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.
Seriously, I don't know if youtube's algorithm is crazy or genius. Why am I here ? *Why did I watch the entire video ?* Lately i waste most of my time on Vtuber hololive weeb shit, why did this pop up and how did youtube know I would watch it till the end ??? It knows something about me that I don't.
Had a measure theory teacher. She literally had equivalence classes for characters she denoted by the same symbol (such as 'mu', 'm', 'M', 'w', 'W', 'n', 'N' -- any differnace between these were not discernible even under the closest inspection). Frankly was a tough class...
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 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"
For beginners who actually want to learn topology, here are a couple resources: 1. Lectures by Dr Tadashi Tokieda (focus is on intuition and pictures instead of formal proofs): ua-cam.com/video/SXHHvoaSctc/v-deo.html 2. M335 Topology Videos (has lots of topological sculptures and pictures for visualizing things): ua-cam.com/play/PLJHszsWbB6hq40r_aSVlCXDvTT0VcrgcT.html 3. Snoopy Notes (written by a class of students): www.math.colostate.edu/~renzo/teaching/Topology10/Notes.pdf
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!
@@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.
@@jakeupboy Ah, but what did your fake analysis professor do? You can only tell real from fake (or from imaginary for that matter) if they behave differently.
This is very similar to what my first year of Higher Mathmatics at Uni looked to me, minus the fun pictures at the beginning. Sadly, this was before UA-cam, The Khan Academy, 3b1b, etc...
At 3:13, I didn't find the proof confusing but I did find the diagram confusing. In fact, I think it is wrong. Since the intersection of the set C-sub-Rho and the set P is the empty set, the dashed circle should lie outside the boundary of set P, albeit still containing the point P. Then the proof makes sense and is obvious. (Sorry, I'm too old to know how to use time-stamp links or fancy fonts in the comments.)
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...
@Joe Duke Do people still believe the college system isn't about to implode? I can sit at my computer, learn everything in the entire world, for free, at my own pace. I don't understand why people still go.
@@ThatGuyDownInThe because employers value the piece of paper that pops out after thousands of dollars and 4 years of your life are wasted C's get degrees amirite
@@will123134 This. A diploma is a definite proof of what you've learned, people know what they can expect you to know if you have it. If you learned all of it by yourself, the only way for them to validate that is to give you a test during your solicitation. Looking at a diploma is much faster and more cost efficient for an employer, so yeah what do you expect.
@@ThatGuyDownInThe Learning by yourself and with just the internet is no real education. Maybe if people were ready to spent money on textbooks of their subject matter but even then, most don't have the will/motivation to study by themself enough to become profficent.
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.
This has to be the greatest, funniest piece of mathematical humor there is. Good one. Nontheless, a great lecture in topology too. You get 5 stars in an 8 dimensional box.
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."
As a CAD engineer I just push a button that says topology and fun stuff happens. They said Math would be vital to my career, but it's actually mostly pushing buttons.
Year late reply to this as only just seen a notification but I engineer using CAD (technically Design Engineer), 3d printed things, pushing "topology" or "optimise" reduces material whilst maintaining strength, as long as you put the correct inputs in the first place
Thanks, eigenchris! Thanks to this video I was able to quit my maths program and to actually start enjoying my life, saving me thousands of dollars and an existential crisis!
@@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 such an accurate depiction of how irritating and ridiculous the academic lens is when applied to simple concepts and it makes me genuinely upset. Fantastic video.
@@ilanzatonski8826 think of it as building a house. If you build a shed you don't need any foundation. Just build it, simple and practival. If you want to build a skyscraper on the other hand you need to build a very deep and strong foundation. You want to go far into the sky, yet you are digging a deep hole. That feels very unsatisfying, but if you would just start building your skyscraper from ground level it would collapse long before you reach your planned height. So you actually do need to create that monster foundation.
I spent this summer doing topology research at my university. The hardest part is (somehow) trying to answer friends and family who ask the innocent questions "So, what does "topology" mean?" and "What kinds of applications does it have?". The worst part is, nobody actually cares about the answer but they always insist that I try to answer even after I explain that it is hard to explain without using tons of math jargon.
