![Dr. V](/img/default-banner.jpg)
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Dr. V
United States
Приєднався 8 лип 2012
Bringing everything from the most basic to the most advanced mathematics to the world without cost!
Fermat's Last Theorem, Exponent 3: A Better Proof!
Join my Modern Number Theory and Algebraic Geometry Discord: discord.gg/YQZgwZRmkX
Link to Fermat’s Last Theorem Playlist: ua-cam.com/play/PLK-gFjlmrFy7kbHJ7uOmawNTPz9Hea1vp.html
Email Inquiries: imtug7@gmail.com
My Website: sites.google.com/view/dranthonyvasaturo/about
Link to Fermat’s Last Theorem Playlist: ua-cam.com/play/PLK-gFjlmrFy7kbHJ7uOmawNTPz9Hea1vp.html
Email Inquiries: imtug7@gmail.com
My Website: sites.google.com/view/dranthonyvasaturo/about
Переглядів: 274
Відео
Fermat's Last Theorem: Supersingularity and Irreducibility! (13.5, 183)
Переглядів 235Місяць тому
Chapters 1-4 of My Fermat’s Last Theorem Notes Now Available on My Website! Link Below. Join my Modern Number Theory and Algebraic Geometry Discord: discord.gg/YQZgwZRmkX Link to Fermat’s Last Theorem Playlist: ua-cam.com/play/PLK-gFjlmrFy7kbHJ7uOmawNTPz9Hea1vp.html Email Inquiries: imtug7@gmail.com My Website: sites.google.com/view/dranthonyvasaturo/about trine.zoom.us/j/92316204163
Fermat's Last Theorem: Raynaud's Theorems! (13.4, 182)
Переглядів 110Місяць тому
Chapters 1-4 of My Fermat’s Last Theorem Notes Now Available on My Website! Link Below. Join my Modern Number Theory and Algebraic Geometry Discord: discord.gg/YQZgwZRmkX Link to Fermat’s Last Theorem Playlist: ua-cam.com/play/PLK-gFjlmrFy7kbHJ7uOmawNTPz9Hea1vp.html Email Inquiries: imtug7@gmail.com My Website: sites.google.com/view/dranthonyvasaturo/about
Fermat's Last Theorem: Elliptic Curves, Good Reduction, and Flatness! (13.3, 181)
Переглядів 202Місяць тому
Chapters 1-4 of My Fermat’s Last Theorem Notes Now Available on My Website! Link Below. Join my Modern Number Theory and Algebraic Geometry Discord: discord.gg/YQZgwZRmkX Link to Fermat’s Last Theorem Playlist: ua-cam.com/play/PLK-gFjlmrFy7kbHJ7uOmawNTPz9Hea1vp.html Email Inquiries: imtug7@gmail.com My Website: sites.google.com/view/dranthonyvasaturo/about
Fermat's Last Theorem: Elliptic Curves and the Need for Flatness! (13.2, 180)
Переглядів 5302 місяці тому
Chapters 1-4 of My Fermat’s Last Theorem Notes Now Available on My Website! Link Below. Join my Modern Number Theory and Algebraic Geometry Discord: discord.gg/YQZgwZRmkX Link to Fermat’s Last Theorem Playlist: ua-cam.com/play/PLK-gFjlmrFy7kbHJ7uOmawNTPz9Hea1vp.html Email Inquiries: imtug7@gmail.com My Website: sites.google.com/view/dranthonyvasaturo/about
Fermat's Last Theorem: Introduction to the Flat Deformation Functor! (13.1, 179)
Переглядів 1472 місяці тому
Chapters 1-4 of My Fermat’s Last Theorem Notes Now Available on My Website! Link Below. Join my Modern Number Theory and Algebraic Geometry Discord: discord.gg/YQZgwZRmkX Link to Fermat’s Last Theorem Playlist: ua-cam.com/play/PLK-gFjlmrFy7kbHJ7uOmawNTPz9Hea1vp.html Email Inquiries: imtug7@gmail.com My Website: sites.google.com/view/dranthonyvasaturo/about
Fermat's Last Theorem: FINISHING the Proof of R = T! (12.9, 178)
Переглядів 2333 місяці тому
Chapters 1-4 of My Fermat’s Last Theorem Notes Now Available on My Website! Link Below. Join my Modern Number Theory and Algebraic Geometry Discord: discord.gg/YQZgwZRmkX Link to Fermat’s Last Theorem Playlist: ua-cam.com/play/PLK-gFjlmrFy7kbHJ7uOmawNTPz9Hea1vp.html Email Inquiries: imtug7@gmail.com My Website: sites.google.com/view/dranthonyvasaturo/about
