I think I got the joke. He was introducing the point topology, but the last result involves more structure than that, hence it would not be considered in an ordinary introductory course. It is indeed funny to add so much structure that the whole generality of the first definition gets destroyed. It gets slaughtered, imprisoned in the prison of theoretical physics. Which is funny.
@@u.v.s.5583 FYI the last result was a millenium prize problem which remained unsolved for a hundred years and got solved by a recluse russian professor whose proof requires more than hundreds of pages to explain. Assuming you already have advanced knowledge in the subject. Apart from this there are other funny bits which aren't as tragic as he described but still tragically happen in reality... I didn't get your bit about theoretical physics.
@@stavone12 There is a strange, counterintuitive hypothesis in theoretical physics, fought against by many. It professes that the spatial component of our Universe might be a 3D manifold. Hence studying the properties of 3D manifolds such as what can their general topology and geometry be like and how can we know is of some obscure interest for physicists. Funny and ironic, how the only solved Millenium prize problem never resulted in a Millenium prize being payed.
@@aurelia8028 true, but knowing the proof is optional. You can almost always use all theorems as basically axioms on your exam(obviously you don't have to independently prove them again lol). But still it's easier to remember a theorem if you do know how it is proved. So it can be a bummer to not just get the proof right away.
@ie6730 I have studied math and if you are asked to prove something on an exam it's a more advanced result that is dependent on the proofs in your textbook. Your textbook for your course may prove theorems A, B, and C. I didn't get asked to randomly prove thereom B. Instead, they asked me to prove theorem D that wasn't covered in my book. And in order to do so, you may use theorems A, B and C without also having to prove them. I think it's better that way because you need to be trained in logical thinking and not the memorization of proofs.
eigenchris I was thinking to myself as I watched this video “Why the fuck are there two slightly different looking Ps to represent two different factors? That’s just making it confusing, create a new symbol for fuck sake.”
@@eigenchris I had a professor just 3 weeks ago use 'K', 'Kappa', and 'k' in the same handwritten expression, and I couldn't tell the difference between any of them.
Random Processes course in my case. "Now this theorem is the most important theorem of our course. Please pay the most attention. Proof. 1 Exercise 2. Trivial 3. Obvious 4. Exercise"
I have never felt so called out yet so validated by a single video before. I took an undergrad course in topology last year, and every single bit was right on the money. The disappointment at the lack of visual intuition, the constant references to excersises for proofs, the prof saying near impossible-to-parse formulae as if they were obvious, even the exact definition of compactness I hoped I could skip over, only for it to appear literally everywhere after, it all made me think you somehow got inside my head and translated my thoughts into a digital format. I had no idea this was such a universal experience with this subject. 10/10
Sorry to hear you identify with this video so much. If you want to try topology again, just for fun, you can look at my pinned comment for the lectures by Tadashi Tokieda, and also the M335 videos. I feel like a lot of the questions that originally got the field of topology started have basically been cut out of a lot of courses, leaving only the abstract stuff that was figured out later. The result is like trying to climb a ladder with the bottom rungs removed. Prof Tokieda understands this and tries to motivate everything with pictures. The M335 videos also have a lot of topological spaces built using physical sculptures, so you can see how the spaces fit together when they are cut apart and glued together.
I would ctrl-v my proof here in the comments but unfortunately the max length of Yt comments is too short and there's not enough space to fit it into one comment...
I appreciate anybody who releases a video on April Fool´s day telling the truth while offending people who believe content made from BBC News and CNN! Our mission in this world is to educate our fellow man!
@@maythesciencebewithyou nah critical thinking used to be involved At least pre industrial revolution in germany. Or around that time. Now school is just like idk a industrial worker creating factory mostly. Well it isn't anymore "as bad" as it was when the industrial revolution started.
this is a perfect encapsulation of how I felt during 70%+ of my classes in engineering like I get the need for precise, formalized language in textbooks, but can't you give me a very simple and practical overview of what each theorem or chapter or whatever, actually *means* it feels like every new concept introduced just springs out of nowhere with no obvious reason or connection to anything else
"if you can't explain it in easy language, you haven't understood the subject well enough" (or something like that) So I'm just gonna assume my math profs don't understand it themselves and just 1:1 read a script they didn't write themselves [last one sadly was true some times]
I think professors are really bad at emphasising what you shouldnt try to understand in terms of familiar concepts. Abstraction is useful and makes solving problems easier, and often it is far easier to not try to relate back to anything. But professors never say when this is the case.
