Revolutionary Math Proof No One Could Explain...Until Now [Part 1]

[@TheoriesofEverything]

As a listener of TOE, you can now enjoy full digital access to The Economist and all it has to offer. Get a 20% off discount by visiting: www.economist.com/toe Timestamps: 00:00 - Intro 02:14 - Edward’s Background 07:04 - Robert Langlands 15:01 - Physics vs. Mathematics 34:14 - Unification in Math 45:48 - What Does Math Actually Describe? 01:02:57 - Langlands Program 01:22:08 - Counting Problem 01:25:55 - Harmonic Analysis 01:33:58 - “One Formula Rules Them All” 01:51:58 - The Shimura-Taniyama-Weil Conjecture 01:55:55 - Original Langlands Program 02:01:22 - A Twist: Langlands Dual Group 02:01:55 - Rosetta Stone of Math 02:11:33 - The Pleasure Comes From The Illusion 02:14:28 - Support TOE

[@derrickdavis4488]

i had a vivid dream that the yinyang symbol was an actual spliced magnetic device wirh magnetic mirrors produced power

[@NicholasWilliams-uk9xu]

When this Universe takes things to the extreme, it really takes it to the extreme, dude I really hope all these different states can work together and cooperate in a good natured way, and make the world a better place for little children, we don't want to be on the bad side of this machine. We can all flourish, things can get so good, it's unbounding (well, there are critical factors related to controlling great uncertainty increase do to exponential compute, that's the great filter, we have to avoid that). The extremes (Power vacuum = black hole) (Power radiator = Planck unit) (Conscious expression, pleasure/suffering). This is why thing have to get REAL good, we have no choice 🤗

[@TammyDoris]

Hey this is my other account for Samoht sirood Aquarian soul time traveler... For some reason KZbin limited my ability to comment... So I am using this account because I have a 24-hour ban on commenting.

[@TammyDoris]

​@@NicholasWilliams-uk9xubeautiful... Lu other version of WE.

[@TammyDoris]

​@@derrickdavis4488I really like that term magnetic mirror... The reason why is because magnetism has a singularity point... That singularity point is basically like a mirror it is as close to absolute nothingness as you can get...

[@charlesblithfield6182]

Too many KZbin channels literally apologize when anything remotely scientific, mathematical and technical needs to be part of the conversation. This bothers me because “dumbing down” discourse can become a reciprocating process. If it’s hard to understand that’s GOOD because it challenges the intellect. I like how TOE doesn’t feel the need to apologize when the going gets technical because this shows respect to its audience.

[@JohnVKaravitis]

Someone sounds upset.

[@marcc16]

Probably because it’s extremely rare to find a personable, polymath podcast host who is capable of discerning high level topics to a general audience while maintaining engagement and interest. Make no mistake about it: podcasting in general is hard. Curt makes it look easy.

[@shannonbarber6161]

I personally don't find this channel technical at all and would be fine with it going much more in depth.

[@brendawilliams8062]

@@marcc16going from 4 then talking about two phi is seamless for school teachers too. Some just have talent

[@spiralsun1]

I love technical details and big picture stuff too!! I just don’t like when people get bogged down in acronyms and screwed-up terminology 😂🤷‍♀️❤️

[@coder-x7440]

I love this guy, he’s pure entertainment in every interview he does. And that he’s as elite a mind in our world as Ed Witten is too much. He’s like the Feynman of mathematicians. He’s to his bones trying to make a connection and communicate with the person and audience he’s speaking to. Edward Frankel is a star.

[@Achrononmaster]

Yeah, but also don't begrudge existence of Witten. He's clearly high functioning autistic. Society has a place for such unique people.

[@ShayQrchestrals]

@@Achrononmaster Lol what? Where and how do you know Witten is autistic? I cant find anything on that.

[@Steven-bs5hv]

I can't agree more. He's so likeable, that I have to watch every interview he does. And the cherry on top is that he's a scholarly badass.

