Quanta Magazine
Quanta MagazineMathematicians recently proved a central component of the Langlands program, an ambitious effort to develop a “grand unified theory” of mathematics. The monumental proof of the geometric Langlands conjecture totaled more than 800 pages and marked the culmination of 30 years of work by nine mathematicians.
Watch Quanta’s video explainer about the full Langlands program here: https://www.youtube.com/watch?v=_bJeKUosqoY
Read the companion Quanta Magazine article:
PAPER
– D. Gaitsgory, S. Raskin D. Arinkin, D. Beraldo, J. Campbell, L. Chen, J. Faergeman, D. Gaitsgory, K. Lin, S. Raskin and N. Rozenblyum (2024) “Proof of the geometric Langlands conjecture” – https://people.mpim-bonn.mpg.de/gaitsgde/GLC/
CORRECTION 02/24/25: In the end credits, “Qaunta Math Writer” is misspelled. It should have been “Quanta Math Writer.” (Thanks to Milton Lee for catching that)
00:00 Introduction
01:01 What is the Langlands Programs?
01:35 Fourier theory and analysis
02:23 Fourier transform, building blocks and labels
04:37 Sheaves as building blocks
05:49 Geometric Langlands and eigensheaves
06:30 Gaitsgory and his fundamental diagram
07:01 Poincaré sheaf and the solution to conjecture
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Quanta Magazine is an editorially independent publication supported by the Simons Foundation: https://www.simonsfoundation.org
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32 Comments
@QuantaScienceChannel
03/16/2025 - 1:03 PMWatch Quanta’s video explainer about the full Langlands program here:
Read the companion Quanta Magazine article:
https://www.quantamagazine.org/monumental-proof-settles-geometric-langlands-conjecture-20240719/
@cdunne1620
03/16/2025 - 1:03 PMIf mathematics is infinite as he says at the end then it becomes a mindless game no? Is mathematics a crafting of broader and broader symbology, that’s disappointing if true. I thought the truths would be resilient
@hindigente
03/16/2025 - 1:03 PMThe script and editing of these videos is outstanding, but the "pop documentary" cadence of the narration is kind of jarring,
@elijaht5188
03/16/2025 - 1:03 PMThe title seems to be a large exaggeration. If you're not understanding thats probably because this video is more fluff than substance
@Atom15
03/16/2025 - 1:03 PMThanks for the Simons Foundation to making Quanta possible. This is amazing!
@hoo_maan8735
03/16/2025 - 1:03 PMLOL DOUBT IT IF ITS 800 PAGES 😅 just more people talking about non real bs
@matthewleitch1
03/16/2025 - 1:03 PMWill this be useful to anyone and, if so, how so? (Useful, not just interesting, and not just useful to someone else building abstractions.)
@Sailormoonoceanlight
03/16/2025 - 1:03 PMOk but is it too late? A quantum theory is unified in qbits re: quantum computing where the problem and solution are the inverse of each other. Re: unified theory: Do you have all of the necessary parts to make the whole? (Ie why six compartments when there are nine recognized Solfeggio frequencies?) Just a thought…but you shouldn’t have to struggle to unify a theory (esp if you haven’t found all of the parts yet?)
@aidandavis5550
03/16/2025 - 1:03 PMThis video is a great example of how not everything can be communicated well to people without a sufficient background.
@jwplatt9233
03/16/2025 - 1:03 PMYou can't really know it's "one step closer" without knowing the real destination.
@ruudh.g.vantol4306
03/16/2025 - 1:03 PMNever lose sight of the gap between reality and any modeling of it. Make your language express that you are aware of that gap. You can count apples, but no two apples are identical.
@yuefenggao7483
03/16/2025 - 1:03 PMFrom 04:37, I understand every word you and the mathematicians said, but I lost for every sentence when the words conbined.
