Temu is the new Wish. As such, you have poetically described how your brain comes from a relevant place, even if it's not perfectly made. Our brains are precious, even though they are grown from little genetic material, dependant on what we have consumed and affected by their environment. So many factors that make the outcome vary a bit, just like a Temu product. TLDR: You're a genius.
The STATE of Harvard Math: Commentary on Lisa Piccirillo’s (fabulous!) presentation and the reaction of the sexist, egoist judgmental society offered by her would-be peers, as depicted by the Harvard Math dept. This channel has roughly 18,000 subscribers - a niche group. This presentation was posted 2 days prior and ALREADY saw more than 17,900 views, and almost 500 likes. An amazing response given the following TRUTHS Miss Piccirillo faces: Since the field is DOMINATED by egotistical, semi-intelligent males who compete with each other (and go VERY hard against ALL women in the field), we can SAFELY estimate MOST of these views were men. Men! Being so incredibly intelligent, each view represents up to FOUR men, all secretively salivating, huddled around a single screen. Why? So as to NOT allow their desires to be known to Miss Piccirillo nor how badly they wished to view her (excellent, informed, intreprative, state-of-the-art) summations, techniques and conclusions. Gentlemen? The MATH DOESN’T LIE! THE TRUTH BEHIND THE STATISTICS: 17,900 views by Harvard Males = 64,000 (approx) MALE viewers who were too cowardly to allow their ‘view count’ to be added to the total views for this pres-o. A very niche mostly-male group DID manage to vote, ‘awarding’ her almost 500 likes (probably 10 percent female while the remaining are extremely generous male peers or out-right horndogs, as the comments imply). 500 LIKES from 17,900 views? A rare and highly positive response given the aforementioned egotists. Based upon the comments, the ONLY thing that would have given her sexist colleagues MORE reason to LIKE would be if she disrobed and conducted her presentation topless - The comments about her physical appearance dominate the ‘discussions’ and provide further evidence as to our own conclusions regarding the sexism faced by women in academia. 500 LIKES across a field of 18,300 subscribers exceeds and is comparative in equivalence to internet porn. COMMENTARY: The Pee-nut gallery has Only a few comments which are to be taken seriously. In her chosen field, even ONE comment NOT from her team of friends, family and advisors (i.e., even a SINGLE serious questions or comment NOT from her closest collaborators) is an amazing result. Thank you, Miss Piccirillo! From an all-male, non-academic who appreciates intelligence, talent and the ability to communicate at the highest level!
Dumb down Summary: 1. In the flat, 2D world of a piece of paper, we can easily understand different shapes, like circles and squares. But in the 3D world we live in, shapes get much more complicated. 2. Mathematicians are really interested in understanding 4-dimensional shapes, which are even harder to picture. They want to know if there are different types of 4D shapes that look the same on the outside, but are actually different on the inside. 3. Mathematicians have come up with a few different ways to study 4D shapes. They can try to build different 4D shapes and then figure out how to tell them apart. They also use special math tricks called "invariants" to help identify differences between shapes. 4. Over the years, mathematicians have gone through a few different periods of studying 4D shapes. In each period, they've gotten better at both making new 4D shapes and finding new ways to tell them apart. 5. Recently, mathematicians have started using some new, clever tricks to study 4D shapes. They're finding new ways to construct 4D shapes, and they're also finding new "invariants" that can help them figure out if two 4D shapes are really the same or different. 6. One of these new tricks is called the "slic approach." It involves finding a special loop or knot in one 4D shape that doesn't exist in another 4D shape. This can show that the two shapes are different, even if they look the same on the outside. 7. Mathematicians are also using computers to help them find new 4D shapes that might be different. They're making lots of different 4D shapes and then using machine learning to try to figure out if any of them are really different on the inside. 8. One really cool idea is that the differences between 4D shapes can be hidden in a tiny, simple part of the shape. Mathematicians call this part a "cork," and they've shown that this cork is the key to understanding how 4D shapes can be different. 9. Using this idea of the "cork," mathematicians have been able to make some of the simplest possible examples of 4D shapes that are actually different on the inside, even though they look the same on the outside. 10. By understanding these simple, "corky" 4D shapes, mathematicians are hoping to get a better idea of where all the different types of 4D shapes come from, and how they're related to each other. It's like solving a big puzzle, one piece at a time!
just learned that this lady gained significant recognition for solving a longstanding problem concerning the Conway knot, a complex structure in knot theory. In 2018, as a graduate student, she demonstrated that the Conway knot is not "slice," resolving a question that had puzzled mathematicians for over 50 years. Congratulations
Right! I remember reading about her back ago, about the knot theory, when she was “just” a student. Pure inspiration, beautiful mind. Glad to watch a lecture of her
@@Hyphanym I know that you thought that your comment was a smart comment and many unassuming people would obviously co sign it thinking that they would have sounded smart if they said it too. But the first mobile phone technology was created in World War 2 in a device known as an EE-5 Artillery Field Phone which led to generation of mobile telecommunications devices. This technology developed into the first cellular network device for civilians by Motorola with the DynaTAC. So the problem of expedition in communications on the battlefield from Morse code to voice over was not an imaginary problem. Let's do better in critical thinking skills.
Women lecturers should be forced to dress professionally. It's meant to be a catalyst for the greatest young minds, but this will obviously be hindered when they are inevitably distracted.
What really amazes me is that some people (her parents and teachers) must have (I hope) recognized her talent at a young age, nurtured it, encouraged her to be where she is today. When you think about it a little more, you will realize that many, many brilliant people are either born in poverty or die before they can achieve anything significant. But not her. She is unmistakably one of the most brilliant minds in math in the country right now (do check her wikipedia page). This makes me feel an infinite amount of awe and joy, even as I watch (and understand nothing) in this video. The human mind is an amazing thing, but without the right environment, it can't achieve anything of significance.
Right. That were my thoughts too. When I started to learn math at university and had problems with not having money for living expenses mid throw, and I couldn’t find any solution while trying to approach people. They were telling me that not everyone learns math, and go to such university; “relatives” told me to go to work on factory. Not even proposing something specific, but as a metaphor wish for the baddest work. Though I worked lots hard of works in life. Everyone made sure to put me down. Though there are loans for students and there must be some solutions. They didn’t give me it. And no one just was able to talk constructively with good willing, lacking jealousy or bad attitude. And I was very young to be able to deal with such amount of hostility. And even today I couldn’t be able to.
in a way, the fact that this video is public and accesible to everyone was only a dream 30 years ago...still other many human factors need to align (i.e. the Anna Karenina effect they called) but the access to such sources like this can contribute to democratize the knowledge for the ones who are eager to learn more and improve ...
Not to be a jerk, but this theory isn't as brilliant as one might think. Just another language which has been established for decades. Kudos to all who seek knowledge!
The majority of women are in poverty and many are forced to dress and behave certain ways. Unfortunately, being brilliant in math doesn't solve the issue of the majority of women being in poverty and practically enslaved.
