim_Tim Yeah I know... I feel bad for all those MIT grads whose commencement speech was essentially just a youtube video. Unfortunately, I guess it's unfair to expect everyone to be as amazing as Grant.

​@@xavierchoe8074 Why do you feel bad for MIT grads, who cares about it? This speech is great but the whole idea of a ceremony is bullshit.

@@xavierchoe8074 MIT has become so much about marketing in recent years, it was perfect for them.

@@heyman620 no

😂

😂😂

I think this too. I also just finished my second year of undergrad in math, and I’m trying to figure out a way to really learn math. Should I read textbooks/watch videos/do hard problems? Or should I try to figure out what math is myself by sitting down with a pencil and paper and thinking? The former is what I’m used to from school, and (like Grant I’m gonna always point out the positives :)) it’s nice being part of a community bonding over this subject. But sometimes I zoom out and wonder if I’m doing this for the beauty of math, or because it makes me feel smart and productive. So what I want to do more is come up with my own ideas of what math is. Maybe it’ll align with what mathematicians and philosophers think, or maybe it’ll be more of my unique perspective. I’ve been doing a little imagining of math (understanding basics of logic and sets and functions and whatnot) and I’m trying to get more consistent in this new type of learning. For the first time in my life, I can understand why math is so hard. It’s not hard because it looks intimidating, it’s hard because the subject sparks so many possibilities that we don’t have enough time for. But I also wanna make sure I have another perspective to view math from. Math isn’t just a difficult and rigorous field, but it’s a way of thinking about things. We ask ourselves questions, no matter how basic, and then we try (and fail) to find answers. I want to make sure I ask the questions not because they’re well-known or they’re in all the math books, but because I thought of them myself. This is all great in theory, but when school starts again I might get overwhelmed and give up on trying to learn math as a hobby. With school comes our egos, and they can get in the way. I’m not sure what the solution is here, but hearing Grant talk about something like this is great. I feel less alone and very grateful.

​@@desrepeerc206​ First rst paragraph good Second paragraph ego Third paragraph good

​@@desrepeerc206go get your ego checked lol

@@skydivenext What they mentioned in second para is relevant(if I interpreted it correctly). I think of it this way.... see when you are learning/ mastering a subject, you first learn the theory as a basic understanding of the concept is necessary to dwell into the questions. For an ordinary student ,trying and pushing yourself to do difficult questions which are way beyond your understanding is like diving headfirst into a frozen lake. My dad once told me "You understand something when are able to explain it to yourself in a meaningful and a comprehensible way". But if you are exceptionally good at something, you can ponder new possibilities and question what, why and how.. and thats what generates new ideas and intuitions. And it even goes on to show you how much you know about your particular field of interest.

A paper dedicated to understanding mathematics isn't an academic paper, those are just notes. Also about half of maths dedicated to applying results; that's why it's called "applied mathematics"

wish he were ours lol

Hm I don't think that's ego. (Not sure) From my understanding, ego would be feeling superior to others. I think what you described is being selfish/self centered. Of course I completely agree with your view though.

He didn’t mention purity, and honestly hardly disparaged ego

@@SpencerTwiddy Perhaps I should be clearer that this is a fairly minor disagreement I'm having, but 3:32 and 4:13.

It's a good point, I wouldn't want to imply it's dirty to value problems primarily when they pique your own interest. The main thing I wanted to convey is how personally, when I look back on projects that were done based more on my own interest vs those motivated by others' interests, while I often feel happy about both (and would never outright do away with the former), there's a more enriching fulfillment that comes from the latter. Also, from a pragmatic standpoint, the sense in which I meant it may have made the difference between career and hobby is that the latter are what account for more people coming to the channel, more support on Patreon, etc. The specifics of this might not apply to everyone, I can't tell you what your evaluation function should be. The one piece of advice I feel comfortable giving is that time spent reflecting on the question is time well spent.

@@Huntracony I stand corrected

directX moment

@@mastershooter64 Yup. Also glsl/vulkan. I think it worked on all semi-modern devices yet I never tested that.