@@sploofmcsterra4786I had a 1st sem math professor who did this almost perfectly: He was a master at often making analogies and connections to real things (or previous simpler concepts) like using dominoes to illustrate complete induction, or mentioning that human ears do use *some kind* of Fourier analysis to process sound waves, yet at many other points in the lecture he would also caution there is no easy analogy / direct application and advise to simply understand the presented concept/abstraction as it is.
I'm crying, this is so good. I took Real Analysis, which had a section on the topology that covered this, so luckily I understood the jokes! My favorite is, "One could even say that if you don't understand compactness, you don't understand topology."
Dear Creator of this phenomenal topology tutorial, I am writing this comment to express my immense gratitude for your outstanding work in creating and sharing this incredibly informative and captivating tutorial on topology. As someone who has been eager to learn more about this fascinating branch of mathematics, I can confidently say that your video has provided me with invaluable insights and a much deeper understanding of the subject matter. The way you explained the core concepts and principles of topology was nothing short of exemplary. Your ability to convey complex ideas in such a clear, concise, and engaging manner is truly commendable. The visual aids and examples you provided throughout the tutorial made it so much easier for me to grasp the ideas being presented and to see how they are connected to real-world applications. Moreover, I was thoroughly impressed with the pacing and structure of the video. It is evident that a significant amount of effort went into organizing the content in a way that is both logical and accessible. As a result, I was able to follow along with ease and build upon my knowledge incrementally, without ever feeling overwhelmed or lost. I also wanted to express my appreciation for your dedication to fostering a welcoming and supportive learning environment. Your genuine enthusiasm for the subject matter, combined with your patient and encouraging teaching style, made me feel comfortable asking questions and exploring the subject more deeply. This, in turn, has inspired me to continue my studies in topology and to share my newfound knowledge with others. In conclusion, I cannot thank you enough for the positive impact your tutorial has had on my learning journey. Your hard work, passion, and expertise have not only demystified the world of topology for me but have also instilled in me a newfound excitement for the subject. I eagerly await your future content and wish you the best of luck in your ongoing endeavors to educate and inspire others in the field of mathematics. Sincerely, (subscribed) Grigori F.
I have a proof of the Poincaré conjecture. Now, credit where credit is due, it is partly based on the work of Grigori Perelman, but the name in the cover is different.
2:10 I feel that so much. Studying logic in computer science it's so often they'll go 'right you'll need to know the proof for this exam so I'll set it as an exercise to do at home' and then I never do the exercise because if it's that important just teach me it
this actually happened to me for my senior design project it was in computer science, but rather than having our own ideas we just got a list of sponsored projects and had to pick one in a group of up to 5 people almost all of the projects were more for electrical enginnering and computer engineering students, so we went with one about cryptography except they basically just told us to implement some algorithms and test them but upon reseaeching them, it seemed the algorithms only existed in like one paper that read exactly like this video and some other thing saying that these algorithms would be the standard in like a decade and trying to understand them by looking at other algorithms they were based on led to similar results so basically they just told us "here, implement this algorithm that only exists in theory in a paper we can't read" and we spent two semesters trying to figure it out we couldn't do it but they still gave us passing grades in that class anyways
Damn, that definition of compactness let me crying, I’m studying the “basics” of topology and sometimes I want to give up, but mathematics are incredibly beautiful and understanding funny videos like this one are somewhat motivating 😂
General topology and functional analysis used to be a single course in the mathenatics dept of the university of Athens. It had a passing rate of about 1%. When it was split in two separate courses their passing rate finally rose up to 3%.
I always remember in my first lecture of applied math course, the prof. introduced differential geometry in the way just like this video. I thought that he was just having a little chat about the future lecture, and it turn out that he was actually teaching it.