00:02 Lisa Piccirillo speaks on exotic phenomena in dimension four 02:28 Dimension four manifolds and their classification 07:40 Smooth 4-dimensional manifolds are still not well-understood and lack classification theorems. 10:39 Classical process of building Exotica in dimension 4 16:23 Manifolds are built from simple surfaces and basic building blocks called handles. 19:02 Challenges in computing gauge theory explicitly 23:50 Development of Exotica in Different Eras 26:16 Recent work in 2021 has resulted in the first example of a pair of exotic manifolds distinguished by the Slic approach. 31:45 Exotic manifolds in dimension 4 with definite forms and their recent progress 34:00 Ske lasagna module introduced for compact exotic manifolds 40:44 The argument may disprove the ponre conjecture using exotic phenomena. 43:39 Research on the P conjecture and candidates in B4 48:49 Explanations on Exotica origins and co-bound products 51:07 Understanding H cobordism and its relation to exotic pair manifolds 56:00 Existence of exotic contractable manifolds 58:35 Handles are building blocks for creating manifolds. 1:03:37 Building exotic manifolds using two handles and carving 1:06:36 Building different manifolds with the same boundary 1:12:12 Constructing pair of manifolds using disc attachments 1:14:53 Exotic phenomena quantification through cork twisting and construction 1:21:58 Existence of contractable pairs with surprising complexity levels 1:24:34 Exotic four manifolds exist with unique properties 1:30:13 Alpha invariant for a four manifold with a B3 1:32:32 Constructing manifolds with desired invariants Crafted by My college degree from GMU.
i took discrete math with Dr. Piccirillo last year and took an interest in abstract math shortly afterward. one of the best educators and individuals i've been able to meet
That's really cool. I love that these lectures are available online for anyone to access who has a desire to investigate these subjects. Surely nothing beats actually taking the class, but to someone who is interested and might not otherwise have access, this is wonderful.
It's so refreshing to watch a genuine expert discuss her area of specialty and showcase a deep intuition about the subject, with very few notes or supports.
Well if you've not come across them before you're not like;ly to know what they mean. If you picked up a novel and started reading it half way through then you wouldn't be surprised if you didn't know who a lot of the characters were. If it helps, I'm a mathematician who knows enough of the field of Algebraic Topology to pick up a broad idea of what she's on about - but if a mechanic started talking about the manifold in my car then I'd be confused and go glassy eyed very quickly. We're all good at different things - and that's good.
@@steviebudden3397 I think it's funny that people think they are never going to be capable of something because they have never done it before. That's the point of learning, you don't know something, you do some work to understand it, and then you have learned it.
Are there practical applications to what she’s discussing? Not to say that there “should” be, but I’m curious if there are, and what some of them might be?
EDIT: Apparently not all of this is 100% right. See comment of @jestingrabbit This talk is about something called "four-dimensional manifolds," which is just a fancy way of looking at shapes that have four dimensions. You’re used to three dimensions (like up-down, left-right, forward-backward), but here we’re adding one more. It's a bit hard to imagine because we can't see four dimensions, but mathematicians can describe and study them with formulas. What’s a Manifold? A "manifold" is basically a shape or surface that can be very simple or super complicated. Think of a line, a circle, or even the surface of a ball-these are all examples of simple manifolds in 1D, 2D, or 3D. Now, imagine that in four dimensions! Classifying Manifolds The speaker talks about how in lower dimensions (like 1, 2, and 3), mathematicians have figured out how to "classify" or organize these shapes into types, kind of like sorting objects into bins based on their characteristics. But when it comes to four-dimensional manifolds, things get trickier. This is because we know much less about them-they’re sort of like mysterious shapes! Smooth vs. Rough Manifolds Another important idea is "smooth" manifolds versus "topological" manifolds. Imagine a smooth manifold as a super-smooth surface, like glass, and a topological one as something rougher, like sandpaper. They’re both kinds of shapes but are different in texture (smoothness). The speaker explains that in four dimensions, these differences get very interesting. Exotic Manifolds Here’s where it gets fun: some four-dimensional manifolds are called "exotic." This means they look the same as other manifolds if you see them from far away but are actually different in their smoothness if you get close. It’s like two identical drawings of a line that feel different when you touch them-one might feel smooth, and the other rough. Gauge Theory and Invariants The last bit is about how mathematicians study these manifolds. They use something called "gauge theory," which is like a set of super-powered tools for telling different manifolds apart. It's complicated, but it involves using equations to find tiny differences between manifolds. If you know how to work with these tools, you can sometimes discover that two shapes are actually exotic versions of each other. So, to sum up, this talk is about exploring strange four-dimensional shapes and finding out if they are exotic by using mathematical tools that can measure differences that aren't always obvious.
This talk is about glutes and deltoids and triceps and pectorals, which are technically covered with clothing, but this lecture would do equally well at Harward and P*rnhub.
@@mbauducco Alright, let’s make it super simple! Imagine you have a ball of yarn, and you make a knot in it. Now, some knots are easy to untangle, but some knots are really tricky. For a long, long time, people tried to figure out if one special knot-the "Conway knot"-could be untangled in a special way. Then, a very smart lady named Lisa came along. She saw this tricky knot and decided to try solving it, just like how you might try a new puzzle. And guess what? She figured out that this knot couldn’t be untangled in that special way! She solved a puzzle that had been too hard for anyone else, and everyone was super impressed. So now, thanks to Lisa, we understand this knot much better! Isn’t that cool?
@@DelFlo A manifold is pretty easy, it's a space that locally looks like Euclidean space. A classic example is a sphere which locally looks like a two dimensional plane. You can see this because the Earth is spherical but near us on a small scale it's flat. So you can think of it as a deformation of some flat thing like a line, plane, or 3d space. Smoothness here means the opposite of jagged. It's related to the existence of derivatives if you have some calculus. At pinched points these won't exist so you get some jagged. What's wild about this is that you don't typically think of something jagged being flat. So these topological spaces that are not smooth but are still locally flat defies intuition.
@@abebuckingham8198 So would a wormhole be an example of a non-smooth manifold? Because it essentially teleports you across the manifold of space-time while locally it still feels like you’re moving through regular 3D space. Thanks for your answer by the way.
Wicked ! I was so entertained by your explanation. Even as a graduate engineer (having studied a 💩-load of math, calculus, matrices and vectors…) I have no idea whether you are texting truth or just replying in a manner that your peers will find entertaining !! Brilliant. I thank you !!! 🫡
@WattSounds lol, the concepts at large make sense, the specifics and technical methods are far beyond me. That doesn't mean I can't appreciate the gravity of their study.
I thought I learned mathematics. This is the most incomprehensible lecture I have ever listened to. If it was in Chinese I would understand more. I am just glad no one has any questions.
It´s very abstract mathematics. Do not feel bad about it. I am sure, you are pretty good at low abstract math, and honestly, this is going to solve 99% of problems in your life, in the lives of your family, in your stock portfolio, in your job, and in your education by far.
She knows she has beautiful back and shoulders, and she loves showing them. Compensates her lack of boobs and proves she is an attractive woman (she is clever either, but we now this already).
I think this lecture might go down in history as the only one where topology was illustrated both conceptually and physically, showcasing symmetry, strength, and transformations in reality. Bringing theory to life!
Lisa Piccirillo is so clear in communicating the ideas, I actually followed (sort of) the construction around 1:08:05 (I'm not a topologist). Really excellent lecture
Thank you Harvard Mathematics Department for putting the CDM lectures on RUclips. The conference has a long history of very good lectures on recent top research. Piccirillo's talk on 4-manifolds certainly upholds that tradition. I'm not a topologist, but the talk gives me an inkling of what she, her collaborators, and her predecessors have accomplished, and where it fits into our understanding of low-dimensional manifolds.
When she said “The one you’re thinking of… a nice topological space…” made me laugh out loud as the manifold I was thinking of is attached to the exhaust system of my car.
As a math guy I had no idea cars had manifolds. Apparently they have holes in them so they're not simply connected. This means they're more complicated than the objects discussed in this lecture.
In engineering a manifold is a type of structure that is able to deliver fluids at equivalent characteristics (pressure, temperature, density, etc). Your car manifold delivers equal amounts of air and/or fuel to each cylinder. The exhaust manifold allows release of exhaust at equivalent pressures. It’s just a way of saying “balanced fluid system”. No idea how this word ended up describing surfaces of geometry?
