The Biggest Project in Modern Mathematics
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День томуIn a 1967 letter to the number theorist André Weil, a 30-year-old mathematician named Robert Langlands outlined striking conjectures that predicted a correspondence between two objects from completely different fields of math. The Langlands program was born. Today, it's one of the most ambitious mathematical feats ever attempted. Its symmetries imply deep, powerful and beautiful connections between the most important branches of mathematics. Many mathematicians agree that it has the potential to solve some of math's most intractable problems, in time, becoming a kind of “grand unified theory of mathematics," as the mathematician Edward Frenkel has described it. In a new video explainer, Rutgers University mathematician Alex Kontorovich takes us on a journey through the continents of mathematics to learn about the awe-inspiring symmetries at the heart of the Langlands program, including how Andrew Wiles solved Fermat's Last Theorem.
Read more at Quanta Magazine: www.quantamagazine.org/what-i...
00:00 A map of the mathematical world
00:25 The land of Number Theory"
00:39 The continent of Harmonic Analysis
01:20 A bridge: the Langlands Program
01:46 Robert Langlands' conjectures link the two worlds
02:40 Ramanujan Discriminant Function
03:00 Modular Forms
04:36 Pierre Deligne's proof of Ramanujan's conjecture
04:47 Functoriality
05:03 Pierre De Fermat's Last Theorem
06:13 Andrew Wiles builds a bridge
06:30 Elliptic curves
07:07 Modular arithmetic
08:56 Infinite power series
09:20 Taniyama - Shimura - Weil conjecture
10:40 Frey's counterexample to Frey's last theorem
11:30 Wiles' proof of Fermat's Last Theorem
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Quanta Magazine is an editorially independent publication supported by the Simons Foundation www.simonsfoundation.org/
@jcookev Рік тому
Give a raise to whoever the artist of this video is. They have done such a good job at creating visual support to make it easier to understand. Amazing job!
@Arc125 Рік тому
Seconded.
@bjk837 Рік тому
Thirded!!
@QUIQUELHAPPY Рік тому
fourthed
@nemanjavuksanovic3122 Рік тому
Fifthed!
@kinjalbasu1999 Рік тому
seventhed
@Casreor Рік тому
I didn't know mathematicians had their own program of a grand unification just like physicists do. Thank you for the video!
@Cris-kt9df Рік тому
It's a pretty significant overstatement to say that the Langlands program is a theory of grand unification. But! It does make a good story :D, and the use of "bridge building" as a method of problem solving is fundamental to many areas of modern mathematics, at least at this moment.
@micuhh Рік тому
@@Cris-kt9df exactly my words. building bridges is something mathematics and practically every other stream of science achieves to do, and it all falls under that one umbrella of the grand unified theory of everything
@rv706 Рік тому
Mathematicians don't have their own grand unification like physicists (If we exclude axiomatic systems in mathematical logic, such as ZFC, which is a well-established basis of unification for mathematics). The whole "Langlands is grand unification for mathematicians" is just rhetoric used by science popularizers because the public is somehow familiar with the struggles of particle physics.
@Casreor Рік тому
The video says that ''Langlands program may reveal the deepest symmetries between many different continents, a kind of grand unified theory of the mathematical world...''. I didn't mean that Langlands program itself was a grand unification theory but that the idea of grand unification exists within Mathematics itself just like it does in physics. The reason why this was surprising to me is cause in physics, for example, a grand unification sprung from quantitization of General Relativity does not seem possible so scientists come up with new theories and modifications to be able to achieve that whereas Langlands, as far as I understand, is motivated to reveal something we don't know about different fields of Mathematics; are there any further connections between them, if so what are these connections? Whereas physicists are motivated to come up a theory that describes the right symmetries of nature in high energies and large scales, mathematicians in this context would be motivated to uncover all the bridges between different fields. Thus, a grand unified mathematics would be the one where all different ''continents'' are connected.