I was going to make a joke about watching this video upside down cause autorotation was bugging out, but now I just want to try my hand at writing a 5 minute topogy intro. Especially the motivation part.
The best (or was it the worst?) part is that this is a perfect summary of my intro to topology course. Well, no, not exactly. Our professor specifically warned us not to try and prove the Poincare Conjecture, but I'm pretty sure that was just a reverse psychology trick.
I'm a CS student and this video perfectly summarizes my every algebra/calculus/discrete math experience. Hopefully I won't ever have to study topology lol
Even though you're kidding, it's brilliant! Thank you so much for your great vids. This vid summed up my experience when I've first read books and publications on topology, manifolds, diferrential geometry, tensors, etc. in order to understand general relativity during my spare time. It led me to a quite similar existencial issue. And to another practical one: shall I give up? I was stuck. Then, I found your channel. Now, it makes me up with those hard maths. Thanks again
After this I feel lucky I had an astonishingly good teacher in my undergrad topology course that made everything very visual and practical, since some people here are actually relating to the video and that's scary
this is literally what taking a math degree is like except you get to have breaks to cry and regret all your life decisions up to the point of starting a topology course
I found a Scientific American article, "What Does Compactness Really Mean?" (It can be found via google) It turns out that compact surfaces are like jello, while non-compact surfaces are like rice pudding. I hope that clears everything up.
@@eigenchris Wow, I can't even guess how a monad is like a burrito (it sounds like a riddle). It does remind me of a comic that can be googled, "Barbie on Monads"
Even though this is a satire, I am really sorry if this is your experience with topology classes. Topology was one of my favorite undergraduate classes, so I feel obligated to give a little bit more motivation for the course. Topology is the theory of measurements and observations. For a space, we want to define which properties of the space are observable, what properties we can check by doing a series of measurements. We call such an observable property, an open set. Take for instance the real numbers. We can observe whether a real number in decimal expansion is larger than 1, since we need only verify that: either the number before the `dot' is larger than 1, or the number before the `dot' is a 1, and there is a non-zero digit in the decimal expansion. However, the property of checking whether a number is equal to 1 is not observable, which may seem counter intuitive. The problem is with numbers such as 1.00000000000..., in which we need an infinite amount of time to verify whether all decimal digits are zero. As such, "number is equal to 1" is not an observable property, so it is not open. However, it is observable whether a number is not 1, so the property "number is equal to 1" is closed. So, Theorem 1.2 implies, that any observable property on the real numbers can be expressed as a bunch of "larger than" and "smaller than" tests. Continuity of functions should be a natural thing to require, since if we have a test on the image of the function f:X -> Y (observation on Y), then we should be able to translate that in a test on the domain of f (observation on X) as follows: Take the element of X, put it in the function, and check if f(x) satisfies your observation on Y. I could go on and on, widening my explanation, and motivating further concepts, but I will leave it here.
I think topologists would make great gymbros: "Bro, do you even lift? You're lookin' pasty, no homeo" or "Bro, you on T? Yeah bro, T2, completely T2. Bro, you sure that's normal? Bruh, completely normal, perfectly normal. ... Brah, come back!"
See the book Mathematics Made Difficult by Carl E. Linderholm. It's basically this, but as a foundation of mathematics. For instance: "As an axiom on which to base the positive numbers and the integers, which have in the past produced much harmless amusement and are still widely accepted as useful by most mathematicians, some such proposition as the following is sometimes considered as being pleasant, elegant, or at least handy: AXIOM: Equalisers [sic] exist in the category of categories."
Real courses feel like the professor himself has no clue what he's talking about. Just repeating definitions, not explaining anything, regularly calling things trivial so that he doesn't have to explain things. What bugs me the most is that most start very slowly, explain the really simple stuff in great detail, stuff that any idiot should be able to understand right away or know from school, but when it comes to the hard stuff they just sprint from one thing to the next.
Topology is the basis of analysis and differential geometry, much of abstract algebra relies on topology too (you need topology to prove the fundamental theorem of algebra). That's hardly useless.
