You lied to us. You said this was a joke video.

I like how you introduced so many terms so quickly. The course was topologically compact.

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

The C, P, Rho, and Complement part was genius. It seems my professors learned their notation here!

> Poincaré Conjecture > “a fun little problem that you can try and tackle on your evenings and weekends”

legend says that your viewers are still trying to prove theorem 1.9

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.

This is genuinely like the functional analysis course I did.

grigori perelman was able to prove poincare conjecture thanks to this course

you gotta love it when rho and p are in the same expression. its not confusing at all

The Poincare conjecture proof is left as an 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

"1.2 theorem: see 1.3 for proof 1.3 exercise proof 1.2" god damn comedy genius. this is what school feels like.

This is how all of my math classes were. Minus the helpful diagram at 3:16

Sorry I wrote April Fool's instead of April Fools'. I finished this at like 2am.

came for a laugh, left with anxiety :|

This video activated my fight-or-flight response

eigenchris: "Topology is the study of how topological spaces and their properties are preserved under homeomorhpisms" Me: 𝒐𝒐𝒉𝒉𝒉 𝒏𝒐𝒘 𝑰 𝒈𝒆𝒕 𝒊𝒕!

Theorem 1.9 proof: "Homeomorphic to a 3-sphere!" -minecraft menu splash text

instructions unclear. body has transformed into a klein bottle

“As you can see, topology has many practical applications.” Oof, too real.

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?

Instructions unclear, became an expert of number theory instead.

this is top tier content

Oh man, there are easier ways to get one million dollars.

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

where's the joke? this is just like my rl topology courses, but with fewer pics of the professor's cat.

It seem as Perelman had a lot of free evenings and saw this video once

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.

"We'll use capital P. And the roman letter, Capital Rho." Yep. Accurate.

It is so depressing that this is exactly how schools teach these days.

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): kzfaq.info/get/bejne/ib54e9mgxrnHpJc.html 2. M335 Topology Videos (has lots of topological sculptures and pictures for visualizing things): kzfaq.info/sun/PLJHszsWbB6hq40r_aSVlCXDvTT0VcrgcT 3. Snoopy Notes (written by a class of students): www.math.colostate.edu/~renzo/teaching/Topology10/Notes.pdf

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.

the words “every open cover has a finite subcover” still trigger flashbacks almost 15 years later

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.

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!

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.

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.

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 really made me laugh. I tried to read a book on topology once and this was precisely the experience I had.

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 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 love how this joke video is literally every math lecture I ever attended.

2:00 OK, let's give this a shot: An open interval is a set of the form {x in R: a

This will appear in everyone's recommended page in 10 years or so

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.

1.9: The proof of the Poincaré conjecture is left as an exercise to the reader. Grigori Perelman: Say no more

Dude where's my e-certificate? I need to brag about my newfound knowledge on topology

3:50 Proof by triviality is certainly the most powerful mathematical tool mathematicians can harness! 😂

1:25 "Now that we're properly motivated..." lmao

4:17 The joke is that the Poincare Conjecture is one of the Millennium Problems ($1m prize) and has a very advanced proof.

I've had lectures like this at university and I had to actually understand them to pass...

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.

Absolutely superb overview of Topology. This video is the magical key to thoroughly understanding topology.

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 * (...)

Oh god, this hit the nail straight on the head

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!

Watched at 2x speed, learned topology in 2.5 minutes.

Did he just teach me topology as a April fools joke

This is actually easier to follow than many math classes I had in college

0:17 a monad is just a monoid in the category of endofunctors

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 the high qualty content I subbed for

God, it's the driest humor that i have ever seen and i like it!

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.

🤣🤣🤣🤣😂😂😂😂nice, but realistic, sometimes it was like that at the uni

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 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

You don't need to know topology to enjoy this video, you just need to know the pain and suffering that is college

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."*

By the way, it is almost like that textbooks on topology does.

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.

0:40 The first lecture of literally all of my university classes

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 have a real analysis exam with some topology (in the context of metric spaces) tomorrow and this was the refresher I needed, thank you!

Jesus Lord Almighty! This video is scarier than any horror movie ever, including the "new wave extremism" French movies.

Once the motivation hit I was sold lol 😂

This was like over half of my Real Analysis II course.

"Left as an exercise for the viewer. " 😂😂

One of us are having a stroke, the question is who.

Me: my notes are clear and very detailed! My notes:

This is like a summary for those who already know topology.

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

This entire video felt equivalent to the anxiety I accumulated over and entire semester of Advanced Linear Algebra.

Damn you just created the best video on youtube my dude!

🤣 Loved this. I was expecting a "Rho, Rho, Rho your boat" joke around the proof that the closure of an open set is closed.

Topology: I was promised donuts. Did not receive any.

How to never get laid: "Proof left to the reader"

2:24 union of pee

I love that teaching style. It helped me tons in university level math, and it made it much simpler for me to learn programming in Haskell. If only all tutorials were this clear!!!

That's exactly how we are taught math in university

This is not a joke. Can confirm that these summarized my whole course of 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)

I always loved the expression "if, AND ONLY IF, ...", it sounds so alerting and reprimanding. Like a professor raising his index finger.

I burst out laughing the *second* I saw the title "Theorem 1.9 - The Poincaré Conjecture". Absolutely hilarious video.