@Cris-kt9df Рік тому
@@Casreor I think my comment was more directed at the language in the video--which in the end was a very very nice piece of media. If you found it interesting and thought provoking, then that's fantastic :D. I don't mean to rain on anyone's parade. Now, I will take a risk and mention some kinds of physics which I don't understand. As far as I can tell, the Langlands program seems more akin to, say, AdS/CFT correspondences, or mirror symmetry. Or, more directly, there's a paper by Kapustin and Witten which frames (a version of) Langlands duality as an "electro-magnetic duality". So it seemed to me that these kinds of comparisons are more appropriate, rather than to grand unification. But that's really in the weeds. Have a good day!
@ajaysabarish9645 Рік тому
The visual of Ramanujan writing in a slate is an authentic touch! Context: Ramanujan was born to a poor Indian family and did not have money to purchase papers(which was expensive at that time) and he always worked on slates.
@vinitrout3679 10 місяців тому
Writing on slates is more satisfying than slamming your hand on keyboard.
@cryingwater 3 місяці тому
@@vinitrout3679 True. Solving on paper(not PC) is so much better
@canyoupoop 26 днів тому
Do mathematics handwritten, publish paper on computer = peace
@leandrocarg Рік тому
Being depicted as an engineer must be a mathematician's worst nightmare
@sepg5084 Рік тому
Only if they a childish enough to encourage such gatekeeping
@thefourthbrotherkaramazov245 Рік тому
😅 So true
@MrQwerty15ification Рік тому
@@sepg5084 Well when you look at the fact that engineers do a lot of rounding and mathematicians love precise numbers you can see why mathematicians wouldn't want to be depicted as engineers
@machida58 Рік тому
I am a coward. I wasted my life.
@Yunuet Рік тому
As a Mathematician I can confirm this.
@micuhh Рік тому
Alex Kontorovich is such a great narrator for any math related videos, its genuinely SO fun to watch!
@Ben-kh2rh Рік тому
YES I LOVE HIS VOICE!!!
@brazni Рік тому
I just realised now it is Kontoroviches voice :o awesome
@6884 Рік тому
is it related to... that Kontorovich?
@micuhh Рік тому
@@6884 by "that" if you mean Alex Kontorovich, then yes
@micuhh Рік тому
and the Langlands program is not directly related to Alex, he just narrates math related topics like these in a comprehensive and easy to digest way
@MedlifeCrisis Рік тому
This was a wonderful explanation and video. I also love that we’re still puzzling things Ramanujan and Fermat thought about hundred(s) of years ago.
@NotSomeJustinWithoutAMoustache Рік тому
Last time I was this early to a verified reply.
@bagochips1208 Рік тому
didnt expect to see you here
@fragileomniscience7647 Рік тому
@@bagochips1208 He's more open minded than a neurosurgery patient
@miguelpereira9859 Рік тому
@@fragileomniscience7647 Hahaha
@awesomedata8973 Рік тому
They also didn't have smartphones and technology to distract them. A lot of those kinds of thoughts happen when the mind is quiet.
@AlexYouTubeTips Рік тому
Alex Kontorovich (guy who voices this video) was my calculus professor in college. Very talented man and incredible teacher.
@bencardwell5545 Рік тому
fellow rutgers student! Regrettably i never got to take number theory with him
@AlexYouTubeTips Рік тому
@@bencardwell5545 Yeah, he was great, I wish I was able to take one of his other courses as well
@maribelmenese4845 3 місяці тому
Yo fr tho he was the best teacher.
@vecter Рік тому
I would watch an infinite playlist of this content. As an amateur math enthusiast with a somewhat undergrad level of understanding, this stuff is fascinating and beautiful.
@randomirrelevant1788 Рік тому
Stuff like this makes me want to pursue a degree in Mathematics, however I don’t trust our school system to teach it properly. It’s very sad to me. Math is very visual but I was only taught the rules, not what we’re actually trying to accomplish with our proofs and equations. I wish I knew better way to fill in the gaps.
@orangenostril Рік тому
Some sort of infinite series??
@jona8659 Рік тому
@@orangenostril As the parts of the infinite series go into smaller and smaller detail, it will become integral to our understanding of the bigger picture of modern mathematics.