You lied to us. You said this was a joke video.
I think I got the joke. He was introducing the point topology, but the last result involves more structure than that, hence it would not be considered in an ordinary introductory course. It is indeed funny to add so much structure that the whole generality of the first definition gets destroyed. It gets slaughtered, imprisoned in the prison of theoretical physics. Which is funny.
I think that was the joke.
Some people have a very strange sense of humour
Anyway, I'm off to laugh at Peter Griffin's face on things it would not normally be on.
@@u.v.s.5583 FYI the last result was a millenium prize problem which remained unsolved for a hundred years and got solved by a recluse russian professor whose proof requires more than hundreds of pages to explain. Assuming you already have advanced knowledge in the subject.
Apart from this there are other funny bits which aren't as tragic as he described but still tragically happen in reality...
I didn't get your bit about theoretical physics.
@@stavone12 There is a strange, counterintuitive hypothesis in theoretical physics, fought against by many. It professes that the spatial component of our Universe might be a 3D manifold. Hence studying the properties of 3D manifolds such as what can their general topology and geometry be like and how can we know is of some obscure interest for physicists.
Funny and ironic, how the only solved Millenium prize problem never resulted in a Millenium prize being payed.
"1.2 theorem:
see 1.3 for proof
1.3 exercise
proof 1.2" god damn comedy genius. this is what school feels like.
I'm currently going through a geometric calculus textbook and this is exactly the experience
For real though, textbook authors _do_ do this shit
@@aurelia8028 true, but knowing the proof is optional. You can almost always use all theorems as basically axioms on your exam(obviously you don't have to independently prove them again lol). But still it's easier to remember a theorem if you do know how it is proved. So it can be a bummer to not just get the proof right away.
@@dekippiesip As a math student your professors ask you about proofs in exams so it’s very important for you know it
@ie6730 I have studied math and if you are asked to prove something on an exam it's a more advanced result that is dependent on the proofs in your textbook.
Your textbook for your course may prove theorems A, B, and C. I didn't get asked to randomly prove thereom B. Instead, they asked me to prove theorem D that wasn't covered in my book. And in order to do so, you may use theorems A, B and C without also having to prove them. I think it's better that way because you need to be trained in logical thinking and not the memorization of proofs.
I like how you introduced so many terms so quickly. The course was topologically compact.
topological compactness isn't related with real life compactness.
@@igormorgado I know almost nothing about Topology and after watching this video I know even less. :D
@@igormorgado but some of it was still topologically compact
I'd say it was pedagogically compact. You know, with respect to the pedagogical topology.
We can say that it is topologically compact if it is closed, bounded, and is an element of the Euclidian Topology
you gotta love it when rho and p are in the same expression. its not confusing at all
Inspired by a real life class I was in where a professor used K and Kappa in the expression, but wrote them nearly identically.
@@eigenchris "You can tell them apart by this stroke here"
"You're going crazy the stroke is exactly the same"
"no no no if you look very closely..."
eigenchris I was thinking to myself as I watched this video “Why the fuck are there two slightly different looking Ps to represent two different factors? That’s just making it confusing, create a new symbol for fuck sake.”
@Zoe Foxx should probably learn something from EEs. They use j to denote complex numbers.
@@eigenchris I had a professor just 3 weeks ago use 'K', 'Kappa', and 'k' in the same handwritten expression, and I couldn't tell the difference between any of them.
This is genuinely like the functional analysis course I did.
Random Processes course in my case.
"Now this theorem is the most important theorem of our course. Please pay the most attention.
