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...
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.
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.
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 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...
@@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 RU-vid, 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 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!
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."
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.
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!
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.
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.
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): ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-SXHHvoaSctc.html 2. M335 Topology Videos (has lots of topological sculptures and pictures for visualizing things): ru-vid.com/group/PLJHszsWbB6hq40r_aSVlCXDvTT0VcrgcT 3. Snoopy Notes (written by a class of students): www.math.colostate.edu/~renzo/teaching/Topology10/Notes.pdf
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.
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.
@@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 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.
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.
@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.
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
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.
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 * (...)
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.
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.
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."*
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.
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
@@eigenchris it popped up in my recommended just now, I think you have been blessed by the RU-vid algorithm. Great vid btw, nice choice of variable names P and capital Rho, makes the proof crystal clear
This is literally more informative than half of the online classes I took, and the 900$ textbook that you never once refer to is something one should expect in every course through college.
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 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.
This was an awfully fun video to watch while being dyslexic. I could understand each one of these if I paused, but I believed that would take away from the joke.
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%.
This made me exhale throug my nose. Thanks for the proof with C, P and Ρ: the notation is a lot easier than the one in my textbook: with o (Latin o), ο (omicron) and о (cyrillic o).