@Soken50 Рік тому
@@randomirrelevant1788 I'd highly suggest online sources like Brilliant so you can do it at your pace whenever you want with plenty of visuals and examples. Or Khan Academy if you'd rather not spend money. (don't tell Brilliant I said that)
@todorstojanov3100 Рік тому
@@randomirrelevant1788 That's how school maths is. On college/university, it's a whole different story. You have to prove pretty much everything
@jacobkatzeff Рік тому
I’ve always struggled to understand how Wiles proof worked - this is the best explanation I’ve heard!
@lonestarr1490 Рік тому
One noteworthy point in this context is that Wiles did not prove the whole of the Taniyama-Shimura-Weil conjecture. He "only" proved it for semistable elliptic curves, which the curve one obtains from a^p+b^p=c^p happens to be. So this was enough to imply Fermat's Last Theorem. The full conjecture was shown later by former students of Wiles', in 2001 or so.
@whannabi Рік тому
@@lonestarr1490 That student is basically in Wile's shadow then because you don't even seem to remember their name.
@saravananjeeva5258 Рік тому
@@whannabi at keast the guy narating the video said his full name , so we can search him up
@ricobarth Рік тому
@@whannabi Which is fair, since Wiles is the one who proved the most famous unsolved problem in mathematics.
@magicmulder Рік тому
@@ricobarth Along with Taylor who closed the gaps in Wiles’ proof.
@handsini1281 Рік тому
This is a stunning piece of math. It almost feels like art, it's so poetic.
@bidyo1365 Рік тому
What a beautiful profile picture you have...
@handsini1281 Рік тому
@@bidyo1365 thanks 😊
@awesomedata8973 Рік тому
Fitting for the trash bin of modern day egos, sadly enough. :/
@handsini1281 Рік тому
@@awesomedata8973 who shit in your coffee
@hyperduality2838 Рік тому
Elliptic curves are dual to modular forms. Duality creates reality!
@swd127 Рік тому
I am a professor of applied mathematics. I have been trying to understand the basics behind the proof of Fermat's Last Theorem and this is the first explanation I have seen that makes sense to me. Kudos to Alex and the creators of this video. The graphics is amazing as well.
@evm6177 Рік тому
🍷👍
@fatmilf1498 9 місяців тому
How are you a professor and not know this
@user-ld6dz2pm4l 8 місяців тому
He said he is a professor of applied math. Math is currently so varied that no one can learn many branches of math at the same time. The last universalist was Henri Poincare.@@fatmilf1498
@epicmarschmallow5049 7 місяців тому
@@fatmilf1498Because maths is a huge subject and a specialist in one branch doesn't necessarily know much about another advanced field. Especially because Fermat's Last Theorem, and the maths behind the proof (modular forms, elliptic curves and other bits) don't fall under "applied mathematics"
@matheusrossetto5091 Рік тому
This is a truly beautiful video, from the design to the script, everything is on point and the overall product looks amazing, thank you for inspiring while informing.
@ReynaSingh Рік тому
The hidden beauty of math never fails to astound me. This video was great. Keep it up
@paulcoy5201 Рік тому
Just what is so beautiful about math?
@sauravgupta4639 Рік тому
@@paulcoy5201 it's intangible
@Soken50 Рік тому
@@paulcoy5201 That by just fiddling with numbers you can probe the universe and discover fundamental truths of its inner workings and underlying laws, plus if it weren't for algebra, geometry, calculus and all that, you wouldn't have all the fancy tools and knowledge that make today's society possible, you might not even have cohesive agrarian societies since you'd be too busy fighting your neighbour over the alleged size of their plot. Also humans generally find beauty in order emerging out of chaos and finding patterns in seemingly random collections of information, solving puzzles. There is no shortage of beautiful, fun and/or useful things to find in math
@SamSam-yx4xq Рік тому
It helps us quantify and understand our beautiful world, of course.
@greg77389 Рік тому
God's work reveals itself in many forms...
@Burubrikoos Рік тому
Quanta, you've done it again. Stunning visuals, engaging and vivid explanations, and an overarching scope to the it all up. I love what you all breng out to into the world, thanks so much!
@1.4142 Рік тому
Quanta is creating a bridge between cutting edge math and the public. We need more of these.