I loved this presentation despite the fact I didn’t understand the first sentence let alone the rest. Sigh! But you know in my day women like my wife were told women couldn’t really do Math so I absolutely love to see a young woman put that BS to rest.
I am really high, but i am enjoying this class. It is clear that the professor is a person who has achieved excellence in her field of study and that is something really interesting. We are used to seeing the body at its maximum potential but not the minds, this is also something admirable to see.
@@regwatson2017lol. you sure do not look like that just because you are skinny. trust me, i know. as others have mentioned, she probably does rock climbing with a back like that. this is pure trained and used muscle
I absolutely loved Lisa's approach on this. She truly expands classical thinking on this subject in such a way to truly give us a new way of looking and thinking on three traditional manifold topology in the fourth dimension. Dont know why I didn't see it before. Thank you Lisa!
I have the utmost respect for science and scientists. I don't feel that respect obligates me to watch a lecture which I haven't the slightest chance of understanding. Do your thing, Dr. Piccirillo!
Outstanding lecture, Lisa! This was a GREAT talk! I am compelled by your enthusiasm and skill to add: Having spent a decade listening to my professors, this was both and expert delivery and very well informed - On all fronts 😊 Gracias!
@@Herlock-vc6ch are you sugesting this is a bad lecture and someone only could comment on it because of the women who lectures? Or do you not understand a word she says so the only thing you can focus on is that she is an attractive women.
"Howard", this is "Sheldon", why are you even leaving a comment to this video, never mind clicking this video on? Also, can you or Bernadette drive me to the comic book store tomorrow, because Leonard and Raj are mad at me again and Amy and Penny are going to a spa together.🤣🤣
Thank you for the insightful lecture! The discussion on the Alpha invariant and its construction through cobordism was particularly enlightening. I would love to hear more about the practical applications of these concepts in current research. Looking forward to your next talk!
When I was a grad student a classmate of mine used to go to various free meetups around the city for the free food. I almost thought about doing that but there's only so much pizza I can eat.
YT is so broken. I started with watching music videos, it went downhill towards less family friendly ones, through body painting where you can see e v e r y t h i n g, then I saw how elephant downs a tree 5 times the size of it.. and now I am here. All in less than one hour
In 2020, Piccirillo published a mathematical proof in the journal Annals of Mathematics determining that the Conway knot is not a smoothly slice knot, answering an unsolved problem in knot theory first proposed over fifty years prior by English mathematician John Horton Conway.
It's a way to model the fabric of the universe with both spatial and temporal components. Work in this field may lead to a better understanding of worm holes, space/time travel, and quantum physics.
Pro tip for those of us who have no idea what she’s talking about (even if you have a degree in engineering or similar): Ask chatGPT what a 4 dimensional smooth manifold is. I have no idea if chatGPT is correct, but part of the answer was “In physics and mathematics, smooth 4-dimensional manifolds appear in general relativity, where spacetime is modeled as a 4-dimensional smooth manifold, with three spatial dimensions and one time dimension. “
honored to be in the group of folks with a PhD in STEM who have studied topology before and got recommended this video but still could only focus on her back muscles and amazing fashion sense.
She solved the Conway knot problem, which of course is the problem of how knot to laugh when Tim Conway does his Siamese elephant routine on the Carol Burnett Show.
I clicked on the thumbnail because I thought I should spend a little time discovering something interesting today. I’m now two minutes in and realize I need about eight years of courses before I can gain even a rudimentary knowledge of the basic terminology that’s being used.
For those unclear on the significance: In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects, such as how different observers perceive where and when events occur.
First, I find the comments here hilarious. Even if I feel exactly like many commenters I was thinking something here could explain why humanity struggles so with what we call UFO, or maybe it's called UEDs. Thousands of people have reported over decades, but we have not even produced a suggestion of theory. Or maybe she is doing it right there? Especially the famous Zimbabwe event w 60 school children. Some saw both ship and alien. Some saw nothing. Alien was at a distance, then suddenly near. Events as these perplex us so much because they challenge our basic understanding of reality. So we have chosen to ridicule the witnesses. Maybe AI wants us to understand and throws this mathgenius goddess.😁
Makes sense. I was writing today about the shape of infinity which can't be seen but only imagined as rings of rings which can expand or contract but using five dimensions of a pyramid you can find the internexus in the center; it's a spiral really; similar to how we're traveling trough the universe. The architecture is a design for a website lol It's called the Cybersphere with a new pyramid shaped navigator called the neXutool.
@@ddevamEverything spirals here, and what do spirals do? Make bloom outs. Pressure is a spiral in to bloom out floral growth pattern. Find center to bloom out.
@@liberatedcollective2124 See @1:03 where Lisa is adding handles to the curved spaces? Simple logic says you can not see a circle without drawing a line around it; and if you look at a line from the top; like a straw, it also is a circle. So It means that the "white hot spot" defined by Hawkins is where the line and sphere meet; it's point where reality is created or can fall outside to the forth dimension; via "quantum black hole". Now; take an obtuse pyramid; intersect the five corners with three rings of different sizes (they don't touch); the corners represent Lisa's "handles" where they connect to the rings; then spin the pyramid and see what shape it creates; spiral-graph insanity to infinity right? Would it now cause the rings to collide then expand and contract at the same time?
@@ddevam Except it's not insanity, it's the harmony here, we see chaos because we can't read the language. Pressure is a language like ours, nature ONLY DOES SHAPES. POINT BLANK PERIOD. Not math, but you are on the right track. Just remember, zig zag is spiral. 6 is spiral, S is spiral. And spirals go to bloom outs, the five petal bloom is the end of pressure here. ⭐ Its a growth pattern, small to big, key shape in totality 🔑 (where your pyramid shape comes into existence, just remember 3d space, we think and observe embarrassingly in 2d. 🙏
I second that. ❤😊 Wow, I watched the whole thing! I admit that I had an ulterior motive-I’m trying to work out possible topological relationships of frame dragging geometry in supermassive Kerr black holes, and I was looking for inspiration. 🤷♀️😂
Everyone is the same it's just that some people go to school more than others and without all of that work and studying they are just like everyone else 🎉
For all the non-mathematicians, this is a great video to share next time someone downplays the significance of "so-called experts" and acts like they themselves are an expert on something just because they've watched a couple of RUclips videos on a given topic. Bro, no. Actual experts exist and they devote their lives to understanding things on a level that you and I don't and likely never will. I'm a reasonably intelligent person and I'll happily admit this talk is way over my head. Whether it's math or climate science or infectious diseases, experts exist and we do ourselves a disservice when we pretend to know better than them in their chosen field.
@ in recent years I do, since I do a lot of work in insurance mathematics. Differential equations, statistics, probability, linear algebra are all useful there. But the greatest use I have for my degree is that it allows me to continue “studying” maths and physics for enjoyment’s sake, mainly on RUclips :-)
Lisa Piccirillo: “Exotic phenomena in dimension 4”, 3 days ago 52k views, 357 comments . Ivan Losev: “Construction of finite W-algebras”, 8 days ago 160 views, 0 comments.
Lisa the mathematician worked on her physique, and unintentionally found the solution to the youtube algorithm at the gym. Only a tiny fraction of humans would understand these topics. Not the case for "attractive intelligent strong woman" - We have instincts to detect that, hyperactive ones. 😅It's no slight against Ivan.