Proof. 1 Exercise
2. Trivial
3. Obvious
4. Exercise"
@A_commenter lmao same
Wish me luck this upcoming semester lmao
I have never felt so called out yet so validated by a single video before. I took an undergrad course in topology last year, and every single bit was right on the money. The disappointment at the lack of visual intuition, the constant references to excersises for proofs, the prof saying near impossible-to-parse formulae as if they were obvious, even the exact definition of compactness I hoped I could skip over, only for it to appear literally everywhere after, it all made me think you somehow got inside my head and translated my thoughts into a digital format. I had no idea this was such a universal experience with this subject. 10/10
Sorry to hear you identify with this video so much. If you want to try topology again, just for fun, you can look at my pinned comment for the lectures by Tadashi Tokieda, and also the M335 videos. I feel like a lot of the questions that originally got the field of topology started have basically been cut out of a lot of courses, leaving only the abstract stuff that was figured out later. The result is like trying to climb a ladder with the bottom rungs removed. Prof Tokieda understands this and tries to motivate everything with pictures. The M335 videos also have a lot of topological spaces built using physical sculptures, so you can see how the spaces fit together when they are cut apart and glued together.
@@eigenchris for some reason the pinned comment isn't showing up?
Couldn't have said it better
@@technodragon990 ua-cam.com/video/SXHHvoaSctc/v-deo.html probably these
@@eigenchris
Pinned comment isn't visible to me
The Poincare conjecture proof is left as an exercise
🤣
😂😂😂
I would ctrl-v my proof here in the comments but unfortunately the max length of Yt comments is too short and there's not enough space to fit it into one comment...
Seriously though, when I see that in my notes, i cri everytim
To be fair, it is technically a solved problem. So one should be able to do it as an exercise.
@@valeriobertoncello1809 (Y) s ame
Sorry I wrote April Fool's instead of April Fools'. I finished this at like 2am.
eigenchris it’s spelled April fools’?
You fooled me for sure.
I appreciate anybody who releases a video on April Fool´s day telling the truth while offending people who believe content made from BBC News and CNN! Our mission in this world is to educate our fellow man!
@@Yatukih_001 im missing some context at here
Where can I buy this very accessible book you told?
Your P and rho look too different, making the proof of Thm 1.6 hard to follow. Maybe choose a font that makes them look more similar?
That would make it too much like a real math class. I needed sone way of hinting that this video was a joke.
@@eigenchris this video is not a joke. The only joke is in the title that it's a joke. This video is the honest beyond measure
@@ananyapamde4514 especially the last part 😭😭
@@ananyapamde4514 Joke is on us and all our years in university.
@@ananyapamde4514 It takes a smart a** to truly get math. The honesty is the joke and vice versa.
Theorem 1.9 proof:
"Homeomorphic to a 3-sphere!"
-minecraft menu splash text
instructions unclear. body has transformed into a klein bottle
That's topologically impossible. are you sure you didn't turn into a 3d projection of a klein bottle?
@@the314Qwerty In 4D vector space on a computer, without a projection.
Instructions unclear, became an expert of number theory instead.
It is so depressing that this is exactly how schools teach these days.
these days? Geez, you have no clue how much stricter and harder they made it in the past.
@@maythesciencebewithyou nah critical thinking used to be involved
At least pre industrial revolution in germany. Or around that time.
Now school is just like idk a industrial worker creating factory mostly.
Well it isn't anymore "as bad" as it was when the industrial revolution started.
It seem as Perelman had a lot of free evenings and saw this video once
this is a perfect encapsulation of how I felt during 70%+ of my classes in engineering
like I get the need for precise, formalized language in textbooks, but can't you give me a very simple and practical overview of what each theorem or chapter or whatever, actually *means*
it feels like every new concept introduced just springs out of nowhere with no obvious reason or connection to anything else
At least the use of springs is pretty obvious
"if you can't explain it in easy language, you haven't understood the subject well enough" (or something like that)
So I'm just gonna assume my math profs don't understand it themselves and just 1:1 read a script they didn't write themselves [last one sadly was true some times]
I think professors are really bad at emphasising what you shouldnt try to understand in terms of familiar concepts. Abstraction is useful and makes solving problems easier, and often it is far easier to not try to relate back to anything. But professors never say when this is the case.
@@sploofmcsterra4786I had a 1st sem math professor who did this almost perfectly:
He was a master at often making analogies and connections to real things (or previous simpler concepts) like using dominoes to illustrate complete induction, or mentioning that human ears do use *some kind* of Fourier analysis to process sound waves,
yet at many other points in the lecture he would also caution there is no easy analogy / direct application and advise to simply understand the presented concept/abstraction as it is.