@l.w.paradis2108 Рік тому
This! 💖
@KM-co5mx Рік тому
Exactly 👍 & Hilarious 🤣
@brondarch2450 Рік тому
What a consummately excellent video. The premise, art, geographic analogy, and insight. Thank you and keep it up!!
@easports2618 Рік тому
I am amazed by how much I missed in schools I never bothered with maths I always thought it was just boring but now that I’ve seen all this I truly appreciate maths and it’s beauty
@akashchoudhary8162 Рік тому
Almost none of this is taught in schools unless you take Maths at undergraduate level or higher. So you didn't technically miss it.
@easports2618 Рік тому
@@akashchoudhary8162 no,that is not what I meant what I meant was that I missed the beauty of maths because always we were thought to solve only in a particular way and the teachers would get visibly annoyed if I asked them a doubt
@kp5343 Рік тому
@@easports2618 you didn't miss it. It didn't even pass close to you
@_orangutan Рік тому
@@akashchoudhary8162 that’s the problem though, schools don’t teach to think in math only to apply it right away. To some scenarios I don’t understand. We must teach the what, why, and how numbers function instead of memorizing formulas.
@JorgetePanete Рік тому
its*
@tehphoebus Рік тому
It bring me so much joy to know so many others care about math and science.
@pog9238 Рік тому
THIS IS SIMPLY ONE OF THE BESTEST VIDEOS I HAVE EVER SEEN IN MY LIFE. THIS CHANGED MY ADDED TO MY PERSPECTIVE TOWARDS MATHS, THIS MADE MATHS SO MUCH MORE AMAZING TO ME. THANK YOU SO MUCH
@HypernovaBolts11 Рік тому
Thank you! This perfectly illustrates the beauty I've been seeing in my head for years but so often struggle to convey to my friends!
@AndresFirte Рік тому
Wow, I can't imagine how much work, effort and time was put into making this video. Both the animation and script are perfect!
@anonymoose3423 Рік тому
Amazing work, and special compliments to the animation team. It should be noted that this is only an explanation of the arithmetic Langlands Correspondence for so-called global number fields (such as the field of rational numbers Q); in fact, Fermat's Last Theorem which Wiles proved (or rather, the Modularity Theorem which implies it) is a special case of this version of the Langlands Correspondence (for what is known as the reductive group GL(2) of invertible 2x2 matrices). There are various analogues of the Correspondence, such as the Langlands Correspondence for global function fields, the local Langlands Correspondences, and the geometric and quantum Langlands Correspondences, and each can be viewed as a toy model that might help us probe the original arithmetic correspondence, which hopefully will help us understand things like the zeta functions and distributions of primes. There are also many other parallel systems of results and conjectures, such as Langlands Functoriality and Duality, which are too complicated for a UKposts comment, but are arguably even more important than the Langlands Correspondence itself. In fact, the Langlands Correspondence and Langlands Duality should be viewed as two big important lemmas that supports the conjecturally unifying result that is Langlands Functoriality.
@minecrafting_il Рік тому
Hmmm yes this is math talk
@plplplplplpl7336 Рік тому
That sure is a lot bigbwords
@gumikebbap 11 місяців тому
well noted mr. wizard sir
@oroka2984 4 місяці тому
Fascinating! Albeit I do not have the knowledge of any of those complicated subjects, I still sit through all 13 minutes to watch this!
@kgangadhar5389 Рік тому
I have no words to say how great these videos are, I watched this in June and was hardly able to understand, and after 3 months of checking a lot of number theory and modular functions videos, I am able to understand a little more now, I will come back again once I learn some more.
@latefoolstalk676 Рік тому
As a math student videos like this motivates me to keep on studying and research about grand topics like the Langlands Pogram. You are a really great channel for math begginers.
@user-pj5ez1wz3j Рік тому
Thank you for your effort. I've been curious about the proof of Fermat's last theorem for a long time. You makes it easy to be understood by normal people. Thank you!!
@RECTmetal Рік тому
I'm not a math guy, but this video was excellent. Beautiful visuals, great explanation, and captivating flow. Wonderful job!
@stanzigo Рік тому
What an excellent video!. I've wanted to understand the basics of the Fermat proof for years, but this is the first explanation that makes sense.