I seriously doubt she's ever done anything unintentionally. But 🤔 Not sure I got the gist of what you're expressing other than the “explanation” for what brings males in to this video, lays either on her physique, or it lays on our “instincts”, responsibility shifted elsewhere; problem solved. All I was comparing between the 2 videos is wrapping vs. content. As in how a carefully chosen book cover determines whether it flies or stays on the shelves.🙂@@mortenrl1946
I seriously doubt she's ever done anything unintentionally. But I'm not sure I got the gist of what you expressed, other than the ,“explaining” for the high male turnout either lies on her physique or our, “instincts” responsibility shifted elsewhere, problem solved. They even compare her to Lisa Randall on her ‘IQ hotness’ popular sport apparently. I meant to simply compare one video to the other in viewer-interest/time-posted. Wrapping vs. content. Other institutions channels also carry her lecture disable comments, probably because unrelated comments were starting to creep up. @@mortenrl1946
I only took one course of Calculus decades ago and it's a testament to the skill of Lisa Piccirillo that I was able to follow and understand the entire lecture (except a bit about 5 minutes from the end), only needing to stop and google a few words along the way. She walks through the history and builds her story piece by piece keeping everything solid as she goes. This is a fascinating trip to a different world and I have no idea how it got recommended to me but I really enjoyed it. Thanks so much for making this public and thanks again to the lecturer for giving us a glimpse of this world.
![Math for Game Devs [2022, part 10] • Abstract Algebra, Procedural Animation & Splines](http://i.ytimg.com/vi/Pku6WAs1fF8/mqdefault.jpg)
Procrastinated so much that I'm watching a Harvard lecture on 4th dimension
wow i just finished my degree 4 Days ago and procrastinating to ask the school administration to send me the photos from our finals.
I was thinking something similar except listening to vocal fry. So difficult to get past “exxxxxotic”
Oh, hello, me.
could be worse dude, you could be on a marathon of Karen videos like I did a couple of years ago, was fun tho.
@@samuelcarstens6152 I couldn't stop focusing on her traps and delts. If she was any skinnier she would collapse into a 4th dimensional manifold
Not sure how this was recommended to me, but I'm flattered that YT thinks I'm smart enough to understand this type of math.
+1
You're a man of culture I see.
+1
+1 🙂
lol I had exact same thought
she built those back muscles from years of chalk hieroglyphics
Can she do the Tommy gun thing like that old math professor though?
lmaoo
@@trentonclark222 🤣
There's a high probability she's an athlete of some sort in an "unrelated" to math activity.
I was gonna say...wow
After watching im convinced my brain has a Temu sticker on it. 😐
Nah this is a bunch of malarkey
😂
Temu is the new Wish. As such, you have poetically described how your brain comes from a relevant place, even if it's not perfectly made. Our brains are precious, even though they are grown from little genetic material, dependant on what we have consumed and affected by their environment. So many factors that make the outcome vary a bit, just like a Temu product.
TLDR: You're a genius.
😱 😆
I'm pretty sure Temu might convince me to get a YT Premium subscription.
Must include giving lectures on differential topology in my back and shoulders workout routine
Mine is diffeomorphic to hers, so I shouldn't work that hard... Anyway great lecture Lisa!!!
🤣🤣 she's ripped fr
xD
Bro 😂😂😂
The STATE of Harvard Math: Commentary on Lisa Piccirillo’s (fabulous!) presentation and the reaction of the sexist, egoist judgmental society offered by her would-be peers, as depicted by the Harvard Math dept.
This channel has roughly 18,000 subscribers - a niche group. This presentation was posted 2 days prior and ALREADY saw more than 17,900 views, and almost 500 likes. An amazing response given the following TRUTHS Miss Piccirillo faces:
Since the field is DOMINATED by egotistical, semi-intelligent males who compete with each other (and go VERY hard against ALL women in the field), we can SAFELY estimate MOST of these views were men. Men! Being so incredibly intelligent, each view represents up to FOUR men, all secretively salivating, huddled around a single screen.
Why? So as to NOT allow their desires to be known to Miss Piccirillo nor how badly they wished to view her (excellent, informed, intreprative, state-of-the-art) summations, techniques and conclusions. Gentlemen? The MATH DOESN’T LIE!
THE TRUTH BEHIND THE STATISTICS: 17,900 views by Harvard Males = 64,000 (approx) MALE viewers who were too cowardly to allow their ‘view count’ to be added to the total views for this pres-o.
A very niche mostly-male group DID manage to vote, ‘awarding’ her almost 500 likes (probably 10 percent female while the remaining are extremely generous male peers or out-right horndogs, as the comments imply).
500 LIKES from 17,900 views? A rare and highly positive response given the aforementioned egotists. Based upon the comments, the ONLY thing that would have given her sexist colleagues MORE reason to LIKE would be if she disrobed and conducted her presentation topless - The comments about her physical appearance dominate the ‘discussions’ and provide further evidence as to our own conclusions regarding the sexism faced by women in academia. 500 LIKES across a field of 18,300 subscribers exceeds and is comparative in equivalence to internet porn.
COMMENTARY: The Pee-nut gallery has Only a few comments which are to be taken seriously. In her chosen field, even ONE comment NOT from her team of friends, family and advisors (i.e., even a SINGLE serious questions or comment NOT from her closest collaborators) is an amazing result.
Thank you, Miss Piccirillo! From an all-male, non-academic who appreciates intelligence, talent and the ability to communicate at the highest level!
Dumb down Summary:
1. In the flat, 2D world of a piece of paper, we can easily understand different shapes, like circles and squares. But in the 3D world we live in, shapes get much more complicated.
2. Mathematicians are really interested in understanding 4-dimensional shapes, which are even harder to picture. They want to know if there are different types of 4D shapes that look the same on the outside, but are actually different on the inside.
3. Mathematicians have come up with a few different ways to study 4D shapes. They can try to build different 4D shapes and then figure out how to tell them apart. They also use special math tricks called "invariants" to help identify differences between shapes.
4. Over the years, mathematicians have gone through a few different periods of studying 4D shapes. In each period, they've gotten better at both making new 4D shapes and finding new ways to tell them apart.
5. Recently, mathematicians have started using some new, clever tricks to study 4D shapes. They're finding new ways to construct 4D shapes, and they're also finding new "invariants" that can help them figure out if two 4D shapes are really the same or different.
6. One of these new tricks is called the "slic approach." It involves finding a special loop or knot in one 4D shape that doesn't exist in another 4D shape. This can show that the two shapes are different, even if they look the same on the outside.
7. Mathematicians are also using computers to help them find new 4D shapes that might be different. They're making lots of different 4D shapes and then using machine learning to try to figure out if any of them are really different on the inside.
8. One really cool idea is that the differences between 4D shapes can be hidden in a tiny, simple part of the shape. Mathematicians call this part a "cork," and they've shown that this cork is the key to understanding how 4D shapes can be different.
9. Using this idea of the "cork," mathematicians have been able to make some of the simplest possible examples of 4D shapes that are actually different on the inside, even though they look the same on the outside.
10. By understanding these simple, "corky" 4D shapes, mathematicians are hoping to get a better idea of where all the different types of 4D shapes come from, and how they're related to each other. It's like solving a big puzzle, one piece at a time!
Thanks for the high level breakdown! My friend did a PhD in manifolds so I know nothing about them.
Dimensions are multi and can be manifested by the individual who has the correct resonance.
So if I understand your summary, that makes me dumb? Looks like I’m smart after all.
Thanks for the breakdown! This is some wicked shit to fall asleep to. Hopefully my brain absorbs it
Tl;dr?
I subscribed because I find it fascinating that I'm listening to my native language and a foreign language simultaneously.
Amazing comment. Yes. This.
Excellent reason for subscribing my dear fellow !!!
No you subscribed because it's a woman teaching advanced physics and you're simping
Epic comment! 😂
@@niket527physics?
I know some of these words.