[@ottomondo1368]

@@coder-x7440 I hear a sucking noise coder.

[@palahnuk1]

@@Achrononmaster witten … meh

[@SetemkiaFawn]

I wish I could remember how I got onto this but I was reading an article about Frenkel that caused me to buy his book Love And Math. The story of how he came to be interested in mathematics and how he was educated USSR is absolutely amazing. There were so many things that had to go exactly right in order for him to be here in the U.S. with the knowledge and experience that he has. As much as he loves mathematics, he loves being able to communicate it to others at their level. So he is an excellent math communicator. I am extremely thankful for this opportunity to listen to him talk about the Langlands program. Thank you for this extended interview with him. Two and a half hours. Wow.

[@austin4768]

Frenkel is a deep thinker, and not just about mathematics itself but also about the human side of the discipline and what's more, he's got a real passion for communicating these insights in a clear and compelling way! I would listen to another 10 interviews with him, but one more will do for now. Glad there's someone interviewing such people at a level of a mathematically educated non-specialist.

[@kennethvalbjoern]

I always love to hear and see Edward Frenkel's casual and entertaining speeches. He is a very intelligent man.

[@ahmadsaffi2227]

This is one of my favorite conversations. Thank you for continuing to bring on wonderful guests and diving into the deep areas we seldom find elsewhere!

[@TheoriesofEverything]

Glad you enjoyed!

[@TwoStepsFromAnywhere]

Wow, his passion makes the exposition more riveting than a thriller. We need many, many seasons of this series !!!!!

[@YoutubeSucksTheBigOne]

@@TwoStepsFromAnywhere I smell a comment bot.....

[@James-ll3jb]

Why?

[@YoutubeSucksTheBigOne]

@@James-ll3jb If you haven't heard, KZbin is full of comment bots making generic comments like this with no substance. I don't know what the point is. I am not blaming the channel creators though, many of them are just as irritated because they have to wade through all the fluff to find actual comments that give real feedback.

[@grzegorzmajcher9237]

Please, give us more of Edward Frenkel!!! I could listen to him forever!

[@asterixx6878]

Put this video on repeat. 😄

[@MarkoTManninen]

Exceptionally talented teacher. I have listened the first 30 minutes and I'm impressed. His choice of concepts and gradual development of ideas makes difficult subjects sound comprehensible. Iceberg melted!

[@FrancisGo.]

Edward Frenkel and Sean Carroll both have beautiful enthusiasm and resonating euphony. 💞

[@FrancisGo.]

Emily Reihl has that too. She would be a great guest.

[@curtjaimungal]

Agreed ​@@FrancisGo.

[@mrhassell]

Add Chi-Shen - Terence Tao to the converstion, and I'd be intrested to see that! Another, (of which, maybe there are too many?) great Aussie lad's.

[@fronx1984]

I could listen to Edward all day. He cares so much about making sure that the listeners see the beauty of it for themselves. Sometimes he dwells a bit too long on spelling out the connections, but I can live with that. Looking forward to the continuation!

[@sullenpuffin]

Yes Edward, we definitely dig these kinds of discussions! Thank you for this, and as always, thank you Curt!

[@rodrigoviverosphoto]

Remember that all this talk is for free. Amazing. Thank you!!

[@brian8507]

... besides the time theft the ads take from u. Remember u only have finite amount of time on earth... ads steal this from you

[@ChrisShawUK]

"when was the last time you saw a sheaf on the street?" has to be one of the best one-liners ever

[@rudrendrakashyap-zg6do]

True :) i don’t think people are so fascinated with sheaf cohomology. :(

[@lucascardoso5332]

Great interview. Looking forward for part 2.

[@Tabu11211]

What an amazing talk! Helped me understand what I need to learn better. It made me appreciate things more too.

[@TheMikesylv]

It’s very easy to like Edward Frenkel he is charismatic.