@ahlamamr4659 Рік тому
I love this video it’s a masterpiece even tho I don’t really understand what’s going on . I am still at the beginning of my journey in mathematics but I think it’s really exciting to connect everything together and the illustration is amazing.
@LucasPreti Рік тому
I’ve see some people on UKposts trying really hard to explain taniyama-shimura and why it’s related to Fermats last theorem, but you just went there and did it. Bravo
@ryangross6886 10 місяців тому
This video makes my heart race. The idea that seemingly separate areas of mathematics are intimately connected is so tantalizing that it makes me smile.
@georhodiumgeo9827 Рік тому
This is by far the BEST video on Fermat's last theorem. Thank you!
@ophello Рік тому
I can’t believe how good this is! Please make more overviews of giant math concepts. I would love an intuitive explanation of the sporadic finite groups, and the monster group / monstrous moonshine theory and how it relates to Lie algebra and the E8 manifold.
@ingolifs Рік тому
I would like to see this too, with plenty of explanation of the intermediate steps. All too often I see " Group theory is the study of symmetries. Here are all the ways you can rotate a triangle and it remains the same. Got that? Well onto the Monster Group..."
@hayekianman Рік тому
@@ingolifs now you can ask chatgpt and it wont be bored of providing as many intermediate steps you would like. everyone has their own personal tutor now
@epicmarschmallow5049 7 місяців тому
@@hayekianman in my experience chatgpt is terrible at maths
@Juttutin Рік тому
Truly awesome video. And such a beautiful and simple explanation of how Fermat's got proved as well!
@ytrichardsenior Рік тому
Thank you for explaining Wiles' proof of Fermat! It's by far the best explanation I've seen.
@MyAnttila Рік тому
Thank you for explaining it so clearly without oversimplifying! Great storytelling!
@trdi Рік тому
Excellent explanation. Never seen anything close to making this extremely complex proof being explained in a relatively accessible way.
@QuantaScienceChannel Рік тому
Dig deeper into the Langlands program at Quanta Magazine. You can explore all of our past coverage of developments in the Langlands program here: www.quantamagazine.org/tag/langlands-program/
@masternobody1896 Рік тому
gigachad math like this
@lordjellyfish4745 7 місяців тому
Honestly I did not expect such high quality in all aspects, cought me off guard. The way how all aspects of communitcation work together is facinating. The audio, the grafics, the writing and last but not least; the explaining. It all works so harmonicly together
@marco.nascimento Рік тому
Beautiful. This video is a work of art. The visuals add such a charm to the explanation, truly mesmerizing how well they help illustrate this complex subject.
@jonashallgren4446 Рік тому
Amazing video, I loved the visuals and very nicely explained!
@moustaffanasaj1584 Рік тому
I remember Andrew Wiles explaining in an interview how he solved Fermat's Last Theorem. Obviously he didn't go into detail, but it was all very abstract, and one of the things that stuck with me was him saying that if he could solve Taniyama-Shimura, he would get Fermat for free. I've been wondering how that would technically work, and I'm happy I've stumbled across this video that explains it so well!
@tonedeaftachankagaming457 Рік тому
Loved the analogy, really helps show the sort of "fields" there are within math and this intriguing relationship!
@Biersoful Рік тому
The visuals in this video are so amazing, congrats to the team who created this!
@ElOroDelTigre Рік тому
This is a beautiful presentation, explained in a simple manner. Whoever made the script and the animation needs to get recognized a lot.
@evm6177 Рік тому
🍷👍
@eduardotenorio-lopez3679 Рік тому
The almost miraculous achievement this channel and Alex make by explaining incredibly complex concepts simply enough to intellectually engage both neophytes and seasoned individuals . Whilst also creating a curiosity which is priceless. Bravo 👏. Thank you 🙏
@SolaceAndBane 10 місяців тому
Incredible visual representation and art in this video and it demonstrates such a deep understanding to be able to convey these concepts so well.