Exactly what I was thinking. Also, I think there is a manifold on my car engine. I don’t think it’s exotic or in the 4th dimension or homeomorphic.
and after watching this i know some more of them. is scary
@@Rob_132 differentiable engine manifold - it probably means that it is marked so that it can be distinguished from others of the same kind.
😁
this comment....im dying
just learned that this lady gained significant recognition for solving a longstanding problem concerning the Conway knot, a complex structure in knot theory. In 2018, as a graduate student, she demonstrated that the Conway knot is not "slice," resolving a question that had puzzled mathematicians for over 50 years. Congratulations
Right! I remember reading about her back ago, about the knot theory, when she was “just” a student. Pure inspiration, beautiful mind. Glad to watch a lecture of her
So basically she solved an imaginary problem with an imaginary solution. Ah modernity.
@@AdamFontenet-g3f the tech youre commenting on happens to be a development aided by the imaginary solutions you are talking about. Whatever works man
Einstein famously stated that, "Imagination is more important than knowledge."
In a world of fluid dynamics, flux capacitance is king...✨️🤙💫
@@Hyphanym I know that you thought that your comment was a smart comment and many unassuming people would obviously co sign it thinking that they would have sounded smart if they said it too. But the first mobile phone technology was created in World War 2 in a device known as an EE-5 Artillery Field Phone which led to generation of mobile telecommunications devices. This technology developed into the first cellular network device for civilians by Motorola with the DynaTAC. So the problem of expedition in communications on the battlefield from Morse code to voice over was not an imaginary problem. Let's do better in critical thinking skills.
Lifting weights and doing maths as ours big ancestors.
Aristotle would be proud
Iguess, she´s climping a lot
And Plato, who liked to flex after an argument.
I think it comes from extensive chalkboard writing
Aristotle would have no idea about anything she wrote
just skinny ...
Bold of RUclips to recommend this to me. They must have seen the gold star on my recent math test.
I can't even do school maths yet here I am 😂😂
I have AI do my math for me, easy button stupid
I suddendly realize that I've been watching the video because she made me feel that i was understanding everything when i did not understand a word.
I now know exactly how Penny felt every time Sheldon tried to explain what he does for a living.
🙃
This got recommended to me and I randomly watched 28 minutes of it for no reason
Oh, there was a reason! Just admit it.😂
@@timprescott4634 you caught me I tried to play it off like it didn’t matter but the algorithm knew I couldn’t run from it any longer
me too
I'm here to learn about manifolds
Watch the real 4D muscle orchestration. 😊
This is the person that gets recruited to meet aliens
😆 😂
A she looks young as fuck
this is a serious comment, don't take it lightly
Guess I need to watch 'Arrival" again.
Well then, must be why it's been recommended, to a certain populist...take care & engulf this Masterpiece Theater of Mathematica.
The fact that there's a person out there with the job title "low dimensional topologist" makes the world a better place!
Primary takeaway from this lecture: My back workout is reeeeeeally lacking.
A search suggested she has bouldering as a hobby. (powerful rock climbing moves)
@@PB-sk9jn I could tell it was a climber's back. Bodyweight exercises just look a certain way.
Women lecturers should be forced to dress professionally. It's meant to be a catalyst for the greatest young minds, but this will obviously be hindered when they are inevitably distracted.
Baby got back 😭🤦♂️
She knew what she was doing with that shirt
What really amazes me is that some people (her parents and teachers) must have (I hope) recognized her talent at a young age, nurtured it, encouraged her to be where she is today. When you think about it a little more, you will realize that many, many brilliant people are either born in poverty or die before they can achieve anything significant. But not her. She is unmistakably one of the most brilliant minds in math in the country right now (do check her wikipedia page).
This makes me feel an infinite amount of awe and joy, even as I watch (and understand nothing) in this video. The human mind is an amazing thing, but without the right environment, it can't achieve anything of significance.
Right. That were my thoughts too.
When I started to learn math at university and had problems with not having money for living expenses mid throw, and I couldn’t find any solution while trying to approach people. They were telling me that not everyone learns math, and go to such university; “relatives” told me to go to work on factory. Not even proposing something specific, but as a metaphor wish for the baddest work. Though I worked lots hard of works in life. Everyone made sure to put me down.
Though there are loans for students and there must be some solutions. They didn’t give me it. And no one just was able to talk constructively with good willing, lacking jealousy or bad attitude. And I was very young to be able to deal with such amount of hostility. And even today I couldn’t be able to.
Plotline to White Tiger
in a way, the fact that this video is public and accesible to everyone was only a dream 30 years ago...still other many human factors need to align (i.e. the Anna Karenina effect they called) but the access to such sources like this can contribute to democratize the knowledge for the ones who are eager to learn more and improve ...
Not to be a jerk, but this theory isn't as brilliant as one might think. Just another language which has been established for decades. Kudos to all who seek knowledge!
The majority of women are in poverty and many are forced to dress and behave certain ways. Unfortunately, being brilliant in math doesn't solve the issue of the majority of women being in poverty and practically enslaved.
00:02 Lisa Piccirillo speaks on exotic phenomena in dimension four
02:28 Dimension four manifolds and their classification
07:40 Smooth 4-dimensional manifolds are still not well-understood and lack classification theorems.
10:39 Classical process of building Exotica in dimension 4
16:23 Manifolds are built from simple surfaces and basic building blocks called handles.
19:02 Challenges in computing gauge theory explicitly
23:50 Development of Exotica in Different Eras
26:16 Recent work in 2021 has resulted in the first example of a pair of exotic manifolds distinguished by the Slic approach.
31:45 Exotic manifolds in dimension 4 with definite forms and their recent progress
34:00 Ske lasagna module introduced for compact exotic manifolds
40:44 The argument may disprove the ponre conjecture using exotic phenomena.
43:39 Research on the P conjecture and candidates in B4
48:49 Explanations on Exotica origins and co-bound products
51:07 Understanding H cobordism and its relation to exotic pair manifolds
56:00 Existence of exotic contractable manifolds
58:35 Handles are building blocks for creating manifolds.
1:03:37 Building exotic manifolds using two handles and carving
1:06:36 Building different manifolds with the same boundary
1:12:12 Constructing pair of manifolds using disc attachments
1:14:53 Exotic phenomena quantification through cork twisting and construction
1:21:58 Existence of contractable pairs with surprising complexity levels
1:24:34 Exotic four manifolds exist with unique properties
1:30:13 Alpha invariant for a four manifold with a B3
1:32:32 Constructing manifolds with desired invariants
Crafted by My college degree from GMU.
who cares? totally useless to the real world
I was just sitting on the toilet wondering about this. Glad YT recommended this at such a crucial and convenient time!
😂😂😂😂
i took discrete math with Dr. Piccirillo last year and took an interest in abstract math shortly afterward. one of the best educators and individuals i've been able to meet
That's really cool. I love that these lectures are available online for anyone to access who has a desire to investigate these subjects. Surely nothing beats actually taking the class, but to someone who is interested and might not otherwise have access, this is wonderful.
Did you take her class at UT Austin? I live in Austin.
I had a romance with her. She is a great lover.
@@spawnterrorsure thing buddy
She was able to prove that the Conway knot is not a smoothly slice knot, a problem that had stumped mathematicians for half a century!
It's so refreshing to watch a genuine expert discuss her area of specialty and showcase a deep intuition about the subject, with very few notes or supports.
It's fascinating
I am not a genius. This lecture has really driven home that point.
Well if you've not come across them before you're not like;ly to know what they mean. If you picked up a novel and started reading it half way through then you wouldn't be surprised if you didn't know who a lot of the characters were.