Fermat's Last Theorem: Finishing the Prep Work for R = T Minimal Case! (12.8, 177)
Переглядів 2613 місяці тому
Chapters 1-4 of My Fermat’s Last Theorem Notes Now Available on My Website! Link Below. Join my Modern Number Theory and Algebraic Geometry Discord: discord.gg/YQZgwZRmkX Link to Fermat’s Last Theorem Playlist: ua-cam.com/play/PLK-gFjlmrFy7kbHJ7uOmawNTPz9Hea1vp.html Email Inquiries: imtug7@gmail.com My Website: sites.google.com/view/dranthonyvasaturo/about
Fermat's Last Theorem: A Twist on an Old Theorem! (12.7, 176)
Переглядів 1574 місяці тому
Chapters 1-4 of My Fermat’s Last Theorem Notes Now Available on My Website! Link Below. Join my Modern Number Theory and Algebraic Geometry Discord: discord.gg/YQZgwZRmkX Link to Fermat’s Last Theorem Playlist: ua-cam.com/play/PLK-gFjlmrFy7kbHJ7uOmawNTPz9Hea1vp.html Email Inquiries: imtug7@gmail.com My Website: sites.google.com/view/dranthonyvasaturo/about
Fermat's Last Theorem: Eisenstein Ideals and Differentials! (175, 12.6)
Переглядів 934 місяці тому
Chapters 1-4 of My Fermat’s Last Theorem Notes Now Available on My Website! Link Below. Join my Modern Number Theory and Algebraic Geometry Discord: discord.gg/YQZgwZRmkX Link to Fermat’s Last Theorem Playlist: ua-cam.com/play/PLK-gFjlmrFy7kbHJ7uOmawNTPz9Hea1vp.html Email Inquiries: imtug7@gmail.com My Website: sites.google.com/view/dranthonyvasaturo/about
Fermat's Last Theorem: T_Q vs. T_Empty! (174, 12.5)
Переглядів 585 місяців тому
Chapters 1-4 of My Fermat’s Last Theorem Notes Now Available on My Website! Link Below. Join my Modern Number Theory and Algebraic Geometry Discord: discord.gg/YQZgwZRmkX Link to Fermat’s Last Theorem Playlist: ua-cam.com/play/PLK-gFjlmrFy7kbHJ7uOmawNTPz9Hea1vp.html Email Inquiries: imtug7@gmail.com My Website: sites.google.com/view/dranthonyvasaturo/about
Fermat's Last Theorem: The Magic Number r! (173, 12.4)
Переглядів 2945 місяців тому
Chapters 1-4 of My Fermat’s Last Theorem Notes Now Available on My Website! Link Below. Join my Modern Number Theory and Algebraic Geometry Discord: discord.gg/YQZgwZRmkX Link to Fermat’s Last Theorem Playlist: ua-cam.com/play/PLK-gFjlmrFy7kbHJ7uOmawNTPz9Hea1vp.html Email Inquiries: imtug7@gmail.com My Website: sites.google.com/view/dranthonyvasaturo/about
Fermat's Last Theorem: R_Q vs. R_Empty! (12.3, 172)
Переглядів 635 місяців тому
Chapters 1-4 of My Fermat’s Last Theorem Notes Now Available on My Website! Link Below. Join my Modern Number Theory and Algebraic Geometry Discord: discord.gg/YQZgwZRmkX Link to Fermat’s Last Theorem Playlist: ua-cam.com/play/PLK-gFjlmrFy7kbHJ7uOmawNTPz9Hea1vp.html Email Inquiries: imtug7@gmail.com My Website: sites.google.com/view/dranthonyvasaturo/about
Fermat's Last Theorem: How Big is R Sigma? (12.2, 171)
Переглядів 1016 місяців тому
Chapters 1-4 of My Fermat’s Last Theorem Notes Now Available on My Website! Link Below. Join my Modern Number Theory and Algebraic Geometry Discord: discord.gg/nmFg6BNvsg Link to Fermat’s Last Theorem Playlist: ua-cam.com/play/PLK-gFjlmrFy7kbHJ7uOmawNTPz9Hea1vp.html Email Inquiries: imtug7@gmail.com My Website: sites.google.com/view/dranthonyvasaturo/about
Fermat's Last Theorem: INTRO to the R = T Minimal Case: The Cohomology Product Formula! (12.1, 170)