@paulconway5693 Рік тому
This is an absolutely wonderful explanation of the connection between these two once disparate fields of math
@TheMornom Рік тому
I loved the video, it was very well explained! Good job. I found a small typo: at 11:40 one should read y^2 = x(x- a^p)(x + b^p) for the Frey's elliptic curve.
@badhbhchadh Рік тому
Yeah lol, noticed the powers move down there too
@john38825 Рік тому
That was great, i would love to see more modern math problems explained historically and simply lile this.
@dpie4859 Рік тому
I absolutely adore this video. Interesting topic, unbelievable beautiful animation and great narration. Please do more videos like this!
@jamesheller2707 Рік тому
Artwork and storytelling are amazing men keep it up, you guys are gonna hit a million soon
@zubrz Рік тому
cool animations! do you plan to cover "L-functions, motives, trace formulas, Galois representations, class field theory", which you mention that you omitted?
@michaliskokkinos9740 Рік тому
Great video, thank you! Until now I was aware that langland's program relates number theory with representation theory and that Ramanujan was a Number Theorist. We live to learn every day !
@satyam4336 Рік тому
I heard Alex's podcast with Grant Sanderson and I really admire him, and to find a video like this narrated by him is a treat.
@donsanderson Рік тому
Alex, that was a brilliant video. You knocked it out of the park with the one describing the Reimann Hypothesis, and yet somehow you may have even topped yourself here. Well done
@ashwanishahrawat4607 Рік тому
Videos like these should be collected to create a modern school to teach our next gen. There is a lot to understand and catchup very quickly as humanity progress, and these quick explanation and visualization really helps to get the basics and motivation for advance. Thank you and your whole team for the efforts.
@deast156 Рік тому
I loved this; it's a fascinating summary even for the math dunces like myself. I especially enjoyed it because it gives a follow-up to a particular favorite old bit of TV documentary I watched years ago: a PBS NOVA episode called "The Proof" about Andrew Wiles and Fermat's Last Theorem. It's actually quite touching. Highly recommended for anyone who enjoyed this (and can track it down).
@sanuvithanage Рік тому
❤💕💖
@neomorphicduck Рік тому
Great description of the connections! Love the video and explanation style!
@FinnReinhardt Рік тому
Amazing visualization and narration. Loved every bit of it!
@muthusid Рік тому
I would love to see videos on the contributions of Grothendieck. He seems to have been a world-historical genius, but I don’t really understand his contributions.
@yaoliu7034 Рік тому
Deligne, mentioned in this video, was a student of Grothendieck.
@vaibhavdimble9419 Рік тому
Basically he gave new struture that are abstraction of Algebraic and geometric structure. His genius was unparalleled as he broke all the ancient laws of mathematics and create way of thinking that have more çomplex ways of navigation and intuition. He created mathematical tower heigh above the contents to see mathematics far about normal range.
@rv706 Рік тому
Mathematicians are still grappling with his work. Unfortunately, it would be a bit difficult to convey the spirit of his contributions to a lay audience, because his style of thinking was extremely abstract. He always looked for the "right level of abstraction" in which to see a problem, and it turns out that that level is often pretty high. For example, who would've thought that the right way to understand shapes defined by polynomials involves category theory?
@yash1152 Рік тому
whats the connection between abstration in maths, and abstraction in computer science?
@TBOTSS Рік тому
@@rv706 Excellect but I think ""the next level of deeper abstraction" might convey be a bettter approximation of his work. Michael.
@alanrodriguez7988 Рік тому
This made me cry! Math is just so beautiful, almost poetic❤
@shukrantpatil Рік тому
it makes me cry as well , but mostly when its related to physics and astro physics .
@tmquangvn Рік тому
Very sastified with your explaination and visualization for such a complex problem in maths. Thanks so much!
@tfexx Рік тому
What an insanely cool video. Excellent delivery and explanation with amazing visuals to support it.
@dantev2209 Рік тому
Srinivasa Ramanujan is a fucking baller. Dude's almost entirely self-taught and made so many advancements to mathematics in his short life. Whichever y'all know, put them in the comments. I would love to know what you guys think of this man.
@awwabientg4845 Рік тому
You indian?