@@eigenchris I am an 3rd year undergrad doing research with one of the professors at my university. So far, I have just being doing preliminary work to build up the necessary expertise to be actually helpful since I had no experience with topology before working with him. The general topic is fundamental groups, but I don't know exactly we will be working on yet. He mentioned that he has recently been working with non-Hausdorf spaces so maybe trying to describe the fundamental groups of certain non-Hausdorf spaces? I can't wait to find out myself.
This may be unsatisfying but I describe topology as the study of convergence. Its useful to be able to talk about going to something else precisely and topology is basically the weakest structure needed to accommodate this notion. Once you start looking into this, and adding more structure, other intriguing properties come up.
This is exactly what my former math professor did as a lecture, except it wasn't April Fools and he was completely serious the whole time. Also I'm scared that I understood as much as I did.
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 tried reading a book on topology called 'introduction to topology' by someone called bert mendelson. This video exactly mirrors the experience I had.
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.
LOL for people who haven't study math in college, this is actually exactly what an intro topology course would look like (or any advanced math courses for that matter). The only joke is that a professor would usually spend a solid 50 minutes instead of 5 to cover all those to us poor math students.
I genuinely haven't laughed out loud at a video more than this one. This is literally how my Topology course felt life. Shit went straight over my head lol
This was great! I loved how the proof for the only solved millennium problem was left as an exercise to the reader. Especially since the proof took several years to verify, if I'm not mistaken.
This made me chuckle. I did my Maths degree about 40 years ago but it brings back memories... like complete and utter bewilderment during a 3rd year Algebraic Topology lecture. "Clearly..." a phrase used in so many mathematics texts. Thanks for sharing this, superb!
1:20: * we need adjoint functors to understand monads * we need monads to understand F-Algebras * we need F-Algebras to understand catamorphisms * we need catamorphisms to understand the Bird-Meertens formalism (BMF) * we need the BMF to understand functional programming * we need functional programming to understand countable intervals * we need countable intervals to understand topological spaces * (...)
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
Having taken those 2 grad Topology courses during my last 2 semesters as an undergrad made me a musician. 19 years later, and now having published in peer reviewed physics journals, and attend too many conferences, I find eigenchris's work to be that one point in Cantor's Leekee Teepee where true humor can be found. My deepest appreciation, sir.
"these images make topology look way more fun and interesting than it actually is. I will not be referring to these images again at any point during the course."
I was terrified that Theorem 1.6 was gonna start including 0's to make this both a visual and phonetic nightmare. *"And clearly, we can see that C-Rho has zero points of intersection with P."*
thank you so much for this. this really put the edges to the nodes and made my thesis perfect. as a side note, this allowed me over the weekend to solve the P vs. NP problem writing on a grain of rice that i heated up and morphed into a printing press.
4 роки тому+11
This is actually easier to follow than many math classes I had in college
Thanks for the harsh reminder that I have no education or experience in any area that even sniffs at math like this. Didn't understand a single sentence
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
I’ve always thought I was terrible at maths but everything I’ve just seen made absolute perfect sense to me. Also the walls have started laughing at me and the kitchen is on fire.
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 really wish I had been taught "Theorem speak" when I was in highschool so maybe I could have gotten used to it, for some reason it just doesn't fit into my brain.
I understand topology in more art than maths. I'm a 3D artist. In communities' forums, you'd often hear artists talking about making "clean topology" - meaning tidy meshes with quads, least possible tris and no n-gons (polygons with five or more vertrices). Clean topology means easier subdivision, easier manipulation for animators.
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"
Here's how to understand compactness. Consider a game of infinite whac-a-mole. It's just like the regular game of whac-a-mole, except that once you kill a mole it stays dead. And, there might be an uncountable infinity of moles. Compactness means that if you can kill all the moles with a possibly infinite number of hammer blows with hammers of various sizes, if you were clever you could have only had to use a finite number of those hammers.
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.