Переглядів 606 місяців тому
Chapters 1-4 of My Fermat’s Last Theorem Notes Now Available on My Website! Link Below. Join my Modern Number Theory and Algebraic Geometry Discord: discord.gg/nmFg6BNvsg Link to Fermat’s Last Theorem Playlist: ua-cam.com/play/PLK-gFjlmrFy7kbHJ7uOmawNTPz9Hea1vp.html Email Inquiries: imtug7@gmail.com My Website: sites.google.com/view/dranthonyvasaturo/about
Fermat's Last Theorem: PROVING R = T in the GENERAL Case! (11.18, 169)
Переглядів 896 місяців тому
Fermat's Last Theorem: PROVING R = T in the GENERAL Case! (11.18, 169)
Fermat's Last Theorem: Proving Ihara's Lemma! (11.17, 168)
Переглядів 967 місяців тому
Fermat's Last Theorem: Proving Ihara's Lemma! (11.17, 168)
Fermat's Last Theorem: FINALLY Proving Theorem TH! (11.16, 167)
Переглядів 3877 місяців тому
Fermat's Last Theorem: FINALLY Proving Theorem TH! (11.16, 167)
Fermat's Last Theorem: It's TRICKY to Prove that the T and H Modules are Free! (166, 11.15)
Переглядів 1027 місяців тому
Fermat's Last Theorem: It's TRICKY to Prove that the T and H Modules are Free! (166, 11.15)
Fermat's Last Theorem: FINALLY Proving Proposition 4 on Congruence Modules! (11.14, 165)
Переглядів 2857 місяців тому
Fermat's Last Theorem: FINALLY Proving Proposition 4 on Congruence Modules! (11.14, 165)
Fermat's Last Theorem: Returning to the Symmetric Square L-Function! (11.13, 164)
Переглядів 1458 місяців тому
Fermat's Last Theorem: Returning to the Symmetric Square L-Function! (11.13, 164)
Fermat's Last Theorem: The T and H Modules for R = T! (163, 11.12)
Переглядів 1138 місяців тому
Fermat's Last Theorem: The T and H Modules for R = T! (163, 11.12)
Fermat's Last Theorem: Reduced Hecke Algebras for R = T! (162, 11.11)
Переглядів 1249 місяців тому
Fermat's Last Theorem: Reduced Hecke Algebras for R = T! (162, 11.11)
Fermat's Last Theorem: Examining Hecke Algebras for R = T! (161, 11.10)
Переглядів 1129 місяців тому
Fermat's Last Theorem: Examining Hecke Algebras for R = T! (161, 11.10)
Fermat's Last Theorem: Cohomology vs. Congruence! (160, 11.9)
Переглядів 1579 місяців тому
Fermat's Last Theorem: Cohomology vs. Congruence! (160, 11.9)
Fermat's Last Theorem: An Important Bound on Cohomology Ratios! (11.8, 159)
Переглядів 14510 місяців тому
Fermat's Last Theorem: An Important Bound on Cohomology Ratios! (11.8, 159)
Fermat's Last Theorem: Universal Modular Type Sigma Deformations! (11.7, 158)
Переглядів 10510 місяців тому
Fermat's Last Theorem: Universal Modular Type Sigma Deformations! (11.7, 158)
Fermat's Last Theorem: Type Sigma Universal Deformations! (11.6, 157)
Переглядів 12211 місяців тому
Fermat's Last Theorem: Type Sigma Universal Deformations! (11.6, 157)
Fermat's Last Theorem: Using Fontaine's Equivalence! (11.5, 156)
Переглядів 26011 місяців тому
Fermat's Last Theorem: Using Fontaine's Equivalence! (11.5, 156)
Fermat's Last Theorem: A Lemma on Unramified Classes! (11.4, 155)
Переглядів 140Рік тому
Fermat's Last Theorem: A Lemma on Unramified Classes! (11.4, 155)
This is, as far as presentations in the year 2024 go, ok. At least the text is legible and not handwritten. I would prefer animated contents in the style of 3Blue1Brown though, since the didactic animation greatly helps understanding.
What book would you recommend for someone who is not that bright and only has time to read one book, but nonetheless is interested in fermat's last theorem?