[@johnvonleibniz]

Wild timing on this. I've been thinking deeply about Ed Frenkel for the past few days. Anyway, fantastic upload Curt!

[@ontheballcity71]

That was quality. I look forward to the second installment!

[@quantumkath]

Mathematics beautifully describes physics, and at the beginning of the video, Edward Frenkel passionately illuminates the profound merging of the two, showcasing the remarkable results that encapsulate our universe. Then, Frenkel takes us on a captivating journey, exploring intricate mathematical constructs culminating in the groundbreaking Langlands Program, unveiling hidden patterns across diverse mathematical domains. I love mathematics. So, following Professor Frenkel's logic wasn't too difficult. Although I didn't understand the graduate equations, overall, I understood his reasoning with the help of Curt Jaimungal, asking for clarity. I did acquire knowledge. It's time to read his book, Love and Math. Maybe then I can call myself Quantumkathmath.

[@mrhassell]

groundbreaking? lol - hmmm yeah, not really... still, whatever blows your hair back, I suppose!

[@ydas9125]

Inspiring, clear and passionate explanation and discussion. Love all the detours. Thank you very much and cannot wait for part two.

[@MoeFH]

This is really great stuff, can't wait for the geometric correspondence in part 2.

[@MrFlaviojosefus]

This is one of the most fantastic videos I have ever seen!!!! I am completely baffled.

[@Tordvergar]

That "digression" on String Theory is the best digression I've ever heard!

[@tears_falling]

good video, excited for part 2

[@alexdamman6805]

Thank you! for this very entertaining, enthusiastic and illuminating background discussion, from THE guy who can come out and communicate it so well. I am eager to hear about the geometry connection.

[@user-cg3tx8zv1h]

Thank you for hosting best ideas and bringing crème de la crème individuals... They are here because of you... Formidable service... ❤

[@PeoplesScience]

He's without a doubt my favorite popular mathematician. The 'Forrest Gump of Mathematics' couldn't have been a more apt analogy!

Fascinating. The main topic, and also the incidental discussion about String Theory which showed up quite surprisingly into the foreground.

[@grandeau3802]

After listening to Edward Frenkel closely, I’m convinced that he understands everything he’s talking about.

[@ricodelta1]

Love how deep this goes. I think this sort of technical analysis must assume that the audience has the capability to undergo phd level study. This was.excellent

[@grzegorzmajcher9237]

Edward Frenkel is SUPER!

[@PGB55]

I've never in my life so much enjoyed hardly understanding anything. Conceptually a lot of it made sense but to fathom actually doing this work is mind-boggling.

[@James-ll3jb]

@@PGB55 why?

[@ozachar]

What a pleasure and privilege to have an opportunity on KZbin to hear and learn from the thoughts of such people. A highlight for me was understanding that Andrew Weils solution to "Fermat last theorem" was much more interesting and important than the seemingly obscure detail of Fermat's theorem. It shows that hidden under what seemed to be some curiosity theorem of Fermat, was a hint at a much more general aspect of mathematics. Fermat theorem was basically some tempting shiny gem that showed the way to a real treasure box.

[@stianaslaksen5799]

I must admit I did not understand much of this, but it's such a pleasure to listen to prof. Frenkel explain stuff so I watched the whole thing anyways.

[@gencshehu]

Very, very much appreciated! :D

[@Haroldus0]

I am so grateful to the algorithm that brought me here - a perfect balance of higher math, music, with overtones of something else. I cant wait for part Two. There is a lot to digest here but it is presented in a very gentle and wise way, with a welcome light touch and humor. Thank you both so much. The marriage of music maths and physics has been my life's work

[@TheoriesofEverything]

Welcome Harold! Hope you enjoy the channel

[@hypat1aa]

This is beautiful. I came upon something like this when trying to understand 3D mathematics, it was like having to relearn everything. I started thinking of whole numbers like twisted cylinders, similar to winding the string around a finger. So much more for me to learn. I think of another surface in this structure, the helicoid.