@evm6177 Рік тому
🍷👍
@sankalp2520 Рік тому
Fr. It seems that Ramanujan was addicted to infinite series and prime numbers. I love his work on infinite series for π that converge incredibly fast and are still used today to calculate π digits up to trillion decimal places. Surprisingly, most of his works lacked proofs, only conjectures, like how tf did he arrive at those complicated results?
@l.w.paradis2108 Рік тому
@@sankalp2520 Yeah, this is beyond amazing. Savants with no disabilities, just abilities.
@amogus7316 Рік тому
@@awwabientg4845 I don't think so looking at his profile
@dprophecyguy Рік тому
I wish if such quality of videos can be made for our fundamental curriculum. Say for class 1 to 10th. This problem needs to be solved only once and then the whole world can make use of it. No need for fancy tech startups or any thing. These kind of beautifully drawn and curiously narrated videos can do wonders for children learning new things.
@teratoidmaple0987 Рік тому
The visual, voiceover and music are really amazing... I learned something new as well!
@MsThekiller02 Рік тому
I still fondly remember when I first studied number theory and modular arithmetics at university, really opens a new perspective on numbers and mathematics in general
@vviggyy1236 Рік тому
Quanta Mag's videos simply do not miss. They're so unparalleled in their ability to explain complex topics in such a friendly, engaging way!!
@Artsmitica Рік тому
An absolute gem of a video, from math content to explanation, from artistic graphics to rhythm. Pure awe !
@ChocolateMilkCultLeader Рік тому
I have no idea how you managed to summarize this so well. Shared with all my audience in my newsletter and Articles
@kenmacallister Рік тому
Wow- that was beautiful. So we’ll done. The writing, the research, the animation and artwork. The background music. Just brilliant. If there was a standing ovation emoji, I would post it here. 🔥
@pladselsker8340 Рік тому
There are so many talented people out there creating incredible visuals and narratives that sometimes, I fail to see how insanely good their work is. I think this video is amazing. I don't think I understood the whole point it's trying to make, but the visual support helped a lot. Thank you for your work.
@williamdarko1142 Рік тому
One thing I always found so cool was how *Andrew Wiles'* work built on top of *André Weil's* work lol... coincidence, I think not
@rv706 Рік тому
Not a coincidence. Weil (and, later, that giant of modern mathematics that was Alexander Grothendieck) worked on the foundations of algebraic geometry and extended it so vastly that number theory itself could be expressed in geometric terms. This is called arithmetic geometry. That's where "elliptic curves over the rationals", the main theme of the Fermat-Wiles theorem, live.
@williamdarko1142 Рік тому
@@rv706 yeah I’m aware of that. My comment was more of a joke on how similar their names are
@rv706 Рік тому
@@williamdarko1142: Oh I see! Well, guess what, I was also about to write "Fermat-Weil" in my comment and then I corrected myself :D
@TranscendentBen Рік тому
I've been learning all this informally in recent years. When I first saw the name Andre' Weil, I thought "wait, that's NOT the guy who proved Fermat's Last Theorem, is it?" Indeed it's not, but maybe there's some (I say this semi-jokingly) Langlands Theorem of Mathematicians, tying together those who work in different-but-now-known-to-be-overlapping fields, maybe something like an Erdos Number.
@isidorregenfu9632 Рік тому
This is not a coincidence because nothing is ever a coincidence
@tadtastic Рік тому
the visuals are absolutely stunning. outstanding video!
@alvarodominguez2899 Рік тому
This is actually the best Mathematics video I've ever seen. Congrats!
@tretolien1195 Рік тому
Danm this was such a nice video that it almost made Weil's proof idea seem 'obvious'/intuitive, now I really need to see his proof of the Taniyama-Shimura conjecture!
@theflaggeddragon9472 Рік тому
Check out Anthony Vasaturo's YT channel where he is uploading videos daily on Wiles' proof.
@wayneqwele8847 Рік тому
This is an absolutely stunning video, well done to the team that made it!
@marcusklaas4088 Рік тому
This is a seriously impressive piece of math exposition and explanation. Bravo!
@avb20540 10 місяців тому
One of the best UKposts videos I have ever seen. Please make more of these
@neonsilver1936 Рік тому
This single video got me more excited about Mathematics than any other I've ever watched. Well done!