If it helps, I'm a mathematician who knows enough of the field of Algebraic Topology to pick up a broad idea of what she's on about - but if a mechanic started talking about the manifold in my car then I'd be confused and go glassy eyed very quickly. We're all good at different things - and that's good.
@@steviebudden3397 I think it's funny that people think they are never going to be capable of something because they have never done it before. That's the point of learning, you don't know something, you do some work to understand it, and then you have learned it.
@@steviebudden3397 very valid point
Are there practical applications to what she’s discussing? Not to say that there “should” be, but I’m curious if there are, and what some of them might be?
@@Rob_132I was curious about that as well. Hopefully someone answers…
EDIT: Apparently not all of this is 100% right. See comment of @jestingrabbit
This talk is about something called "four-dimensional manifolds," which is just a fancy way of looking at shapes that have four dimensions. You’re used to three dimensions (like up-down, left-right, forward-backward), but here we’re adding one more. It's a bit hard to imagine because we can't see four dimensions, but mathematicians can describe and study them with formulas.
What’s a Manifold?
A "manifold" is basically a shape or surface that can be very simple or super complicated. Think of a line, a circle, or even the surface of a ball-these are all examples of simple manifolds in 1D, 2D, or 3D. Now, imagine that in four dimensions!
Classifying Manifolds
The speaker talks about how in lower dimensions (like 1, 2, and 3), mathematicians have figured out how to "classify" or organize these shapes into types, kind of like sorting objects into bins based on their characteristics. But when it comes to four-dimensional manifolds, things get trickier. This is because we know much less about them-they’re sort of like mysterious shapes!
Smooth vs. Rough Manifolds
Another important idea is "smooth" manifolds versus "topological" manifolds. Imagine a smooth manifold as a super-smooth surface, like glass, and a topological one as something rougher, like sandpaper. They’re both kinds of shapes but are different in texture (smoothness). The speaker explains that in four dimensions, these differences get very interesting.
Exotic Manifolds
Here’s where it gets fun: some four-dimensional manifolds are called "exotic." This means they look the same as other manifolds if you see them from far away but are actually different in their smoothness if you get close. It’s like two identical drawings of a line that feel different when you touch them-one might feel smooth, and the other rough.
Gauge Theory and Invariants
The last bit is about how mathematicians study these manifolds. They use something called "gauge theory," which is like a set of super-powered tools for telling different manifolds apart. It's complicated, but it involves using equations to find tiny differences between manifolds. If you know how to work with these tools, you can sometimes discover that two shapes are actually exotic versions of each other.
So, to sum up, this talk is about exploring strange four-dimensional shapes and finding out if they are exotic by using mathematical tools that can measure differences that aren't always obvious.
ChatGPT, pasted the transcript of the first 30 minutes with the prompt "explain to 12 year old kid"
knots
Can you prompt it for a three year old. I'm still confused😮
This talk is about glutes and deltoids and triceps and pectorals, which are technically covered with clothing, but this lecture would do equally well at Harward and P*rnhub.
@@mbauducco Alright, let’s make it super simple!
Imagine you have a ball of yarn, and you make a knot in it. Now, some knots are easy to untangle, but some knots are really tricky. For a long, long time, people tried to figure out if one special knot-the "Conway knot"-could be untangled in a special way.
Then, a very smart lady named Lisa came along. She saw this tricky knot and decided to try solving it, just like how you might try a new puzzle. And guess what? She figured out that this knot couldn’t be untangled in that special way! She solved a puzzle that had been too hard for anyone else, and everyone was super impressed.
So now, thanks to Lisa, we understand this knot much better! Isn’t that cool?
I did not learn anything from what see said but I got an excellent anatomy lesson on shoulder and back muscles from what she wrote.
I have a feeling that this is probably completely amazing for those who understand
It is. Just the fact that there are topological manifolds that are not smooth manifolds is pretty wild and she starts with that.
@@abebuckingham8198 What does that mean and why is it wild?
@@DelFlo A manifold is pretty easy, it's a space that locally looks like Euclidean space. A classic example is a sphere which locally looks like a two dimensional plane. You can see this because the Earth is spherical but near us on a small scale it's flat. So you can think of it as a deformation of some flat thing like a line, plane, or 3d space.
Smoothness here means the opposite of jagged. It's related to the existence of derivatives if you have some calculus. At pinched points these won't exist so you get some jagged.
What's wild about this is that you don't typically think of something jagged being flat. So these topological spaces that are not smooth but are still locally flat defies intuition.
@@abebuckingham8198 So would a wormhole be an example of a non-smooth manifold? Because it essentially teleports you across the manifold of space-time while locally it still feels like you’re moving through regular 3D space. Thanks for your answer by the way.
@@abebuckingham8198 😉
Wicked !
I was so entertained by your explanation. Even as a graduate engineer (having studied a 💩-load of math, calculus, matrices and vectors…) I have no idea whether you are texting truth or just replying in a manner that your peers will find entertaining !!
Brilliant. I thank you !!! 🫡
Best ever math lecture if you're an art student.
I understood absolutely nothing, but... i was mesmerized by that back. Viva l'Italia !
i watch shorts of cats and family guy, why would youtube do this to me
😂😂😂😂
You have potential
They observe you, not just online
which pill did you take, red or blue? (in case you are too young, this was a movie reference 😊)
I got recommended this after watching a guy doing pullups lmao
When your math professor comes in with slippers, golden pants and being absolutely ripped :D
It's weird, very very weird, not a good look. She looks like she has a tinder date after the lecture.
Soo fine ❤
Two important things she forgot though
@sungazer454 Most modern women don't know how to dress anymore. They will get mad when you notice.
And a thong😮
This is so cool, truly shows you how complex the universe is. We are barely scratching the surface of understanding its basal language.
You're just trying to sound clever aren't you... admit it.. the only sentence she said that made sense was "Any questions"
@WattSounds lol, the concepts at large make sense, the specifics and technical methods are far beyond me. That doesn't mean I can't appreciate the gravity of their study.
That rug really ties the room together.
😅😂😅😂😅😂😅
You're too silly 😅😂😅
Would be a shame if someone pissed on it
This guy peed on it.
@ at least I’m house broken.
Smokey, my friend, you're entering a world of pain. A world of pain.
I thought I learned mathematics. This is the most incomprehensible lecture I have ever listened to. If it was in Chinese I would understand more. I am just glad no one has any questions.
It´s very abstract mathematics. Do not feel bad about it. I am sure, you are pretty good at low abstract math, and honestly, this is going to solve 99% of problems in your life, in the lives of your family, in your stock portfolio, in your job, and in your education by far.
For sure. In Chinese you talk about the same things as in English. This talk is about something you don’t even know it exists.
@@PandaPanda-ud4neIt solves ALL problems unless you are a mathematician.
@@entropica what I mean is I do not speak Chinese
Joke has flown over some heads there.
The comment section is something I CAN understand, and enjoyed very much
We can conclude that to solve 4-dimensional manifold problems, you really need to put your back into it.
That’s great! 😂
for the record, if a man were giving this presentation while showing a back this ripped, I would definitely mention it.
Professor Leonard, thank me later
ripped? you don't go to the gym do you.
She knows she has beautiful back and shoulders, and she loves showing them. Compensates her lack of boobs and proves she is an attractive woman (she is clever either, but we now this already).
@@ebog4841 some of us do BOATH 😅
@@ebog4841 i know both and ur mom's back math
This person is incredibly intelligent and captivating to watch. Their videos are very enjoyable and informative.
I think this lecture might go down in history as the only one where topology was illustrated both conceptually and physically, showcasing symmetry, strength, and transformations in reality. Bringing theory to life!
XD
i think she looks a little bit muscular because her body fat is so low but she also has so little body muscle and body mass.