[@15silverblade]

This is simply the best channel ever on this platform

[@haidarhaidar9092]

I can believe that i can follow and understand like 97% of the conversation

[@realBlue2024]

What?? I wish I could understand..0 01% .

[@enriqueruiz6582]

No way, Ed Frankel is back!! I just dropped everything.

[@TheoriesofEverything]

Hope you enjoy it Enrique!

[@rudrendrakashyap-zg6do]

Thanks for this interview.

[@anpsinhasinha8499]

A great mathematician. A very illuminating program

[@tod3632]

Thank you so much for doing this. Amazing for us math nerds to learn

[@RSLT]

I love Ed Frenkel!

[@jacksourlis4151]

Finally finished watching this podcast, their should be many more people on this earth like the professor, loved his ending words.

[@GuzmanTierno]

Vito Volterra: "Mathematicians talk to god and nature, physicists talk to mathematicians and ... the other people talk amongst themeselves" ... I just thought the quote fitted in this really nice podcast.

[@AThagoras]

I love the discussion about whether mathematics is discovered or invented and how discovering/inventing mathematics is like getting a glimpse of something through the fog. I struggled with this question for decades, but lately I've come down on more on the discovery side. After trying to understand epistemology in the light of modern physics, I feel like the two perspectives are the difference between an objective and a subjective view of the same process, so to me, so discovery and invention are really the same. I keep getting excited when I think I've discovered or invented something new, but then google often proves me wrong, i.e. I keep discovering things that already exist (mostly in the past, but sometimes in the future).

[@wwkk4964]

Best youtube channel right now!

[@inplainview1]

This was brilliant.

[@alexander12305]

Berkley math students are lucky to have such a brilliant teacher. He makes learning to look easy.

[@davidkent2804]

Very engaging on every level: presentation, technical education, history, and human interest. These advanced topics are a little sci-fi as well, and on the forefront of discovery. Wonderful value, thanks.

[@agranero6]

"and it failed...spectacularly" as a physicist I must say: thanks for broadcasting that! Many physicists are still shy to say that. To illustrate the difference in visions: Witten avoided Feynman because every time Feynman crossed with Witten, Feynman asked *loudly*: "With how many dimensions are you working today?". This arguably true story was sanitized from Internet.

[@Milan_Openfeint]

It's easy to make fun of string theory, but until you come up with something better, it's not really all that funny.

[@agranero6]

@@Milan_Openfeint It is not even wrong to have something better. It is not a theory it is an schemata of gazillions of theories separated by different compactifitions. It is not background independent. It predicts nothing, it is not falseable then, and anytime it failed at something they refurbished it to fit the facts. This is the reverse if the scientific method according to Popper. The epitome of their delusion came when two starring theorists proposed the change the scientific method because it became clear that string theory could never get anywhere. Their main argument? It is the only game in town. It is abstract nonsense, what can be good for Mathematics (see category theory) but Physics need to have a foot in reality. Forced to choose string theory Vs scientific method is a nobrainer. With how many dimensions are string theorists working with today? It is Monday they are using branes today. It was not only a failure it was an spectacular failure that held Physics behind for 40 years.

[@frankkolmann4801]

Absolutely Amazingly Astoundedly jaw dropping. I could actually follow the presentation. Although I have read physics a long time my understanding was always a mish mash of esoteric ideas that essentially I did not grasp. I still am an ignoramous but Edward has opened a window in my mish mash mind where I see a glimpse of what physicists are on about, and it is mind blowing. Thank you for being able to bring light on math and physics for me. Perhaps someone else listening could brush up on what spatial invariance is and what conformal invariance is and what a CalibiYau manifold is (wikipedia) then listen again to see.

[@homie4025]

I want another interview on this topic he is good 👍

[@macanbhaird1966]

Your videos are excellent and always very informative and interesting. Great work from you and Prof Frenkel - Many thanks!

