Behold a lecture by Fields medalist. What did we do right to deserve this.
@RalphDratman
3 жыл бұрын
He seems like such a kind person. That is why, I think, we did not need to do anything. He did that for us, for us.
@fcheung2888
2 жыл бұрын
covid made him do it lol
@richieforum2894
7 ай бұрын
He is the hero we need but not the one we deserve.
@carlostrujillo1109
3 жыл бұрын
Professor Borcherds, I took your Galois Theory class back in the early 2000s. This video is a real treat and very nostalgic. Thank you for posting this. I look forward to watching all of these over the coming months. Take care.
@kewalmohapatra8340
2 жыл бұрын
What do you do now?
@ViceroyoftheDiptera
2 жыл бұрын
@@kewalmohapatra8340 prostitution
@rbr1170
3 жыл бұрын
My formal and first introduction to any type of mathematics gave me the impression that it was boring and just plain uninteresting. I now believe that most people who either don't like or hate math do so only because their first encounter was bad. My teachers, unintentionally, presented mathematics as the simplest function of memorization of disjointed concepts and solving problems by following instruction (some of my teachers will not even accept a solution that was outside of their instruction) instead of logic. I wish I had more access to people like you. I am now turning 31 and has just started my journey to learning true mathematics. Keep the great contents coming!
@lawrencema9120
3 жыл бұрын
Wow, we have Richard Borcherds giving a lecture on Galois theory. Borcherds is one of the top mathematicians in the world having won the Fields Medal (arguably the highest honors for a mathematician) in 1998.
@donaghcoffey2416
3 жыл бұрын
Bless you. Thank you immensely for going to the trouble of doing this series.
@henkvdpol
3 жыл бұрын
enjoying the historical facts in your lectures!
@user-jc2lz6jb2e
3 жыл бұрын
Damn it really is Christmas
@oskuh.9577
3 жыл бұрын
These online lectures are absolutely great for a beginner like me. Especially the group theory series!
@sidkulkarni5599
3 жыл бұрын
I love these intro videos, it's like a buffet of vastly interesting topics. I look forward to deepening my understanding of Galois theory, particularly gaining an intuitive understanding of _why_ the ability to decompose the Galois group into abelian groups means that the polynomial in question is solvable in radicals.
@joana8502
3 жыл бұрын
search for lagrange resolvents, you probably won't hear about them from formal mathematicians, as they usually despise computation.
@Sharpgamingvideos
3 жыл бұрын
Woohoo! Just started looking into this topic these past few weeks after my fall semester first course in algebra. What great timing
@Viewpoint314
3 жыл бұрын
I just discovered your channel. It has just enough simplicity and complexity to satisfy people who have studied about 4 years of mathematics and are thirsting to really understand the interesting parts of mathematics.
@MatheusDeLimaDilima
3 жыл бұрын
Hello, I'm from Brazil and I'm glad you could make it. This class is so clear, it was really a joy to watch. Keep up the good work, cheers! And thank you for the class.
@lilylikesmarkies
3 жыл бұрын
Very much looking forward to the rest of this series. I wasn't aware of the connections to algebraic topology and fundamental groups, sounds like a very interesting direction to explore.
@theflaggeddragon9472
3 жыл бұрын
It certainly is, if you have some experience with covering spaces, Galois theory, a bit of commutative algebra, and you're willing to learn something about schemes, the book Galois Groups and Fundamental Groups by Szamuely Tamas explores this beautiful area. A key work is "etale fundamental group".
@lilylikesmarkies
3 жыл бұрын
@@theflaggeddragon9472 Thanks very much for the recommendation. I'll need to revise some concepts but I'll check it out.
@tiop52
3 жыл бұрын
@@theflaggeddragon9472 Szamuely paired with Lenstra's wonderful notes "Galois Theory for Schemes" is a very nice intro to this area!
@ben1996123
3 жыл бұрын
the product at 16:55 is missing a 24th power, should be q product (1-q^n)^24
@swaruppaul4417
3 жыл бұрын
Thank you so much professor for starting this course. I am awestruck by this lecture. Eagerly waiting for the next lecture.!!!
@sergioestan8371
2 жыл бұрын
Absolutely amazing introductory video. I am more inclined towards analysis, yet this video has made me want to study Galois theory and algebra in general in greater depth. Btw really cool historical notes on the side
@zapazap
3 жыл бұрын
Thank you very much for priming my intuition -- and thus my motivation -- for this topic.
@atifzaheer2671
3 жыл бұрын
The most awaited course.
@moonlightcocktail
3 жыл бұрын
Thank you so much for this course.