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
i dont know how i got to this video. i dont even like math. i went to community college for culinary arts. where am i
Seriously, I don't know if youtube's algorithm is crazy or genius. Why am I here ? *Why did I watch the entire video ?* Lately i waste most of my time on Vtuber hololive weeb shit, why did this pop up and how did youtube know I would watch it till the end ??? It knows something about me that I don't.
worth it i bet
@@tomfillot5453 wait you too? Is this the pattern?
@@cfish1188 same for me
Maybe if you studied topology you would know where you are.
legend says that your viewers are still trying to prove theorem 1.9
And legend says it was a russian hermit with no Internet connexion who refused 1 million dol.
The proof is relatively trivial but too long to fit in the margin of a page so I'll hold off publishing it ...
Grisha says he has the proof.
@@JgM-ie5jy fermat be like
Grigori Perelman solved it, therefore he watched this video
The C, P, Rho, and Complement part was genius. It seems my professors learned their notation here!
Had a measure theory teacher. She literally had equivalence classes for characters she denoted by the same symbol (such as 'mu', 'm', 'M', 'w', 'W', 'n', 'N' -- any differnace between these were not discernible even under the closest inspection). Frankly was a tough class...
WHY DO PEOPLE DO THIS! YOU CAN USE ANYTHING TO DENOTE THINGS. ITS A VARIABLE! WHYYYYYYY???
@@mewmewgene not variables
@@richardgui2934 Like my statistics course.
p = P(X=x | Y=y) and you could never tell if its uppercase or lowercase P, X,Y etc
Had a professor that only used a with hexadecimal subscripts. So a_1a a_2f a_3d etc.
> Poincaré Conjecture
> “a fun little problem that you can try and tackle on your evenings and weekends”
Specifically every evening and weekend for the next 30 years, only to find out someone beat you to it in 2006
I laughed right out loud at this
D
Fun when you win the $1,000,000 Millenium prize for having solved it.
@@QDWhite And then you reject the money.
I'd be laughing if i wasn't crying from the flashbacks
If this is a joke, then all my years in university were jokes.
Hopefully it was more than one joke per year. Not only were your years at university jokes, they apparently had bad comedic timing.
Sorry you had to find out this way
@@KirkWaiblinger Actually it was gratifying that four decades later I had no trouble keeping up. The old jokes are still the best ones(?)
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
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
For beginners who actually want to learn topology, here are a couple resources:
1. Lectures by Dr Tadashi Tokieda (focus is on intuition and pictures instead of formal proofs): ua-cam.com/video/SXHHvoaSctc/v-deo.html
2. M335 Topology Videos (has lots of topological sculptures and pictures for visualizing things): ua-cam.com/play/PLJHszsWbB6hq40r_aSVlCXDvTT0VcrgcT.html
3. Snoopy Notes (written by a class of students): www.math.colostate.edu/~renzo/teaching/Topology10/Notes.pdf
Okay but do they answer the question we learn in graduate school?
@@cassidity7924 That's still an open problem, I think.
Thanks, I need to know about these funny surfaces to test an old mentor's theories.
Yes! Prof T2, as Tadashi claims himself to be in the video, is an excellent excellent teacher!
Also check out WhyBmaths
grigori perelman was able to prove poincare conjecture thanks to this course
yeah, i think hed had some fun in evenings and weekends with it for sure
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?
"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.
This is how all of my math classes were. Minus the helpful diagram at 3:16
i swear to god my real analysis professor drew the same exact picture
@@jakeupboy Ah, but what did your fake analysis professor do? You can only tell real from fake (or from imaginary for that matter) if they behave differently.
This is very similar to what my first year of Higher Mathmatics at Uni looked to me, minus the fun pictures at the beginning. Sadly, this was before UA-cam, The Khan Academy, 3b1b, etc...
@@donaldhobson8873 Why is this so funny?