[@TheoriesofEverything]

@macanbhaird1966 Glad you like them!

[@drake_sterling]

Maths begin at 1:13, exactly half-way through the video. This is Clock Arithmetic. Number Theory and Harmonic Analysis. Symmetries of the Unit Disc. Rosetta Stone! "The pleasure comes from illusion." The Langlands Program will grind onward infinitely… with NO CONCLUSIONS. Maybe try… geometry? What if? Ehh, Love and Math! Infinite - without ever getting the solution! I literally love this guy, along with Lex Fridman. Superb! Solutions are much, much harder to get.

[@kingsouther]

@@drake_sterling u da mvp! U meant 1 hour 13 mins in btw!

[@primetimedurkheim2717]

Nice! Love Ed

[@MarekDenko3D]

Great episode!

[@MichaelJones-ek3vx]

I feel like a miniature Darwin, I wish I took time to study mathematics more. Excellent! Kurt, this is an unfolding of ideas that are elegant. Thank you and your guest.

[@TheoriesofEverything]

Glad you enjoyed it!

[@NimrodTargaryen]

I am a physicist by Training and I love the sincerity of calling out the failures of string theory

[@Iophiel]

Truly priceless. Thank YOU, Curt Jaimungal

[@Mik1604]

I subscribe tot everything where Mr Frenkel appears. Such an intelligent and also entertaining man.

[@happyshadow]

the vocal sound from that RODE NT1a is very good, such a solid mic. You could do with a touch more deesing as well as the podcast auto mix. great work!

[@FXK23]

d/dt (math) = 0 | d/dt (physics) = 'ongoing mystery'

[@leonardor8264]

0/0 lim fx

[@mrhassell]

Time dilation can also occur due to differences in gravitational potential. Clocks closer to massive bodies (e.g; Yo Mamma!) experience less elapsed time than clocks farther away.

[@XXfea]

Fantastic!! GREAT!

[@Cosmiccuriosity__c]

This is incredible

[@jazzvickyvenkat]

Awesome , breth taking insight . It just brilliant yest it humbles you so much. Human mind is truly wonderful and we need to understand it more and understand it's capabilities.

[@geraldkennally5517]

This idea of unification sounds like what Descartes did by inventing coordinate geometry and unified geometry and algebra.

[@bhaskarbagchi1643]

That is a very good analogy indeed. Only, the Langland program is a connection at a much deeper level.

[@mrhassell]

Nice! Little bit more like Hardy and Ramanujan's work on partitions, Hardy refined with Littlewood and another intresting aspect, Ramanujan’s congruences. The first congruence, means If a number is 4 more than a multiple of 5, i.e. it is in sequence 4, 9, 14, 19, 24, 29, . . . Therefore the number of its partitions is a multiple of 5. Evolved into other congruences of this type being discovered, for both numbers and "Tau-functions", of Fourier series. Sigma, Ligma.. lol Digma own hole

[@FrancisFjordCupola]

Edward seems like a great guy. I'm no physicist and technically speaking he's more a mathematician... but I'm sure having a conversation with him deep into a long night would be eye opening. I'm just not sure I'd have enough ideas to tease and bounce off of him. To me it seems like progress in physics comes from accepting different perspectives. Which is why string theory is deadly as it fixates on one single perspective.

[@MrOreo76]

Fascinating, thank you

[@polymloth]

Oh no I certainly won’t be able to sleep before part 2 comes out!

[@halneufmille]

Some disciplines like theoretical physics may be in rough places lately. But hearing this makes me think we may be living in a golden age of mathematics. And certainly, thanks to the internet and youtube, we live in a golden age of science communication.