I'm crying, this is so good. I took Real Analysis, which had a section on the topology that covered this, so luckily I understood the jokes! My favorite is, "One could even say that if you don't understand compactness, you don't understand topology."
That's a real thing I've seen people say. Extra-fun to hear after the word-salad definition of compactness.
the words “every open cover has a finite subcover” still trigger flashbacks almost 15 years later
Compactness is a beautiful concept. :)
Dear Creator of this phenomenal topology tutorial,
I am writing this comment to express my immense gratitude for your outstanding work in creating and sharing this incredibly informative and captivating tutorial on topology. As someone who has been eager to learn more about this fascinating branch of mathematics, I can confidently say that your video has provided me with invaluable insights and a much deeper understanding of the subject matter.
The way you explained the core concepts and principles of topology was nothing short of exemplary. Your ability to convey complex ideas in such a clear, concise, and engaging manner is truly commendable. The visual aids and examples you provided throughout the tutorial made it so much easier for me to grasp the ideas being presented and to see how they are connected to real-world applications.
Moreover, I was thoroughly impressed with the pacing and structure of the video. It is evident that a significant amount of effort went into organizing the content in a way that is both logical and accessible. As a result, I was able to follow along with ease and build upon my knowledge incrementally, without ever feeling overwhelmed or lost.
I also wanted to express my appreciation for your dedication to fostering a welcoming and supportive learning environment. Your genuine enthusiasm for the subject matter, combined with your patient and encouraging teaching style, made me feel comfortable asking questions and exploring the subject more deeply. This, in turn, has inspired me to continue my studies in topology and to share my newfound knowledge with others.
In conclusion, I cannot thank you enough for the positive impact your tutorial has had on my learning journey. Your hard work, passion, and expertise have not only demystified the world of topology for me but have also instilled in me a newfound excitement for the subject. I eagerly await your future content and wish you the best of luck in your ongoing endeavors to educate and inspire others in the field of mathematics.
Sincerely,
(subscribed) Grigori F.
this is top tier content
I love how this joke video is literally every math lecture I ever attended.
I have a proof of the Poincaré conjecture. Now, credit where credit is due, it is partly based on the work of Grigori Perelman, but the name in the cover is different.
Dude where's my e-certificate? I need to brag about my newfound knowledge on topology
This is actually easier to follow than many math classes I had in college
because you're still looking for the joke hiding somewhere ?
Absolutely superb overview of Topology. This video is the magical key to thoroughly understanding topology.
You don't need to know topology to enjoy this video, you just need to know the pain and suffering that is college
1:25 "Now that we're properly motivated..."
lmao
Watched at 2x speed, learned topology in 2.5 minutes.
This is the high qualty content I subbed for
Thank the youtube recommendation gods, this litle video hits every note in every university math school, i laughed so hard. Thank you for that.
2:10 I feel that so much. Studying logic in computer science it's so often they'll go 'right you'll need to know the proof for this exam so I'll set it as an exercise to do at home' and then I never do the exercise because if it's that important just teach me it
0:40 The first lecture of literally all of my university classes
I didn’t have to be unaware of this video being a joke, but until I reread the title at the end of it puzzled, I was.
I always loved the expression "if, AND ONLY IF, ...", it sounds so alerting and reprimanding. Like a professor raising his index finger.
Conway had "unless, and only unless," written (of course) as 'unlesss'.
Thank you. I've been looking everywhere for a video that explains this in easy terms, and this is the first one that I was able to follow.
This was like over half of my Real Analysis II course.
@@Wワイ I don't remember this in my Analysis II course, only integrals, differential equations and limitless suffering.
UA-cam is gonna think I wanna watch Topology videos now.
Thank you YT for recommending this to me over and over until I finally clicked on it. This is amazing XDXDXD
Me: my notes are clear and very detailed!