At 3:13, I didn't find the proof confusing but I did find the diagram confusing. In fact, I think it is wrong. Since the intersection of the set C-sub-Rho and the set P is the empty set, the dashed circle should lie outside the boundary of set P, albeit still containing the point P. Then the proof makes sense and is obvious. (Sorry, I'm too old to know how to use time-stamp links or fancy fonts in the comments.)
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.
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
eigenchris: "Topology is the study of how topological spaces and their properties are preserved under homeomorhpisms"
Me: 𝒐𝒐𝒉𝒉𝒉 𝒏𝒐𝒘 𝑰 𝒈𝒆𝒕 𝒊𝒕!
Why wouldn't you get it, what's not clear in this sentence?
Yeah there you go, you got it
Wait we can do italics in UA-cam comments? Sweet
That's exactly what the teacher is imagining will happen when they try to explain it to their students
@@DogeMcShiba Don't you mean that they are saying, " Thank God he got it, I never did."
This video activated my fight-or-flight response
Instructions unclear, became an expert of number theory instead.
came for a laugh, left with anxiety :|
The cycle of life
Yeah, especially with the question he anticipates at the end. Easy way to make you question all your life choices lol
Theorem 1.9 proof:
"Homeomorphic to a 3-sphere!"
-minecraft menu splash text
“As you can see, topology has many practical applications.” Oof, too real.
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.
where's the joke? this is just like my rl topology courses, but with fewer pics of the professor's cat.
It’s funny cause they always think it’s quirky and original even though that’s literally the most common ‘quirky’ thing professors do
Maybe it's less cynical than you think and they just really like their cats
holy shit same
Oh man, there are easier ways to get one million dollars.
@Joe Duke Do people still believe the college system isn't about to implode?
I can sit at my computer, learn everything in the entire world, for free, at my own pace. I don't understand why people still go.
@@ThatGuyDownInThe because employers value the piece of paper that pops out after thousands of dollars and 4 years of your life are wasted
C's get degrees amirite
You pay for the diploma, not the education
@@will123134 This. A diploma is a definite proof of what you've learned, people know what they can expect you to know if you have it. If you learned all of it by yourself, the only way for them to validate that is to give you a test during your solicitation. Looking at a diploma is much faster and more cost efficient for an employer, so yeah what do you expect.
@@ThatGuyDownInThe Learning by yourself and with just the internet is no real education. Maybe if people were ready to spent money on textbooks of their subject matter but even then, most don't have the will/motivation to study by themself enough to become profficent.
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.
This has to be the greatest, funniest piece of mathematical humor there is.
Good one.
Nontheless, a great lecture in topology too.
You get 5 stars in an 8 dimensional box.
Proof?
@@NichaelCramer The proof is analogous to the proof of Theorem 1.2.
The proof is elementary and therefore does not need to be mentioned.
The proof is left as an exercise for the reader
@@NichaelCramer Self evident
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.
As a CAD engineer I just push a button that says topology and fun stuff happens.
They said Math would be vital to my career, but it's actually mostly pushing buttons.
A CAD engineer? Do you engineer FOR CAD or WITH CAD?
@@samisiddiqi5411 Technically he could also be writing cad software with that title??
What does that button do, exactly?
Year late reply to this as only just seen a notification but I engineer using CAD (technically Design Engineer), 3d printed things, pushing "topology" or "optimise" reduces material whilst maintaining strength, as long as you put the correct inputs in the first place
so there IS a practical use for this?
this is top tier content
Thanks, eigenchris! Thanks to this video I was able to quit my maths program and to actually start enjoying my life, saving me thousands of dollars and an existential crisis!
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.
This is such an accurate depiction of how irritating and ridiculous the academic lens is when applied to simple concepts and it makes me genuinely upset.
Fantastic video.
Omg yes the definitions in graph theory make me go insane for such simple concepts ffs
you'll get used to it eventually
@@ilanzatonski8826 think of it as building a house. If you build a shed you don't need any foundation. Just build it, simple and practival. If you want to build a skyscraper on the other hand you need to build a very deep and strong foundation.
You want to go far into the sky, yet you are digging a deep hole. That feels very unsatisfying, but if you would just start building your skyscraper from ground level it would collapse long before you reach your planned height. So you actually do need to create that monster foundation.