[@macromicrodragon]

Hey, perfect time for 2am insomnia! 2:22 EST! Id highly suggest interviewing Dan Winter. That would be an interesting interview

[@williamjmccartan8879]

Sounds like Edward could write a children's book for primary school aged children to expand their understanding of mathematics, when Edward is describing the layers of a sphere, is similar to pulling apart the layers of an onion,

[@mitchelljacky1617]

You know something well when you can describe a topic to an expert in the field as well as describe it to a child. Well, I think it just makes a person down-to-earth and great at understanding people but I digress

[@williamjmccartan8879]

​@@mitchelljacky1617 I agree with the sentiment, as I have no formal education above the HS, diploma I went back 20 years ago to pick up, when it comes to listening to people discuss their idea's I think about the conceptual space from a generalists perspective, and normally I can glean something from the conversations, it also really helps that Curt digs down when exploring these ideas, peace

[@cammccauley]

The amount of money I’d pay to have Edward frenkel make a series to teach from the basics of math all the way to grad student in that way 😂

[@aidanhite9764]

If Langland's Programs connect "continents of mathematics", I would say that it's not a bridge between two cities on those continents, but more like one of the languages that is shared by some of the people that live on those continents.

[@hammerdureason8926]

Thanks for this ... interesting & important as is inspiring & enjoysble. 👍👍in my top 5.

[@TheoriesofEverything]

Glad you enjoyed it!

[@sjzara]

Wonderful. I never realised the reason for Calabi-Yau manifolds in String Theory.

[@WalterSamuels]

Curt is very intelligent. Must have a killer memory, not sure how he retains so much information. Truly impressive.

[@BeTheGuitar]

Your job is to explain this damn universe. Pure Frenkel GOLD!

[@guillermobrand8458]

I think it would be useful for Edward Frenkel to try to understand the role that human language plays in the “configuration of realities” based on the definitions that are made through language, without leaving aside “mathematical language” and the relationship that exists between mathematical language and the language that uses words.

[@eloyfernandez1640]

Bring this man back please!

[@geirtobiassen7926]

Thank God for ppl like this..

[@Billybo121]

I dont know shit about math, but I love listening to Ed Frenkel!

[@shoopinc]

Super excited for part 2! My only question is does the lie group G associated with number theory and the Langlands dual group LG on the Harmonic analysis side have applications to differential equations? Particularly the differential equations of physical equations of motion like Lie group U(1)'s role in quantum mechanics?

[@jonlasa9034]

Thanks Edward for your inspiring explanations, it is a pleasure to hear you both. At some point in your talk you mention electromagnetic duality symmetry and that it is closely related to the Langlands program. Indeed, EM duality seems to be the starting point in many references regarding the Langlands program. My question is: how close does this analogy between EM duality and Langlands program hold? For instance, EM duality is, in general, a continuous transformation between electric and magnetic fields (not just E->B and B->-E). Does this fact also reflect in Langlands construction?

[@jacksourlis4151]