My notes:
this actually happened to me for my senior design project
it was in computer science, but rather than having our own ideas we just got a list of sponsored projects and had to pick one in a group of up to 5 people
almost all of the projects were more for electrical enginnering and computer engineering students, so we went with one about cryptography
except they basically just told us to implement some algorithms and test them
but upon reseaeching them, it seemed the algorithms only existed in like one paper that read exactly like this video and some other thing saying that these algorithms would be the standard in like a decade
and trying to understand them by looking at other algorithms they were based on led to similar results
so basically they just told us "here, implement this algorithm that only exists in theory in a paper we can't read" and we spent two semesters trying to figure it out
we couldn't do it but they still gave us passing grades in that class anyways
Damn, that definition of compactness let me crying, I’m studying the “basics” of topology and sometimes I want to give up, but mathematics are incredibly beautiful and understanding funny videos like this one are somewhat motivating 😂
Yo if I ever wanted to become rich from selling math textbooks I would just brand them as "and no proofs left as excersises to the reader!"
Then you just cite other books for proofs, and in those books proof is left as an exercise for the reader ;)
oh god this video is bringing back unfortunate memories of my linear algebra classes
This is more detailed, than what my college teaches
General topology and functional analysis used to be a single course in the mathenatics dept of the university of Athens. It had a passing rate of about 1%. When it was split in two separate courses their passing rate finally rose up to 3%.
3:33 nooooo that's just quasi-compact but it also has to be Hausdorff to be compact (obviously I won't explain what any of this means)
This video makes me laugh, but I start topology in a few days and I'll be crying by then
I have topology in the fall. I plan to cry from September to Christmas.
Ironically, this 'joke video' briefly explained concepts I was searching about :"DD
I always remember in my first lecture of applied math course, the prof. introduced differential geometry in the way just like this video. I thought that he was just having a little chat about the future lecture, and it turn out that he was actually teaching it.
This was so beautiful it made me weep. 😂 And then I wept for real, because this is how it really is most of the time.
Topology when it's on the top
I don't know never did it.
this might have actually been the first lecture in my grad topology course. where did you get this recording?
This the subject that needs to be explained to me like I'm a kindergartner
I spilled my coffee all over my hardcover copy of Munkres and really wished I had spilled my doughnut instead.
This felt longer than 5 minutes
this unironically made me miss (competently taught) math courses
You talk so slowly, you could've explained everything we can't figure out alone just by talking faster.
That was by far the best proof of Heine-Borel I have ever seen!
When he mentioned the graduate school I felt that
I was going to make a joke about watching this video upside down cause autorotation was bugging out, but now I just want to try my hand at writing a 5 minute topogy intro. Especially the motivation part.
The best (or was it the worst?) part is that this is a perfect summary of my intro to topology course. Well, no, not exactly. Our professor specifically warned us not to try and prove the Poincare Conjecture, but I'm pretty sure that was just a reverse psychology trick.
All the contents of the book are left for the reader as excercise.
I'm a CS student and this video perfectly summarizes my every algebra/calculus/discrete math experience. Hopefully I won't ever have to study topology lol
Looking at the proof to the Heine borel theorem really fucking made me HOWL with laughter.
I really hope that Grigorij Jakolevlic Perelman is viewing this
So funny and real! The "see problem ..." and the problem is "prove theorem..." actually happens.
Just so you know the actual joke starts at 0:00
you can thank me later
When your topography final is in five minutes and two seconds
If p-bar is closed... Find another bar to drink at!
I cannot explain how funny this video is. It speaks to the depths of my heart and i don't even study math
Even though you're kidding, it's brilliant!
Thank you so much for your great vids.
This vid summed up my experience when I've first read books and publications on topology, manifolds, diferrential geometry, tensors, etc. in order to understand general relativity during my spare time. It led me to a quite similar existencial issue. And to another practical one: shall I give up? I was stuck. Then, I found your channel. Now, it makes me up with those hard maths.
Thanks again
I am so utterly lost right now. Great video.
"So as you can see topology has many practical applications"
I died
After this I feel lucky I had an astonishingly good teacher in my undergrad topology course that made everything very visual and practical, since some people here are actually relating to the video and that's scary
this is literally what taking a math degree is like except you get to have breaks to cry and regret all your life decisions up to the point of starting a topology course
Wow, I'm glad that I now know all there is to know about topology!