@rapidfire8223
03/16/2025 - 1:03 PMFascinatingly informative, yet as clear as… mud
@akirakato1293
03/16/2025 - 1:03 PMisn't your explanation for Fourier transform insufficient since you make no mention of the amplitude associated with each frequency being a critical variable in the reconstruction of the original signal
@cantoon8616
03/16/2025 - 1:03 PMWait, what? Number theory derives from geometry; indeed, ALL math derives from geometry. How is this some "breakthrough"? Did something happen to higher education in the last 40 years? Did everyone just become extra dumb or forget the basics?
Sadly, my gut instinct is that the Marxist takeover of academia put a lot of soft-headed people in charge of education. The drug addled hippies of the free love movement are still clogging up academic posts.
@djtomoy
03/16/2025 - 1:03 PMmaths is hot right now
@lolmanthecat
03/16/2025 - 1:03 PMFinally some cool math facts!!!
The explanation was so nice too!
@importantname
03/16/2025 - 1:03 PMSounds simple enough?
@santhoshshivan1452
03/16/2025 - 1:03 PMSpent 8:47 mins to learn nothing about the topic. Useless video
@RawLu.
03/16/2025 - 1:03 PMThe United States of Fascist 👿
@ParticlePulse
03/16/2025 - 1:03 PMThere is no use in making a grand unified theory in mathematics at the moment.
We lack so many concepts that are at the basis of our foundation of mathematics such as Prime numbers, 3X+1 and many more
What is the use of a grand unified theory that is BOUND to be updated in a while?
@kwanarchive
03/16/2025 - 1:03 PMI invented an efficient signal processing algorithm to calculate changes between two files of Japanese text.
Fast and Fouriers: Tokyo Diff.
@CC1.unposted
03/16/2025 - 1:03 PMI thought AI Feynman Algorithm was slow and ineffecint But now I think it's a universal Rule, you just showed someone doing it manually
@gorkemvids4839
03/16/2025 - 1:03 PMDont take your audience as dumb and actualy explain the thing.
@markwrede8878
03/16/2025 - 1:03 PMBecause Godel believed in god, he described Arithmetic as Incomplete. Because the requirements for membership are polar opposites between Multiplication, which requires uniformity, and Addition, which requires nothing, Arithmetic is better characterized as Inconsistent. This manifests in the notion of Infinity, where Multiplication imposes a functional capacity that generates infinite results at values far smaller than those infinite values available to Addition.
@eliotspencer9874
03/16/2025 - 1:03 PMA key thing to mention is that the relation to physics is based on supersymmetric theories only and right now this theory is basically not part of reality. I was excited to learn this subject until I realized that 😅
@drover7476
03/16/2025 - 1:03 PMI swear I've seen all this Fourier content before
@EconAtheist
03/16/2025 - 1:03 PMBröther may I have an eigenlööp
@StP-g8f
03/16/2025 - 1:03 PMGet out of here with this "Grand Unified Theory" nonsense.
@rhysmeyers9396
03/16/2025 - 1:03 PMWhen you give analogies to those abstractions you lose all hope of understanding anything.
@ArgumentumAdHominem
03/16/2025 - 1:03 PMYour channel is amazing! But you also have a bit of a strange focus. I struggle to identify who is the target audience of these videos. You go into huge detail about trivial concepts like fourier analysis and then 2 seconds later jump to crazy equations without defining any terms. It would be super helpful if you could decide on whether you want to be educational, scientific, or scientifically-popular channel.
1. If you choose to be educational, you need detailed videos, explaining all the necessary basics for the listener to begin to grasp the concept
2. If you choose to be scientific, then its ok to dive into complex topics directly, without spending any time on building blocks, as the target audience is already familiar with them
3. If you choose to be scientifically-popular, then presenting just the finding in abstract language is the key. No need for basic educational content, or for complex formulae
I would be happy, regardless what you choose. But, at the moment, it feels like a bit of a mismash, with 60% scientifically-popular, 30% educational and 10% scientific or sth.
@knight3481
03/16/2025 - 1:03 PMThis video should be explaining Galois representation and automorphic forms if it wants to say something about Langlands.