@@the_eternal_student Ribenboim's "Fermat's Last Theorem for Amateurs"
The proof is trivial and left as an exercise to the reader.
ok gimme a minute
Maybe a good mathematician, but a bad narrator or even worse sound editor. Or simply an very outdated sound system for recording. So much fading and wobble in sound makes it almost incomprehensible...
I read a proof where you work mod 2 (I.e. in F4) instead of mod 3. You prove the statement: if a,b,c in Z[w] and a+b+c=0 with a,b = 1 mod 2 and c = 0 mod 2, and abc is a cube, then abc=0. This clearly implies FLT. To prove it, note that WLOG gcd(a,b,c)=1, so a,b,c are all units times cubes. But the only cubes are 0 and 1 mod 2 (I.e. not w or w+1), so a and b (and hence c) must be true cubes, say a=m^3, b=n^3, c=p^3. But then (m+n)(wm+w^2n)(w^2m+wn) equals (-p)^3, (m+n)+(wm+w^2n)+(w^2m+wn)=0, and m+n=0 mod 2 and wm+w^2n and w^2m+wn are 1 mod 2. Thus infinite descent can be done.
@@noahtaul sorry, I'm not following this. What is w?
The third root of unity!
@@noahtaul Got it. I will try to write down the details later!
What does this sentence fragment mean: "But the only cubes are 0 and 1 mod 2 (I.e. not w or w+1)?"
@@Entropize1We’re working mod 2, and Z[w]/2Z[w] is F4, the field of 4 elements. The cubes in this field are only 0 and 1, the other two elements are not cubes
Im gay
Been watching these for a while (great work). A tip from another LaTeX user: add \beamertemplatenavigationsymbolsempty to your beamer doc, that removes the nav icons at the fottom of the frame that you have no use for anyway.
This whole series is absolutely insane
Im gay
Thanks for the video! 😊
One small correction I noticed, Principles of algebraic geometry was Griffiths and Harris. Fulton and Harris was Representation theory a first course.
@@MichaelGuerry yep! This is fixed in my notes.
Thanks for the videos
Next one tomorrow!
I think I’ll hold out for the hope that a simpler proof will be found before I die. Seriously though, I’m not a mathematician so forgive my naïveté, is there any hope that someone will ever come up with a simpler proof? Maybe one that could be understood by, say, an undergrad in math? When I think about how simple it is to understand the theorem and how monumentally difficult it is to understand the proof, I get the impression that it’s just a matter of time before someone comes up with another approach that will be much shorter and much easier to follow.
Not really. The theorem is false in Q_p, destroying any hopes of a congruence based proof, which is what most people think of when they think of "simple proof." There are simplifications to the method I presented, but the main narrative remains the same. There is also the Khare-Wintenberger proof, but I am not knowledgeable of how that works, and it is still quite complicated.
Love these proofs! 🎉😊
Quoting a comment I remember in Jan Misali's polygon video: Higher math be like: *Nothing is real* 😂😮
Hello Professor. Excellent Video. I have a request. Can i get the pdf of the slide used in this video?
@@tahsinabrar-sl7yq running an FLT course this fall with notes that utterly dwarf these videos in quality. The course notes along with background reading notes will be publicly available.
It would probably take a month to read the books outlined here word for work, understanding it probably a decade
@@aronhegedus it would take far longer than a month to get through all this, even without understanding. Years!
You forgot " Fermat's Last Theorem for dummies". Does anyone have the time to read all these books?
Surprisingly, kind of
... the proceedings of my investigation into the peculiar case of Monsieur Pierre de Fermat's last unproven theorem suggest that even if a simple proof exists, its discovery would be met with false rebuttals, ridicule and unanimous disbelief.
...and consequently, as was indeed the case with Wile's discovery of his proof, it is a far better approach to be completely secretive until a point of certainty is reached that at least some merit would be earned for novelty or effort, even in the event of still being completely in error. A difficulty then immediately arises that any simple proof of FLT will be so underwhelming and deflating that the greater majority of high schooled mathematicians with a passing interest in a simple proof will overwhelm and moderate any public narrative with their incredulity such that a (largely) correct simple proof will never reach the attention of the infinitesimal minority of those able to sufficiently understand Wile's proof to make an authoritative determination as to its veracity. The latter, being mostly already convinced anyway that there is no such simple proof, will never take notice of yet another simple proof of FLT to be bothered with it, lest they put their professional reputation and career at risk. This is the current state of any purported simple proof of FLT, and it is extremely unlikely to ever change, despite Wile's proof's failure to explain "Why is it so?" (ie. axiom of choice) apart from the apparently patently obvious observation that "A circle is a elliptic curve in disguise". Thus any simple proof of FLT, and especially one that can also show "Why it is so." will be lauded only in the Hall of Ridicule and thereafter quickly lost to science, if not utterly banished from, the journals of western academic literature.