It seem as Perelman had a lot of free evenings and saw this video once
I spent this summer doing topology research at my university. The hardest part is (somehow) trying to answer friends and family who ask the innocent questions "So, what does "topology" mean?" and "What kinds of applications does it have?". The worst part is, nobody actually cares about the answer but they always insist that I try to answer even after I explain that it is hard to explain without using tons of math jargon.
If I might venture to ask, what were you researching, specifically?
@@eigenchris I am an 3rd year undergrad doing research with one of the professors at my university. So far, I have just being doing preliminary work to build up the necessary expertise to be actually helpful since I had no experience with topology before working with him. The general topic is fundamental groups, but I don't know exactly we will be working on yet. He mentioned that he has recently been working with non-Hausdorf spaces so maybe trying to describe the fundamental groups of certain non-Hausdorf spaces? I can't wait to find out myself.
This may be unsatisfying but I describe topology as the study of convergence. Its useful to be able to talk about going to something else precisely and topology is basically the weakest structure needed to accommodate this notion. Once you start looking into this, and adding more structure, other intriguing properties come up.
@@robvdm u clearly don’t understand topology then this is so vague
@@harmonicarchipelgo9351how did it go
This is exactly what my former math professor did as a lecture, except it wasn't April Fools and he was completely serious the whole time. Also I'm scared that I understood as much as I did.
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 tried reading a book on topology called 'introduction to topology' by someone called bert mendelson. This video exactly mirrors the experience I had.
@*S U C T I O N* You can try!
try munkres it has some intuation
yeah munkres is good, down the road it gets very confusing tho
I suggest to all the Dugundji's book "Topology"
I'm vibin on Lee's Topological Manifolds book.
"We'll use capital P. And the roman letter, Capital Rho."
Yep. Accurate.
greek* sorry
2:00 OK, let's give this a shot:
An open interval is a set of the form {x in R: a
the words “every open cover has a finite subcover” still trigger flashbacks almost 15 years later
Compactness is a beautiful concept. :)
4:17 The joke is that the Poincare Conjecture is one of the Millennium Problems ($1m prize) and has a very advanced proof.
This really made me laugh. I tried to read a book on topology once and this was precisely the experience I had.
Based on other comments, this seems to be a pretty common feeling among math students.
This will appear in everyone's recommended page in 10 years or so
XD
Hope everyone can live through 2020
Alejandro Reguera Diaz Lol yes! We are making history by even commenting on this video.
Bold of you to assume civilazation will have crawled back from the ashes of 2020 by then.
Very unique
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.
LOL for people who haven't study math in college, this is actually exactly what an intro topology course would look like (or any advanced math courses for that matter). The only joke is that a professor would usually spend a solid 50 minutes instead of 5 to cover all those to us poor math students.
I genuinely haven't laughed out loud at a video more than this one. This is literally how my Topology course felt life. Shit went straight over my head lol
This was great! I loved how the proof for the only solved millennium problem was left as an exercise to the reader. Especially since the proof took several years to verify, if I'm not mistaken.
no, you're mistaken. its a fun little problem that can be done on your evenign and weekends
1.9: The proof of the Poincaré conjecture is left as an exercise to the reader. Grigori Perelman: Say no more
I love how this joke video is literally every math lecture I ever attended.
Watched at 2x speed, learned topology in 2.5 minutes.
This made me chuckle. I did my Maths degree about 40 years ago but it brings back memories... like complete and utter bewilderment during a 3rd year Algebraic Topology lecture. "Clearly..." a phrase used in so many mathematics texts. Thanks for sharing this, superb!
Absolutely superb overview of Topology. This video is the magical key to thoroughly understanding topology.
0:17 a monad is just a monoid in the category of endofunctors
1:20:
* we need adjoint functors to understand monads
* we need monads to understand F-Algebras
* we need F-Algebras to understand catamorphisms
* we need catamorphisms to understand the Bird-Meertens formalism (BMF)
* we need the BMF to understand functional programming
* we need functional programming to understand countable intervals
* we need countable intervals to understand topological spaces
* (...)