@jordimartinez4295
Жыл бұрын
These lectures are such a treat. I don't remember much of the mathematics I studied over 20 years ago and I am looking forward to watching the whole series. Thanks very much for posting them and sharing your knowledge with the rest of the world, this is very generous of you. I have noticed you haven't posted videos for a long time. Are you going to create more content?
@sachalucienmoserferreira2233
3 жыл бұрын
Nice to find your channel on yt,its a great pleasure to be see a lecture from a field medallist. Hugs from Brazil,keep going on your videos for sheare with us a bit of your knowledgment.
@user-sm8bc4oi1k
2 жыл бұрын
"Galois managed to die in..." I love how this is phrased
@JethroDjan
3 жыл бұрын
this is gold! Is this how it feels to be taught my a field's medalist?
@KripkeSaul
Жыл бұрын
Thank you for putting these online. I wish others would follow your example!
@Planckwu
3 жыл бұрын
What a good man you are,thank you for your sharing
@joshzeitlin3069
3 жыл бұрын
This is a fantastic channel -- really helped me out, thanks!
@ImPresSiveXD
3 жыл бұрын
thank you for this course!
@atomiccompiler9495
3 жыл бұрын
Thank you very much!
@RalphDratman
3 жыл бұрын
This is marvelous
@CubicPostcode
3 жыл бұрын
Extremely useful. Very clear and well done. Many thanks.
@ja524309
3 жыл бұрын
It would be nice if you ever come back around to give some lectures on actually computing Galois groups
@stevenwilson5556
2 жыл бұрын
Really great lecture! I did not study quite a few of the topics in this video as my undergrad degree in math focused more on stats and probability than group theory and algebra. But I really like seeing areas I never studied explained in relatively clear terms.
@davidpitkanen4237
3 жыл бұрын
Thank you for the video.
@mathismind
Жыл бұрын
This analogy is so cool! Grothendieck indeed was flying wery high in the sky...
3 жыл бұрын
from Morocco...thank you a lot mr professor Brocherds....the Galois theory fascinate and hypnotise me....i still not understand its basis ideas....i feel a while understanding but realize soon NOt....thank you....i subscribe to your chanel
@argonwheatbelly637
3 жыл бұрын
Lovely, this. Thank you!
@Suav58
3 жыл бұрын
7:14 In case like this one Gromov mentions "5 year old Cro-Mangnon" as an imaginary paragon of fresh mind not spoiled by upbringing and education. The point seems to be, that we start to teach mathematics both too late and not quite in the right way. My personal experience is, that quite tricky concepts are digested with more ease and comfort by 10 year olds, than 17 year olds. We acquire some rigidity and this skeleton guiding further thought might be inadequate.
@annaclarafenyo8185
3 жыл бұрын
This is the opposite of the truth, it's much easier to understand this stuff when you are old, if you are trained. What's easier when you are young is to have a crazy new idea.
@Suav58
3 жыл бұрын
@@annaclarafenyo8185 That's not a cricket. As far as I remember myself as a young person (I'm 63), I always had a storm of crazy ideas, most of them wrong, of course, but in a torrent fast enough, to pick the right one at last. To have any relevant ideas at all one has to be current with the state of knowledge in the area. Galois got where he did following work of Lagrange, whose works he read at the age of 15. Not teaching young people early enough about the current state of mathematics is the problem here. (I remember, for instance, listening to Mozart and trying to guess his next move, but you do have to listen to some scope of music beforehand)
@digxx
2 жыл бұрын
Anyone care explaining how you systematically arrive at order 20 for the Galois Group of x^5-2 ? So you have 5!=120 permutations in total and 20=5!/3!, so by observation I would assume that from all permutations, there is a subgroup of permutations that violate the algebraic relations. But for instance a1*a3=a2^2 may allow the permutation 13, but it would violate the relation a3*a4=a1^2. So how would you approach this in practise? For these types of algebraic relations we have in general a_m*a_n=a_k*a_l iff m+n=k+l mod 5. But there are probably many other relations, or?
@lucianonotarfrancesco4443
3 жыл бұрын
I’m enjoying very much your lectures, thank you. I wonder if at some point you could talk about Galois rings… I found no results on KZitem for Galois rings, they are usually not mentioned in undergraduate courses either, and they are very beautiful and have many interesting applications
@sidharthdembi4400
Жыл бұрын
Sir, Your lectures are amazing. I especially like the focus on concepts rather than detailed proofs. Thank you so much. Can you suggest any book/books which gives the big picture of abstract algebra concepts like in your lectures, especially the first one.
@qbqbqdbq
3 жыл бұрын
this is excellent
@ahmadrezakhazaie6305
3 жыл бұрын
Does anybody know similar video lectures on Geometry and Topology?