The likelihood of there being a quick proof of FLT is incredibly low, since it is false in Q_p. Moreover, the interesting part of FLT is the Modularity Theorem, which a quick proof of FLT would not provide.
Don’t stop please !!!! This is legendary !!!!
Next one up tomorrow!
Fermat a menace for just leaving this problem on his paper's margins
Are you talking into a can??? WTF!?! I had to stop watching the video, because sound quality is so annoyingly bad, that it actually made me angry listening to you...
Holy macro, this is a challenge not climbing the Mount Everest!
I am in highschool and i am planning to understand (briefly) any one famous big theorem or result (i don't care if it takes 20+ years), should i do this?
I was hoping to find some insight into what is meant by "elliptic curve" as opposed to "ellipse" (I know what Elliptic Functions are). Although I have an advanced degree in engineering from a very reputable university, this awe-inspiring document appears to be in a foreign language, using terms I have never even seen on every line. While I don't doubt that those with the required background can understand this work, I do not see the need for showing the pages of your document and reading them (although it does teach one how all these symbols and notations are to be read). I was expecting some kind of diagrams or illustrations or graphics that would justify a video, but no .... Mind you, I am totally in awe of this degree of facility with mathematics at a level wholly inaccessible to me, but I was hoping for some bridge from the land of UA-cam viewers reasonably competent in general mathematics .... Congratulations on this awesome work!
Hi there. Admittedly, by this far into the playlist, the intended audience is advanced graduate students in Number Theory. I recommend doing a quick UA-cam search along the lines "what is an elliptic curve?" and checking out any one of the excellent videos that pop up.
@@Entropize1 Yup, one already came up - haven't watched it yet. I remember how excited I was in high school to see (in my own library research) how a full-strength elliptic integral solves the general pendulum problem. I did browse some of your other vids, particularly the one with the list of hundreds of books. It goes without saying that 95% of that math did not exist in the time of Fermat, no? I can't imagine that even Euler or Gauss had it available either(?) Either Fermat didn't really have a proof (was mistaken), or there seems (naively) something awry in the structure of the universe --- thank you for your answer!
Elliptic curves are related to ellipses by a very long historical line, with the name "elliptic" being passed down until the object no longer had anything to do with ellipses. First, we had elliptic integrals. These were originally developed to find the arc length of an ellipse, but grew to be much more general. Then, we had elliptic functions, which arose when you took the inverse of elliptic integrals and extended that to the complex plane. The Jacobi elliptic function is still closely related to ellipses, but it is the last link you'll find. Of course, we finally have elliptic curves, which come from the Weierstrass elliptic function, and that comes from a certain elliptic integral which has nothing to do with ellipses. :)
@@zswu31416 I wouldn't say they have nothing to do with ellipses since they show up in the formula for the arc length of an ellipse. There's also a somewhat recent theorem relating elliptic curves to ellipses, but I can't recall it. I'll have to go digging.
@@Entropize1 The elliptic integral that comes from the arc length of an ellipse and the elliptic integral that leads to elliptic curves are quite different integrals, and only look similar. Correct me if I'm wrong
Honestly i’ve actually Always wondered how you solve these awesome theorems. But it was only a thought. And now there’s a 20 min vid about everything you need to know
Well, almost everything. I'm still learning myself! Check out the linked video below for what you really need to get started.
truly inspiring that some people have spent thousands of hours mastering these courses and concepts in order to use all of those hours in trying to understand further unknown concepts in mathematics
I guess I'll just watch the pop math videos
The legendary Axler book.
Did Fermat study all that before proving his theorem?
Idk Honestly that guy got into math late in his life cause he was a lawyer. So you’d have to do math 24/7 to study all this
He didn't, because half of this math didn't exist when Fermat "proved" his theorem. We don't actually have his original proof, he just said it as a fact, added a footnote that he can't fit the proof into the book because it's too long and promptly died before passing it forward. It took about 3 centuries after that for the theorem to be confirmed, so unless Fermat was simply that ahead of his time and just didn't tell anyone, he probably made a mistake somewhere
@@asd-wd5bj ...or there is a different way to prove it...