If you could bring up this concept of equal PathTimes…within the context of bridging… The notion of equal PathTimes in trigonometric functions can be used as a basis for drawing parallels with continuous deformations and mappings in algebraic topology, particularly in the context of homotopy equivalence. By considering how different sine functions with varying amplitudes or frequencies complete a full circle in the same amount of time on the unit circle, one can draw an analogy to the continuous transformations that establish homotopy equivalence between topological spaces. The equal PathTimes in trigonometric functions serve as a mathematical foundation for exploring the idea that different functions can exhibit similar behaviors in terms of completing cycles within a fixed time frame. This commonality in PathTimes can then be related to the concept of continuous deformations and mappings that define homotopy equivalence in algebraic topology. By leveraging this common principle of equal PathTimes, one can potentially establish connections between the properties of trigonometric functions and the fundamental concepts of continuous transformations and equivalence in a broader mathematical context. Understanding the perspective on referring to the concept of equal PathTimes around the unit circle as a metaphorical representation of the homotopy equivalence principle relationship. By drawing this analogy between the consistent completion of cycles in trigonometric functions and the continuous transformations establishing homotopy equivalence, you can highlight the underlying symmetry and invariance shared between these seemingly disparate mathematical concepts. This comparison underscores the fundamental principles of continuity and equivalence that are inherent in both trigonometry and algebraic topology, and yes interconnected nature of mathematics, (with all islands). In the context of trigonometry and the unit circle, the radius of the circle is always considered to be 1. This unit circle is central to defining the sine and cosine functions. When we refer to different radius circles, we are essentially scaling the unit circle by a factor of the desired radius. This scaling factor affects the amplitude and period of the sine and cosine functions but does not change their fundamental properties. By adjusting the radius of the circle, we can generalize the sine and cosine functions to different scales while preserving their essential characteristics. Homotopy Analogy * This property of equal PathTimes amid radius scaling can be used as a metaphor for continuous deformations in algebraic topology: * Just as different scaling of the unit circle preserves the structure and behavior of trigonometric functions, continuous mappings between topological spaces preserve their topological properties (such as loops and paths) during transformations. Discovery of Invariance * The focus on equal PathTimes emphasizes the invariance shared between trigonometric functions under scaling: * Invariance under transformation:
Like escalated or deformed shapes in topology, trigonometric functions demonstrate how paths maintain their cyclic characteristics even when their dimensions (or scales) change. Conclusion * By integrating the idea of radius scaling with the principle of equal PathTimes, one can appreciate how different representations of functions maintain their core cyclic behavior. * This connection highlights the broader themes of continuity and equivalence in mathematics, showing how concepts from different areas, such as trigonometry and topology, can reveal deeper insights about the nature of mathematical transformations. * The use of equal PathTimes within
Fourier series emphasizes that different functions can undergo transformations (like shifts or scaling) while retaining their periodicity-a reflection of the essence of homotopy equivalence. * As different manifestations of periodic functions are expressed through their Fourier series, the essential properties (such as continuity and cycles) remain invariant across transformations. * This approach highlights a new way to link these established ideas, focusing on equal PathTimes as a metaphor for invariance in both Fourier series and homotopy equivalence.

[@jacksourlis4151]

And from this you can get an inclination of how you are able to use and why modules works

[@karagi101]

😴

[@jacksourlis4151]

@@karagi101 Honestly thank you for your response, I could be wrong and I do question myself and that’s why even a small response helps me, but yes this concept is inundated and also a concept where a child before development of Piaget stages and thus put many people to sleep and yet keeps me awake and possibly I have placed myself in this predicament and do need any feedback so I may help myself. I believe the above is another notion of sameness which yes is a weak notion of sameness also similarly to the notion which comes up in topology which is called homotope equivalence in which here are the ideas two spaces are homotopic equivalent if you can continuously deform one to another and such a simple of an idea as the example of all of euclidean space you know three-dimensional euclidean space is homotopic equivalent to a single point so you could imagine of this homotopia equivalence as like the reverse big bang but the one I mentioned goes forwards and reverse so you imagine three-dimensional euclidean space and “assuming” it has a centre (but my notion can work without a centre) the origin point of the universe and then all the other points in the universe and the universe is three-dimensional you are going to continuously move all the points in the universe back in a straight line (doesn’t need to be a straight line, which makes equal PathTimes shine) to the center of the universe or to the origin and they'll move kind of faster and slower(if using a straight line but if not a straight line would be more of variable frequency) depending on how far away they are so at time zero every point is where it is and then at time one they've all crashed home into the the center of the universe so that it is describing a continuous deformation that reveals that three-dimensional euclidean space and the point are the same so here's an example a sort of everyday example of a homotopic equivalence, the reason why this is an interesting example is because the point and three-dimensional space are homotopy equivalent they can be continued. You can actually do the same from mapping from a 1 dimensional world to a 3 spatial dimensional world by the use of equal PathTimes.

[@ximono]

André Weil had a sister who was a great philosopher with a short but fascinating life, Simone Weil. Albert Camus called her "the only great spirit of our times." (Edit: Oh, he mentioned her later on.)

