The CRAZY Amount of Math You Need for Fermat's Last Theorem! (1.4, 3)
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- čas přidán 26. 06. 2024
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The Math You Actually NEED To Start Learning Fermat's Last Theorem: czcams.com/video/h38D5_dcR7w/video.html
You know the theorem (and the proof) is hard when it takes 20min to introduce the prerequisites
*When it takes 20 minutes to introduce (only a good chunk of the main) prerequisites!
What is the best book/course of proofs you advice to undergraduates? Thanks
@@KRYPTOS_K5 just learn math, writing proofs will come naturally
Don’t tell me that I just started watching 🥲🤣
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
The legendary Axler book.
As people suggest additional/different references, I will post them here:
Galois Theory: Stewart
okay, i'm 40 now, i should be able to finish all these books by the time I'm 50. /REMIND IN 10 YEARS
This is a lifetime of reading...
But it's a motivation by itself
There's truth to the video, but see my video about the math you REALLY need to get started.
@@Entropize1 Where is it?
@@KRYPTOS_K5 I just pinned it in the comments here!
@@Entropize1 I got it. Is it enough to an ultimate comprehension of the last theorem?
PS in your (philosophic) opinion, Physics and Mathematics could reach an end game of knowledge?
@@KRYPTOS_K5 Unfortunately, I'm not sure what you're asking. What I can say is that if you want to understand FLT from ground zero, you have a lifetime of work ahead of you. Regarding your second question: no, I don't think it's possible.
I have an undergratuate math degree, and I was happy with myself through maybe the first slide. "Crazy ammount" is right. I stopped being able to say "I can do that" very very early for how much longer the prerequisite list went.
Check out my other video on the math that you actually need to really get started!
@@Entropize1I will, thank you
By the way, I just pinned the video in the comments here.
I feel like this strategy of learning all of the mathematics needed for FLT before having even read the proof is not the best. I think it would be a lot more motivating and perhaps more efficient to first read the theorem starting with some minimal amount prerequisites (I would be curious to know what you would consider that to be). You could then black boxing everything difficult and focus on the main ideas and intuitions with the help of your videos, only then going back and filling in the holes with the extra references in a second/third/fourth pass to reach a desired level of depth in understanding. Kind of like a mechanic who reads a millions books on engines without ever having popped open a hood vs. a mechanic getting their hands dirty early on to understand what is needed to be studied and how it's used based.
Yes, you are spot on. This video is a bit of a meme to be honest (but only a bit). I do not recommend actually learning all of this before starting the proof. This video is more "here's most all the things you should learn in total if your goal is to have as few questions as possible when learning FLT and to understand the maximal number of details." In reality, provided you have been through a solid undergraduate curriculum (whatever that even means), and a reasonably good MA curriculum (again, whatever that means), I'd say you want my "top 8":
1. Vakil/Hartshorne
2. Neukirch Ch 1-3
3. Class Field Theory (Milne/Neukirch)
4. Silverman 1
5. Silverman 2
6. Diamond and Shurman
7. Diamond, Im
8. Snowden's Torsion Theorem Course (because its proof uses a lot of the tools you'll need to be familiar with before getting into FLT; it's a good warmup)
Then I'd pick up Cornell Silverman Stevens and the DDT notes and start going through the FLT proof. But, see, there are technically many prerequisites one ought to have to begin reading the above 8, and my video simply tries to take a lot of that into account. My video also tries to a) anticipate the questions you will inevitably have if you start reading the proof too early and b) anticipate the questions you will have if your background isn't as thorough as it should be, even if you have gone through a fairly typical education.
Here are some things I recommend blackboxing (initially or forever). This list is not comprehensive; it consists of what I could think of in 2 minutes flat while sitting on the couch talking to my wife:
1. Carayol's Theorem on Vanishing Cycles
2. Langlands-Tunnell (these are the biggest two black boxes by far)
3. Faltings' Theorem
4. Ramakrishna's Thesis
5. Deligne-Serre
6. Jacquet-Langlands
7. The Open Image Theorem (although I actually think you should grapple with this sooner rather than later)
Perhaps I should make a video elaborating on the information I have just given.
Personally i liked this video. So many different topics, and gives me motivation to learn more about those. But a video like the one you suggest would be interesting too.
The reveal at the end that you were recording this whole thing on an IPAD blew me away
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.
Nice attempt man, thanks for the overview
It's crazy how a relatively simple formula thought up 100's of years ago required all this modren advanced math to solve 😮
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).
A list of the prerequisites for inter-universal teichmüller theory would be fun too
Not my forte or my cup of tea, unfortunately.
This book list is great. Thanks!
"Just finish Harshorne" yeah brb in few years :)
That's the spirit!
Are the books on Abelian Varieties interchangable?
No, but pick a good one and have the others to consult when you run into small facts you might have missed. Don't go crazy.
Good!!
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.
I guess I'll just watch the pop math videos
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
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 :)
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.
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 :-)