@@callejohansson5732 We can't rule out that possibility, but ever since Fermat's death mathematicans, some of the greatest ones among them (Euler, Lebesque, HIlbert to name a few) have tried to crack that proof without success (aside from proving few specific cases) Do not underestimate the amount of work that went into solving this problem, if there was another way achievable by 17th century math alone, I'm 100% sure somebody would've found it. Fermat was still human, it's way more reasonable to assume that he simply made an error than that he was a better mathematician that virtually all number theorists (and more) after him combined
@asd-wd5bj Prejudice and preconceptions often make us miss the obvious. It may be better to stay open-minded if we want to learn the truth.
I have a question. Did any of the theorems you learned for FLT use the axiom of choice and did it seem unnecessary?
Yea, but Google Shoenfield's Absoluteness Theorem to see why it doesn't matter.
@@Entropize1 Ok, thank you! I'll check it out.
@@Entropize1 I just checked it out. Math is so cool! Thank you very much
I have about 80% of these books; however, need to work 10 more years before deticating the rest of my life reading all of them
At least!
@@Entropize1 I already made a good way, ie a Ph.D. in Arithmetic Geometry. So yes, the rest of my life still might be too short.
How many math courses are required to understand this proof? Just curious.
I have a couple of videos on my channel about this exact topic. Do some digging and let me know if you still have any questions.
I am really disappointed that no one made a fermat last theorum joke. ( Also i am in 12th grade so ill be back in a few years).
Just discovered this series today. Keep up the good work!
Awesome video! 🎉😊
This video has such a depressive and sad tone that I'm thinking about quitting math
Watch my pinned video below before you do that :)
I think it's pretty exciting to have a chance for someone to give such a comprehensive and concise set of options for learning a broad subset of mathematical ideas! Overwhelming eventually gives way to engaging if you get bored enough :)
Depressive??? On the contrary. This is one of the most exciting and uplifting videos I have seen in a long time. If anyone is even remotely interested in math, this video is a goldmine. Everyone knows about Fermat's Last Theorem and it comes up in discussions now and then. It is an extremely simple problem and often people wonder why it took so long to solve. This video is phenomenal and very helpful to see the math required to prove FLT. It is the first time I have seen it listed in a structured way like this. Thank you for making this video! I will recommend it to my friends.
It's crazy how a relatively simple formula thought up 100's of years ago required all this modren advanced math to solve 😮
A list of the prerequisites for inter-universal teichmüller theory would be fun too
Not my forte or my cup of tea, unfortunately.
"Just finish Harshorne" yeah brb in few years :)
That's the spirit!
I wonder how long it took Fermat to master all of this material!
Fermat didn't know this stuff.
@@Viewpoint314 He did, but didn't have space to write it down.
@@Viewpoint314 Of course! I was joking. But there is still the possibility that Fermat found an alternative proof involving some simple procedure: Wouldn't that be wonderful?!
@@r.w.emersonii3501He did. It's buried in a secret forest, under a special tree. Also, there's a probably a goblin, or something.
@@r.w.emersonii3501 It would! but the boring answer is that he probably just made an error somewhere, still his intuition is incredible to just "feel" the right answer in this case
Serious question, in all honesty (unlike me), is there really any one person who really and truly knows all this stuff at the top of their head?
I haven't met one, and I've talked to many experts. I've even heard several experts say no.
@@Entropize1 Well, i'm welcoming myself to the No Club lol. I didnt finish my Maths degree and now being in my mid 50s and moving to Europe soon, from Australia, wondered whether to go finish it for curiosity sake as i love maths yet there is so much online re lectures etc, i dont know if i could handle stringent academia at my age plus i like debating things as am very unconventional. Back in the days of torrents, i once downloaded a file with maths textbooks only to find there were literally like 5000 of them. I went, oops lol That is a lot of textbooks :-)
@@Entropize1 Then how does anyone know it's true?
@@johnbyrne1022 because multiple experts have come together, each of whom know all the details of various parts of the proof, and have collaboratively exchanged results that allowed the result to be proven. This happens all the time in mathematics. Even though no one person knows all the details, all of the details are written down somewhere in a published journal or book.
The reveal at the end that you were recording this whole thing on an IPAD blew me away
okay, i'm 40 now, i should be able to finish all these books by the time I'm 50. /REMIND IN 10 YEARS
10 years, you think? No way. You must be a genius. 😆
The Math You Actually NEED To Start Learning Fermat's Last Theorem: ua-cam.com/video/h38D5_dcR7w/v-deo.html