[@davidespinosa1910]

The connection between elliptic curves and FLT was first observed by Yves Hellegouarche, in his 1972 thesis. See the appendix to Hellegouarche's 2001 book on the math behind FLT.

[@ihsan_osmanoglu]

Another banger!!!🔥

[@tagexing]

Thanks for the great video! Can Prof. Frenkel maybe explain a bit more about how the PSL_2(Z) works on the hyperbolic plane, right after the example of cos and sin?

[@jesuslopez8404]

Ahh not just great maths but also how nice exposition job, from the heart. The Solaris bit is explained in the 'homotopy groups of spheres' wikipedia, in π₂(S²)=ℤ, so the sentient planet surface of shape S² develops an intuition of the integers as an homotopy group. I think the spherical examples are suspensions of the circular ones, as in the pic of π₁(S¹) earlier. Looking forward for part 2. I'm sold a whole franchise. Love'n'math influenced me decisively when younger, warmly recommend it.

[@Necrozene]

Both maths and physics describe the "Now what?" In Maths, you can refer to your artificial works of declaration. In Physics you also need to refer to experiments in Reality. Both require an entity that can hold itself together and assimilate the information.

[@mrhassell]

The trick . . you "must" formualte a strategy, decided before arriving at that point. It's a choice, and alway remember that! Consider, the 'hidden' beauty of variables, as equal to the riddles of partitions, or the Tau of functions. 51 years of Philosophy, and all I got was a bunch of records... In life, we encounter countless decisions. Some small, some monumental. These choices shape our experiences and define who we are. As Morrie Schwartz wisely said, "The big things - how we think, what we value - those you must choose yourself." Essentially, our core beliefs and values are personal choices that we make consciously or unconsciously. Less intellectually, Wu-Tang Clan: "The Game of Chess, is like a swordfight. You must think first, before you move." - Enter The Wu-Tang (36 Chambers) Nov,93 - RCA.

[@KaliFissure]

Time is compactified. This is why there are limits. This is why there is conservation. Because we have a maxima and a minima ( which there didn't have to be). This creates the topology we observe. The Ricci flow is real geometric thing. The flow is to maxima and then at surface of interaction there is an inversion. Neutron decay cosmology is the physical process which embodies this. Space is a dielectric super fluid and flows in this fluid evolves all QFT

[@Skorezore]

Time for you to brush up on analysis! There are limits because you are playing with a continuous variable. Every closed interval admits extrema. In that sense, compactness implies the existence of absolute extrema. So, indeed, there does have to be a minimum and maximum value taken on by whatever it is you've concocted. If you need more help understanding let me know. If there's one word that describes me it is charitable. Cheers!

[@jpsi9]

7:34 Mathematicians of the world, unite and take over

[@WMAlbers1]

Herbert Spencer wrote at the end of the 19th century in his "First Principles" about the trend of scientific theories that as they get more and more abstract they become more like religion. When you get into these types of theories they are named after hoards of brilliant minds who nobody knows (Langlands, Lafforgue, Taniyama-Shimura, Drinfield, Deligne, Kapustin etc...). These theories remain impenetrable for the common man.

[@nosarcasm1]

Hi. There is one note I want to make about the discovery of the integers about a spinning planet. The formal argument are understandable. But it makes no physical sense. A planet needs to make a fixpoint where it localize the zero to be able to count the rotation. To be able to do so, there must be something other to be observable for the planet, otherwise it won't know that it is spinning. (Maybe it could observe a force and relate it to its spinning, there is nothing else for the planet to observe, so I don't see a chance here. So in the consequence, there has to be something other to be observe. So there are min. two things and therefore the planet is able to think about that and could find the number 1 (it), 2(other) and maybe zero for not being anything there. So the planet observe the digits as we do.

[@raymondbrowning762]

More of this, very good.

[@Khashayarissi-ob4yj]

With luck and more power to you. hoping for more videos.