Listening to this is like watching the turbo encabulator video
This video is homeomorphic to my topology lecture.
I found a Scientific American article, "What Does Compactness Really Mean?" (It can be found via google) It turns out that compact surfaces are like jello, while non-compact surfaces are like rice pudding. I hope that clears everything up.
This is like the time people told me monads were like burritos.
@@eigenchris Wow, I can't even guess how a monad is like a burrito (it sounds like a riddle). It does remind me of a comic that can be googled, "Barbie on Monads"
this is how high school algebra felt to me
Even though this is a satire, I am really sorry if this is your experience with topology classes. Topology was one of my favorite undergraduate classes, so I feel obligated to give a little bit more motivation for the course.
Topology is the theory of measurements and observations. For a space, we want to define which properties of the space are observable, what properties we can check by doing a series of measurements. We call such an observable property, an open set.
Take for instance the real numbers. We can observe whether a real number in decimal expansion is larger than 1, since we need only verify that: either the number before the `dot' is larger than 1, or the number before the `dot' is a 1, and there is a non-zero digit in the decimal expansion.
However, the property of checking whether a number is equal to 1 is not observable, which may seem counter intuitive. The problem is with numbers such as 1.00000000000..., in which we need an infinite amount of time to verify whether all decimal digits are zero. As such, "number is equal to 1" is not an observable property, so it is not open. However, it is observable whether a number is not 1, so the property "number is equal to 1" is closed.
So, Theorem 1.2 implies, that any observable property on the real numbers can be expressed as a bunch of "larger than" and "smaller than" tests.
Continuity of functions should be a natural thing to require, since if we have a test on the image of the function f:X -> Y (observation on Y), then we should be able to translate that in a test on the domain of f (observation on X) as follows: Take the element of X, put it in the function, and check if f(x) satisfies your observation on Y.
I could go on and on, widening my explanation, and motivating further concepts, but I will leave it here.
Thank You
At times I was wondering if it was speech synthesis.
Finnally someone explains it clearly.
Finally I can claim i know at least some of topology.
I had a professor who was like this. Dropped that class and took it next semester with a different one, had a way better experience..
I actually learned things from this video
LOL!!!!! I love the video, please do a five-minute tutorial for other topics as well.
“Well, as we all know…”
“Clearly…”
“It’s trivial to see…”
Flashbacks to my physics and calculus textbooks.
Perelman after watching the video: Hurray!! I proved Poincare Conjecture.
No mention of the hairy ball theorem though...
I'm getting fucking war flashbacks, this is exactly why I left maths and I'm never going back
Lol the Poincaré conjecture
This can be summed up in one word: what.
I think topologists would make great gymbros:
"Bro, do you even lift? You're lookin' pasty, no homeo" or
"Bro, you on T?
Yeah bro, T2, completely T2.
Bro, you sure that's normal?
Bruh, completely normal, perfectly normal.
...
Brah, come back!"
See the book Mathematics Made Difficult by Carl E. Linderholm. It's basically this, but as a foundation of mathematics. For instance:
"As an axiom on which to base the positive numbers and the integers, which have in the past produced much harmless amusement and are still widely accepted as useful by most mathematicians, some such proposition as the following is sometimes considered as being pleasant, elegant, or at least handy: AXIOM: Equalisers [sic] exist in the category of categories."
you tricked me into learning monster
Definition 1.4 to 1?5 got me cracking up
Real courses feel like the professor himself has no clue what he's talking about. Just repeating definitions, not explaining anything, regularly calling things trivial so that he doesn't have to explain things. What bugs me the most is that most start very slowly, explain the really simple stuff in great detail, stuff that any idiot should be able to understand right away or know from school, but when it comes to the hard stuff they just sprint from one thing to the next.
Exercise 1.3 was good. Mixing "cap ρ" with P was truly sinister.
The force is strong in this one.
Thank you I am so glad that I could skip the whole topology course in university because of this video.
Topology is the basis of analysis and differential geometry, much of abstract algebra relies on topology too (you need topology to prove the fundamental theorem of algebra). That's hardly useless.