Fr we need the egoists to devour intimidating problems

Hi, reading your comment I was almost seeing an almost exact copy of myself and you were really able to capture the essence of this precisely twisted mindest and curiosity that drived you and me and worded it, simply in a way that im not able to. I just wanted to "share" my story because there are only so much people that can understand this sort of internal conflict you talked about. I find that talking with these people enlightened me a lot in the past few years. Btw I'm sorry if this come across as self centered its really not my intent, its just a way to spark something that you want to say or take what you find interesting in what I say that makes you think of something else and talk about it. Also I may go into some details I find them necessary but you can skim over them. Just to acknowledge it this is not my native language so my apologies for any eye scratching spelling mistakes. Anyway before the last year in high school I wasn't interested in anything to be honest I just liked to play games because school was boring, maybe because teacher are handed out the impossible task of trying to teach for every possible career path that a student might take, but mainly, because I think i was only interested in physics or maths or maybe the two. I was lazy but I wasnt good I just listened in class and worked enough to pass. In my perspective I just had to have enough points to get my high school diploma because it wasnt really serious in my mind to not get it even though my parents didnt bothered me with it but intrisically, i knew it wouldn't make them happy. Then because I was on youtube I discovered 3b1b Veritasium Mathlogger etc and this really turned my path. It got me interested in more "complicated", "sophitiscated" topics and I think there was a part of curiosity, really learning something, but there was a huge part about being pendantic about it, which of course im not proud of. The main thing was that in high school you are being taught for instance about rc circuit and then you use this weird dU/dt and the teacher says that its a "limit" and you follow along without knowing what that means at all and then you use Kirchoff laws because you need to know them for the test but you have absolutely no idea where they come from and a differential equation pops out and finally the teacher is happy. Pretty quickly I think that with the videos that kind of gave me this attitude to, lets say, "prove things", combined with my feeling of no truly understanding something that was being taught and came out of nowhere, got me to be more skeptical. I think I understood a little that derivatives where taught because they were necessary for integrals which then has like billions of applications probability distribution laplace transform you name it (doing them is now like multiplications its crazy, exagerated but you get the point) but mainly because it shapes the way that a student thinks. What recruiters in engineer broadly speaking want is a guy with problem solving abilities and a mind that can model a problem by hand make some calculations and get a result that is somewhat close to the "true" result without any help. By the way it always staggers me that without games like factorio minecraft civ6 and many more i wouldve been a stupid kid and my problem solving skills and interests all come from games and the internet. One of the stories that my professor jokes about is he's been handed out a pen and then was tasked to compute the magnetic field if it was wrapped around in copper, its basic but that its the kind of question/problem that I love. I wish teachers just explained me this, it would've been easier and much more fun to learn. Nonetheless in my last year of high school I got really interested by electroboom veritasium and lot of people who were doing mostly project videos and this prompted me to learn a lot to be able to tackle and even make my own projects. I researched the path and diploma to go to a kind of electrical engineer job as i understood quickly that I needed to get of my ass i got from almost last to the top 5 and knew stuff that we didnt saw in the course yet and noticed that my classmates were completely oblivious to where was situated the thing they learned in this greater map of knowledge leading to uni stuff and just applied the course like printing machines, of course i bragged about this a lot too and felt a selfish feeling of domination... Then i got to prepa. Prepa is the french equivalent of uni with the same framework as high school and a lot of suffering. Its the most well regarded way to get an engineer school and the companies knows the value of this experience and that's tipically the profile they are looking for. I can go into further details (honestly this is the most intellectual growth period of my life) but this comment is already way too long and its been 5h of writing at this point, basically, i got crushed exactly like you. My self esteem was ruined and, most of all, my confidence was at an all time low so I basically couldnt learn anything and needed to smile everyday to not attract pity. We had exams in the last two year but its doesnt matter because these two years are only useful for the written and oral exams next week that last a couple months that occur at the engineering schools themselves. I promise you, these years have been the most painful of my life and I mean it. I have an certain ego and I was humbled, but when i see people working in jobs where they break their bodies for pennies, its not that bad, even if its intellectualy painful. What I got away with, is this : -You need to find your techniques/workflow to self study efficiently, no one taught me to self study because i didnt really needed to work in high school to get the grades but it couldnt cut it anymore so it was necessary to react and this was only at the end of my first year that I learned methods online to study efficiently which teachers never told me about. When you achieve a self study routine you are ahead of 90% of people that study the night before the exams thats doesnt remember the content of the first semester going into the second while you can remember all possible things with incredible tools like anki and i promise you this tool is the glitch of learning it saved my ass seriously use it for a certain period it will change your life I mean it ! -This allowed me to be able to study almost anything and become an expert in any field if im interested in it. This is for the most part also what an employer wants, a guy that knows a lot of stuff in the domain, especially in engineering. -The more you advance in the studies the more things are rigorous, everything in high school was hand wavy and questionnable at best. Everything that I learned explained/proved rigorously what I saw in high school and explained the origin and the "why" of large amount of maths and physics. And most of all the higher you go the more you understand why people taught you those topics and the better you can see the landscape of things that you learn and how everything is interconnected. I know how you feel and i dont want to tell you the generic things because you already know them obviously you need to believe in yourself etc.. I just want to tell you this. What helped me was to try to seperate myself from the value that I attributed myself from being bad or good to a particular topic and this really helped me and was key. I really dont think its a way to gaslight myself or some sort i think its the best way to think about it is "I dont understand this concept im not stupid the things in high schools seemed hard at the time and now its childs play this is easy dont be afraid !" I encountered people that understood easily hard concepts, turns out they already learned and trained a lot on some of them, in maths context or boot camps. The only thing that you must always remember is that smart people dont exists. I've always told myself that smart people were talented/gifted and I've been proven wrong every single time. There are only three things to get success in stem, knowing by heart, understanding, practice. In physics I tend to believe that understanding makes everything easy but knowing and practice are key, in maths the knowing by heart and practice outweigh the understanding at some point because the two almost imply the understanding but this is only my take. You need to ratio thoses accordingly and remember its always personnal there isnt a perfect ratio for everyone and my take is vague and not true in certain cases but there is one for you and only you, you just have to find it just like your study methods and routine the only thing you need to do is test them and pick the best. Finally the best thing that i learned from a classmate was "This is just a game, with abilities and skill points you spends" it opened my eyes. For me exercising changed a lot of thing im overweight but not terrible and the workout is just a catalyser for learning. For me im lazy so if i grab every single thing that can make me learn faster just to make my life easy.