Fee fi fo fum, I smell a self referential theorem!
Dude where's my e-certificate? I need to brag about my newfound knowledge on topology
1:25 "Now that we're properly motivated..."
lmao
I've had lectures like this at university and I had to actually understand them to pass...
3:50 Proof by triviality is certainly the most powerful mathematical tool mathematicians can harness! 😂
Oh god, this hit the nail straight on the head
You don't need to know topology to enjoy this video, you just need to know the pain and suffering that is college
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
Having taken those 2 grad Topology courses during my last 2 semesters as an undergrad made me a musician.
19 years later, and now having published in peer reviewed physics journals, and attend too many conferences, I find eigenchris's work to be that one point in Cantor's Leekee Teepee where true humor can be found.
My deepest appreciation, sir.
I'm studying Math right now because I couldn't become a musician. Funny how that works
"these images make topology look way more fun and interesting than it actually is. I will not be referring to these images again at any point during the course."
By the way, it is almost like that textbooks on topology does.
Thank the youtube recommendation gods, this litle video hits every note in every university math school, i laughed so hard. Thank you for that.
I was terrified that Theorem 1.6 was gonna start including 0's to make this both a visual and phonetic nightmare.
*"And clearly, we can see that C-Rho has zero points of intersection with P."*
thank you so much for this. this really put the edges to the nodes and made my thesis perfect. as a side note, this allowed me over the weekend to solve the P vs. NP problem writing on a grain of rice that i heated up and morphed into a printing press.
This is actually easier to follow than many math classes I had in college
because you're still looking for the joke hiding somewhere ?
This is like a summary for those who already know topology.
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)
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 is the high qualty content I subbed for
This video managed to summon up flashbacks of the early morning (why were they always at 8-10am?!) math classes at uni...
This video makes me wanna turn down a million dollars, not shave my beard, and live with my mom
Thanks for the harsh reminder that I have no education or experience in any area that even sniffs at math like this. Didn't understand a single sentence
0:40 The first lecture of literally all of my university classes
UA-cam is gonna think I wanna watch Topology videos now.
Did he just teach me topology as a April fools joke
I have a real analysis exam with some topology (in the context of metric spaces) tomorrow and this was the refresher I needed, thank you!
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
I was unsure about whether this video was serious or not until he said that the images made topology seem more fun than it actually is
This is not a joke. Can confirm that these summarized my whole course of topology.
A monad is just a monoid in the category of endofunctors, what’s the problem?
What is a nomad then?
I’ve always thought I was terrible at maths but everything I’ve just seen made absolute perfect sense to me. Also the walls have started laughing at me and the kitchen is on fire.
This really makes you *FEEL* like you're learning something.
I went and watched the lectures by Tokieda, thank you so much. It was the most mindblowing course i ever watched in youtube
I'm glad the depressing joke video helped you find some decent lectures.
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%.
One of us are having a stroke, the question is who.
It's me.
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'.
I really wish I had been taught "Theorem speak" when I was in highschool so maybe I could have gotten used to it, for some reason it just doesn't fit into my brain.
Topology: I was promised donuts. Did not receive any.
I understand topology in more art than maths. I'm a 3D artist. In communities' forums, you'd often hear artists talking about making "clean topology" - meaning tidy meshes with quads, least possible tris and no n-gons (polygons with five or more vertrices). Clean topology means easier subdivision, easier manipulation for animators.
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"
🤣🤣🤣🤣😂😂😂😂nice, but realistic, sometimes it was like that at the uni
Here's how to understand compactness. Consider a game of infinite whac-a-mole. It's just like the regular game of whac-a-mole, except that once you kill a mole it stays dead. And, there might be an uncountable infinity of moles. Compactness means that if you can kill all the moles with a possibly infinite number of hammer blows with hammers of various sizes, if you were clever you could have only had to use a finite number of those hammers.
It's usually like this in Uni. But my Topology prof is actually really great
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.