I concur.
I’m just impressed at her chalkboard writing speed. Now back to reading my 45th romance novel for the year.
At least you're reading!
Lisa Piccirillo is so clear in communicating the ideas, I actually followed (sort of) the construction around 1:08:05 (I'm not a topologist). Really excellent lecture
After having so much fun reading the comments it's probably best to conclude that's what the yt algorithm had in store for me here.
Thank you Harvard Mathematics Department for putting the CDM lectures on RUclips. The conference has a long history of very good lectures on recent top research. Piccirillo's talk on 4-manifolds certainly upholds that tradition. I'm not a topologist, but the talk gives me an inkling of what she, her collaborators, and her predecessors have accomplished, and where it fits into our understanding of low-dimensional manifolds.
"I'm not a topologist". That's a good one.
@@SimonMilesresearch but I know where Paris is on a map...
Rock climbing frees the manifold mind. Thank you, Dr. Lisa!
When she said “The one you’re thinking of… a nice topological space…” made me laugh out loud as the manifold I was thinking of is attached to the exhaust system of my car.
Exactly the same here 😅
As a math guy I had no idea cars had manifolds. Apparently they have holes in them so they're not simply connected. This means they're more complicated than the objects discussed in this lecture.
LOL same. The one currently plaguing me has a slow leak grrr
Same ….. 😂
In engineering a manifold is a type of structure that is able to deliver fluids at equivalent characteristics (pressure, temperature, density, etc). Your car manifold delivers equal amounts of air and/or fuel to each cylinder. The exhaust manifold allows release of exhaust at equivalent pressures. It’s just a way of saying “balanced fluid system”. No idea how this word ended up describing surfaces of geometry?
Man...she is something else!!No notes at all and she recalls everything at lightning speed!What a mind!!
thats how it works when you understand what you're talking about :D
I think she’s AI 😂
I apreciate that this was recommended, this inspires me schooling higher learning.
I loved this presentation despite the fact I didn’t understand the first sentence let alone the rest. Sigh! But you know in my day women like my wife were told women couldn’t really do Math so I absolutely love to see a young woman put that BS to rest.
But she aint black, you racist!
WOW, what a mind she has and you can also feel her energy and passion for her domain of expertise and I absolutely love that.
I am really high, but i am enjoying this class. It is clear that the professor is a person who has achieved excellence in her field of study and that is something really interesting. We are used to seeing the body at its maximum potential but not the minds, this is also something admirable to see.
She does a phenomenal job of laying out and explaining every step. I like that. Very well explained.
She needs to make a tutorial on back workouts as well.
Ngl the muscle tone is amazing.
No she is just a skinny frame so all her bones and muscles are visible.
Rock climbing my friend
@@varunrathi36I think you nailed it by suggesting she does rock climbing. It’s very popular in Austin.
@@regwatson2017lol. you sure do not look like that just because you are skinny. trust me, i know. as others have mentioned, she probably does rock climbing with a back like that. this is pure trained and used muscle
@namesashhousewares8337 If that's the case then she is narcissistically showing off. Like a guy with big biceps wearing a muscle shirt.
I absolutely loved Lisa's approach on this. She truly expands classical thinking on this subject in such a way to truly give us a new way of looking and thinking on three traditional manifold topology in the fourth dimension. Dont know why I didn't see it before. Thank you Lisa!
I don't have a clue what she is talking about, I do know people. What a beautiful and vibrant mind she has developed.
Bravo!!!
🎉
I have the utmost respect for science and scientists. I don't feel that respect obligates me to watch a lecture which I haven't the slightest chance of understanding. Do your thing, Dr. Piccirillo!
I thought this was gonna be a dj set but I get I’m listening to physics lectures for my workout, love it.
Outstanding lecture, Lisa! This was a GREAT talk! I am compelled by your enthusiasm and skill to add: Having spent a decade listening to my professors, this was both and expert delivery and very well informed - On all fronts 😊 Gracias!
Stop it, She's not gonna sleep with you
@Herlock-vc6ch Here come the inc3ls.
@@jonathanxavier2026 and here comes the s1mp
@@jonathanxavier2026 Here comes the slmperono
@@Herlock-vc6ch are you sugesting this is a bad lecture and someone only could comment on it because of the women who lectures? Or do you not understand a word she says so the only thing you can focus on is that she is an attractive women.
Serious Mathlete right there. Respect. 💪🏼🙏🏼
thank you harvard math department for uploading stuff like this it helps me fall asleep every night
What a great video for art students learning to draw backs.
On a sidenote, this passion is inspiring.
Saying this as an engineering student that has no idea what is going on here.
"Howard", this is "Sheldon", why are you even leaving a comment to this video, never mind clicking this video on? Also, can you or Bernadette drive me to the comic book store tomorrow, because Leonard and Raj are mad at me again and Amy and Penny are going to a spa together.🤣🤣
Yeah I'm a forklift driver...
So this channel got recommended to me more than once; different videos. I'm convinced that YT thinks I'm this smart. I'll take it as a compliment.
Thank you for the insightful lecture! The discussion on the Alpha invariant and its construction through cobordism was particularly enlightening. I would love to hear more about the practical applications of these concepts in current research. Looking forward to your next talk!
Luring unsuspecting pedestrians with free food and filming their reactions to lectures like this would be RUclips gold.
yesss!
When I was a grad student a classmate of mine used to go to various free meetups around the city for the free food. I almost thought about doing that but there's only so much pizza I can eat.
2:47 - those are some impressive lat and delt muscle definition.
Yeah. She must work out...
That's what most people including me concluded from this video
YT is so broken.
I started with watching music videos, it went downhill towards less family friendly ones, through body painting where you can see e v e r y t h i n g, then I saw how elephant downs a tree 5 times the size of it.. and now I am here. All in less than one hour
I'm glad there are people who love studying this type of stuff. If it was up to me, we would be at stone age forever.
getting teached on the 4th dimension by a ripped mathematic princess in probably the last thing i was expecting tonight im all in for it
My Mom used to tell me stories like this at bedtime...
Then you are Jesus
Congratulations, in two weeks your lecture surpasses every lecture uploaded on this channel but one
Which one
I just find it interesting to see other people's worlds.
WOW! Thanks for this! Just had to add to the accolades for work well done and presented!
In 2020, Piccirillo published a mathematical proof in the journal Annals of Mathematics determining that the Conway knot is not a smoothly slice knot, answering an unsolved problem in knot theory first proposed over fifty years prior by English mathematician John Horton Conway.
What an accomplishment
It's a way to model the fabric of the universe with both spatial and temporal components. Work in this field may lead to a better understanding of worm holes, space/time travel, and quantum physics.
Voyager 1 is less over my head than this material is.
It’s amazing how most of her shirt is in the fifth dimension
Most of her pants too 😮
Lmao
Criminally Underated
👍
You understood most of the lecture.
What blackboard? @@John-wd5cb
This level of genius deserves a better microphone.
My brain just melted watching this 😢
Pro tip for those of us who have no idea what she’s talking about (even if you have a degree in engineering or similar): Ask chatGPT what a 4 dimensional smooth manifold is. I have no idea if chatGPT is correct, but part of the answer was “In physics and mathematics, smooth 4-dimensional manifolds appear in general relativity, where spacetime is modeled as a 4-dimensional smooth manifold, with three spatial dimensions and one time dimension. “
Ahhh, NOW I understand! (Not)
Thank you. You gave me end of a thread I can hang on to.
Yep, but that's obvious - where is the genius chatgpt in-depth analysis we're all told it can produce ?
honored to be in the group of folks with a PhD in STEM who have studied topology before and got recommended this video but still could only focus on her back muscles and amazing fashion sense.