@debadityasaha1684 Рік тому
Maths is the most beautiful subject.
@lordvipul Рік тому
What a great video! The narration, the visuals, the music, all top notch.
@Olegan903 Рік тому
Simply the best math videos, this one and the other on Riemann Hypothesis. The content is very clear and entertaining. Music, animation, narration, creativity, everything is just amazing. Your videos help understand math, not just use formulas.
@NithinThomas Рік тому
We need this type of storytelling in our schools!
@uzulim9234 Рік тому
Quite pleasantly surprised that this highly abstract program is getting a quality visual exposition. We do'nt often see this.
@thecomputer5515 Рік тому
Is English your native tongue?
@timothebillod-morel2620 Рік тому
That is one of the most incredible video I have ever watched about the story of the proof of Fermat’s last theorem. 13minutes, and there is so much inside of it. Incredible work, of vulgarisation, animation, congratulations to the author !
@varungupta9020 Рік тому
can we talk about the music in this video?? like at the beginning the shift in feeling from number theory to harmonic analysis is SUCH a good touch
@diegorodriguezv Рік тому
My admiration and respect to the graphic designer behind these unbelievable animations. The combination of creativity and thorough technical knowledge blend harmoniously in the representation of such intangible concepts. Total mastery of art and craft.
@sostotenonsosjojododahohlo4580 Рік тому
I study mathematics and this video gave a great explanation to the Wiles proof of Fermat’s last theorem. I love the visuals also, got me inspired to study more and to explore the vast landscape of mathematics :)
@Karmush21 Рік тому
Beautiful done video. Thank you, Quanta!
@5alpha23 Рік тому
When you finally revealed to proof of Ferma's Last Theorem, I got goosebumps all over my body. This is pure beauty.
@lukaskrause6022 Рік тому
Good video, one small thing, portraying the bridge between Fermat’s last theorem and elliptic curves as something Wiles just dreamed up is unfair and inaccurate. Some earlier mathematicians established a proof that proving a special conjecture would prove Fermat’s last theorem, and it was Wiles who proved that conjecture. Edit: I know this was touched on later in the vid. I wish it was not painted the way it was at the beginning. Also, it is not just the connection with elliptic curves but the Taniyama Shimura conjecture which gets painted over
@paraconsistent Рік тому
They literally say all of that in the video.
@tinkeringtim7999 Рік тому
Are you trying to tell us you didn't watch the video, or that you don't understand the content?
@lukaskrause6022 Рік тому
@@tinkeringtim7999 I did watch the video, & while I think they did clarify the connection between elliptic curves and Riemman wasn’t wiles, I wish they’d spent more time discussing the mathematicians who made the connection with the later conjectures. However I made this comment halfway through the video, & earlier in the video they had painted it as if Wiles himself came up with the conjecture
@evan Рік тому
This makes me miss studying math so much… but damn was I rough at number theory 😅
@l.w.paradis2108 Рік тому
I just picked up Smullyan again. If you are more of an algebra/logic type, you would love him. Just found out the set of all finite subsets of _N_ is countable and figured out two proofs over the weekend. So it has to be the set of all infinite subsets of _N_ that is not. You can tell I'm such an amateur, but hey. FUN STUFF.
@lakshya5946 Рік тому
THIS IS THE BEST VIDEO I'VE WATCHED FOR EXPLANATION + STORYTIME MATHS
@indylawi5021 Рік тому
Thank you for putting together this very illuminating video on such complex topics in math. Simply amazing and beautiful.
@allenhonaker4107 Рік тому
It never ceases to amaze me how many unknown scientists send ground breaking ideas to the giants of their field change the face of science.
@DirtyDan-qk5bu Рік тому
I'm normally pretty averse to mathematical topics in favor of harder physics and biology, but this is super interesting and relatively easy to understand! I would love if there was a series about more "continents" or something similar about this "World of Mathematics"
@ricardoludwig4787 Рік тому
I don't know enough math to fully appreciate it but what I can gather is still amazing, and the presentation helped so much with it
@ValentinLievin Рік тому
Super well made, truly inspiring!
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