@power9k470
3 жыл бұрын
Tadashi lectures
@bennoarchimboldi6245
5 ай бұрын
@@power9k470garbage
@timjosling9298
Жыл бұрын
It would help if you defined what you mean by "symmetry" in this context. An example does not suffice. My guess is that it means a mapping of the *field* (not the vector space?) to itself that preserves certain unspecified operations? In th example you say it preserves some things but not others - I have no idea which ones matter for your secret definition of a symmetry.
@shunansun899
3 жыл бұрын
Thank you.
@walterrudin35
8 ай бұрын
Classic as usual...
@dr.rahulgupta7573
3 жыл бұрын
Excellent presentation Sir .Thanks . Sir which book is proper for this topic? Rahul.Rohtak Haryana India
@imranq9241
2 жыл бұрын
Thank you for the lecture! Are there assignments we could do based on these lectures ?
@1.4142
Жыл бұрын
22:30 The helix switches directions
@rbr1170
3 жыл бұрын
I am on the same level as this man only in terms of how bad our penmanship seem to be. Mine might be worse than his but I don't like to brag. I mean his is still readable. But damn great lecture. Subscribed! Thanks for this!
@WayneWhitaker314159
3 жыл бұрын
It's nice to see Gandalf has landed on KZitem ;)
@hyperduality2838
3 жыл бұрын
Galois groups are dual to modular forms. Modular forms are dual to elliptic curves. Complex conjugacy = De Morgan's laws. en.wikipedia.org/wiki/De_Morgan's_laws Union is dual to intersection. Disjunction is dual to conjunction. "Always two there are" -- Yoda.
@andylpz3
3 жыл бұрын
I never made the connection that Abelian was named after Abel
@christophersedlak1147
11 ай бұрын
thanks1!!!!!!!!!!!!!!!!!
@francescos7361
2 жыл бұрын
Thanks
@stephcandlish809
3 жыл бұрын
thx you helped a lot
@souravsadhukhan3077
2 жыл бұрын
Sir,I am beginner in msc .which book should I use for strengthening gallois theory ?
@josephmarshall2030
2 жыл бұрын
Thanks professor...you must have been freinds with henry jacobowitz and brieske.....
@JW-ss8es
3 жыл бұрын
How many lectures will this series have?
@djvalentedochp
3 жыл бұрын
yay group theory
@9437256274
3 жыл бұрын
Sir how you are recording your lecture
@richarde.borcherds7998
3 жыл бұрын
I'm using OBS studio.
@jessedevlin9489
2 жыл бұрын
The Mason could have just carved a circle and inscribed the liines into it to show its formation, A shameful Craftsman
@PunmasterSTP
Ай бұрын
Galois? More like "Great; heck yeah!" 👍
@enderwiggins8248
3 жыл бұрын
When the best mathematicians die from consumption and duels 😵
@hyperduality2838
3 жыл бұрын
Galois groups are dual to modular forms. Modular forms are dual to elliptic curves. Complex conjugacy = De Morgan's laws. en.wikipedia.org/wiki/De_Morgan's_laws Union is dual to intersection. Disjunction is dual to conjunction. "Always two there are" -- Yoda.
@brendawilliams8062
3 жыл бұрын
Thankyou I just see a 9. And a 9000480645. So it isn’t symmetrical
@XrcyhikUbhdfbjdf
6 күн бұрын
Taylor Dorothy Lopez Cynthia Lopez Mary
@newsgo1876
8 ай бұрын
Mathematics is a recursive subject in that you were introduced to a topic through some deep knowledge of that topic. Anonther intro with less pain: kzitem.info/news/bejne/pKpozK2foICYg44
@hyperduality2838
3 жыл бұрын
Galois groups are dual to modular forms. Modular forms are dual to elliptic curves. Complex conjugacy = De Morgan's laws. en.wikipedia.org/wiki/De_Morgan's_laws Union is dual to intersection. Disjunction is dual to conjunction. "Always two there are" -- Yoda.
@monkerud2108
2 жыл бұрын
Happens :D
@monkerud2108
2 жыл бұрын
When you realize letters are non commutative. Hehe
@migarsormrapophis2755
3 жыл бұрын
yeeeeeeee EEE
@baronvonbeandip
Жыл бұрын
All mathematicians upon hearing that Galois died in a duel over a woman: ☕
@ThefamousMrcroissant
2 ай бұрын
This is the saddest case of my mysophonia acting up I've come across so far. I can't listen to this man despite the obvious quality of the lectures. He keeps smacking into the microphone constantly...
Пікірлер: 96