Thank you for still using the real OG, Chalk!!😊
You are a fantastic lecturer, Thank you.
In slight fairness, dry-erase board marker would be a poor choice for that surface..
I think it’s hagaromo chalk!!
@ yea, the good stuff. You know you made it when you use that!
I love how pretty much every video on this channel has
The first 3 minutes convinced me that this human is so much smarter than me that I can’t really understand how much smarter than me she actually is.
It is such an experience watching something I understand a perfect nothing about! What a wonderful world!
Correction! I do understand one thing about this presentation: she has an Italian background!
I am so glad they're still using a chalk board.
😅😅😅
Since I didn't understand anything, I still thought: What trained back muscles!
I undestood 1:18 "NOT AN EXIT"
She solved the Conway knot problem, which of course is the problem of how knot to laugh when Tim Conway does his Siamese elephant routine on the Carol Burnett Show.
Highbrow humor. Nice.
She didn’t solve the Conway knot… she proved it’s not a smoothly slice knot…
I clicked on the thumbnail because I thought I should spend a little time discovering something interesting today.
I’m now two minutes in and realize I need about eight years of courses before I can gain even a rudimentary knowledge of the basic terminology that’s being used.
oriented, compact and without boundaries - just how I like my manifolds
Sheldon Cooper is that you?
@@NexusNomad00 I bet it's sheldon
This has got to be the funniest comments section ever !!!
Yeah, it IS pretty damn good!🤣🤣
That chalkwork develops some wicked back muscles. Sweet.
For those unclear on the significance: In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects, such as how different observers perceive where and when events occur.
First, I find the comments here hilarious. Even if I feel exactly like many commenters I was thinking something here could explain why humanity struggles so with what we call UFO, or maybe it's called UEDs. Thousands of people have reported over decades, but we have not even produced a suggestion of theory. Or maybe she is doing it right there? Especially the famous Zimbabwe event w 60 school children. Some saw both ship and alien. Some saw nothing. Alien was at a distance, then suddenly near. Events as these perplex us so much because they challenge our basic understanding of reality. So we have chosen to ridicule the witnesses. Maybe AI wants us to understand and throws this mathgenius goddess.😁
Makes sense. I was writing today about the shape of infinity which can't be seen but only imagined as rings of rings which can expand or contract but using five dimensions of a pyramid you can find the internexus in the center; it's a spiral really; similar to how we're traveling trough the universe. The architecture is a design for a website lol It's called the Cybersphere with a new pyramid shaped navigator called the neXutool.
@@ddevamEverything spirals here, and what do spirals do? Make bloom outs. Pressure is a spiral in to bloom out floral growth pattern. Find center to bloom out.
@@liberatedcollective2124 See @1:03 where Lisa is adding handles to the curved spaces? Simple logic says you can not see a circle without drawing a line around it; and if you look at a line from the top; like a straw, it also is a circle. So It means that the "white hot spot" defined by Hawkins is where the line and sphere meet; it's point where reality is created or can fall outside to the forth dimension; via "quantum black hole".
Now; take an obtuse pyramid; intersect the five corners with three rings of different sizes (they don't touch); the corners represent Lisa's "handles" where they connect to the rings; then spin the pyramid and see what shape it creates; spiral-graph insanity to infinity right? Would it now cause the rings to collide then expand and contract at the same time?
@@ddevam Except it's not insanity, it's the harmony here, we see chaos because we can't read the language. Pressure is a language like ours, nature ONLY DOES SHAPES. POINT BLANK PERIOD. Not math, but you are on the right track. Just remember, zig zag is spiral. 6 is spiral, S is spiral. And spirals go to bloom outs, the five petal bloom is the end of pressure here. ⭐ Its a growth pattern, small to big, key shape in totality 🔑 (where your pyramid shape comes into existence, just remember 3d space, we think and observe embarrassingly in 2d. 🙏
This woman is a superior human.
The Führer has entered the chat
I second that. ❤😊 Wow, I watched the whole thing! I admit that I had an ulterior motive-I’m trying to work out possible topological relationships of frame dragging geometry in supermassive Kerr black holes, and I was looking for inspiration. 🤷♀️😂
@@deleted01 LMAO
Everyone is the same it's just that some people go to school more than others and without all of that work and studying they are just like everyone else 🎉
@@jasongarcia2140
Nope...
Genetics and how wealthy your family is.
For all the non-mathematicians, this is a great video to share next time someone downplays the significance of "so-called experts" and acts like they themselves are an expert on something just because they've watched a couple of RUclips videos on a given topic.
Bro, no. Actual experts exist and they devote their lives to understanding things on a level that you and I don't and likely never will. I'm a reasonably intelligent person and I'll happily admit this talk is way over my head.
Whether it's math or climate science or infectious diseases, experts exist and we do ourselves a disservice when we pretend to know better than them in their chosen field.
I needed simply a pause from all that cute-kittys-videos I've been binging. ;)
My master’s thesis in 1997 was on SW invariants. Very interesting to get a survey of the progress of the field, including the author’s recent work.
Do you use you degree much?
@ in recent years I do, since I do a lot of work in insurance mathematics. Differential equations, statistics, probability, linear algebra are all useful there. But the greatest use I have for my degree is that it allows me to continue “studying” maths and physics for enjoyment’s sake, mainly on RUclips :-)
Loved every single bit of it. Great lecture!
Iam an interdimensional alien and i approve this lecture 👍👽
Oh wow, you too? 😊❤🛸👍🏻
Of course you do.
❤we are here❤
@@careerdog Is the answer correct ?? please verify for us ....
Lisa Piccirillo: “Exotic phenomena in dimension 4”, 3 days ago 52k views, 357 comments .
Ivan Losev: “Construction of finite W-algebras”, 8 days ago 160 views, 0 comments.
Lisa the mathematician worked on her physique, and unintentionally found the solution to the youtube algorithm at the gym.
Only a tiny fraction of humans would understand these topics. Not the case for "attractive intelligent strong woman" - We have instincts to detect that, hyperactive ones. 😅It's no slight against Ivan.
Thank you for the recommendation! Ivan Losev got at least one more view.
I seriously doubt she's ever done anything unintentionally. But
🤔 Not sure I got the gist of what you're expressing other than the “explanation” for what brings males in to this video, lays either on her physique, or it lays on our “instincts”, responsibility shifted elsewhere; problem solved. All I was comparing between the 2 videos is wrapping vs. content. As in how a carefully chosen book cover determines whether it flies or stays on the shelves.🙂@@mortenrl1946
I seriously doubt she's ever done anything unintentionally. But I'm not sure I got the gist of what you expressed, other than the ,“explaining” for the high male turnout either lies on her physique or our, “instincts” responsibility shifted elsewhere, problem solved. They even compare her to Lisa Randall on her ‘IQ hotness’ popular sport apparently.
I meant to simply compare one video to the other in viewer-interest/time-posted. Wrapping vs. content. Other institutions channels also carry her lecture disable comments, probably because unrelated comments were starting to creep up. @@mortenrl1946
Exotic phenomena in dimension 4 just sounds sick as fuck, not comparable
I can watch this all day, no I do not know whats going on but it's beautiful
I only took one course of Calculus decades ago and it's a testament to the skill of Lisa Piccirillo that I was able to follow and understand the entire lecture (except a bit about 5 minutes from the end), only needing to stop and google a few words along the way. She walks through the history and builds her story piece by piece keeping everything solid as she goes. This is a fascinating trip to a different world and I have no idea how it got recommended to me but I really enjoyed it. Thanks so much for making this public and thanks again to the lecturer for giving us a glimpse of this world.