Videos like this make me really wonder if Number Theory, despite seeming so abstract and 'man-made,' may actually eventually lead us to realize that counting, or comparing numbers, is actually something *physical* and objective, not purely mental or subjective... perhaps extremely tiny fluctuations in the EM field or something. There's so much 'structure' in even the simplest arrangement of counts, and our minds are apparently made of electromagnetism after all. I wonder if primitive hominids engraving tally marks on ancient bones in some way intuited this.

This video needs more audience members.

Love this video, been self-studying math as a hobby from late 2023, without any tutoring, this is my savior.

i hope you come back someday

Great video🎉

This explanation of the Euclidean algorithm is starting to make me truly understands stuff like why the GCD is a linear combination, or how to solve linear congruences

Well paced, fun to watch, bravo 👏

8:10 "Any number can be written as a product of primes in exactly one way". I'm not sure I understood this. Did you mean a sum of primes?

If you don't mind can you plz share the book pdf ?

GCD is unique:- Assuming c and d are the GCD of (a,b) then a/c=a/d. also b/c=b/d. I.e. a/c=a/d. I.e. c=d

The GCD of 2 +be integer is last non zero remainder of a,b such that for every ‘ai’ and ‘bi’ a=b.quotient + remainder. For e.g. GCD (42,30) is as Iteration 1 a=42; b=30; a%b= 12. Iteration 2. a=30; b=12; a%b=6. Iteration 3 a=12; b=6; a%b=0. Since here a%b is 0 Therefore the remainder in iteration 2 is the GCD of (42,30) I.e 6. .... (by definition)

great work

kzbin.info/www/bejne/q4TIdId6hNadisk

kzbin.info/www/bejne/p4isYp2Qj8ZljZo

Today I also learnt a little bit English with maths.

Bravo. More please

Great explanation. Bonus points for including fully worked out examples and taking the time to show how you would generalise them

In Neuro-Linguistic Programming (NLP) which describes how humans operate, we are taught that the only things that are worthy of knowing are context, process and structure. This applies, I have found, to everything in life, including mathematics. Mathematics is designed with context, process and structure......it becomes very simple after that.

1. GCD (x,y) := largest n such that x/n and y/n are integers 2. if m and n are both solutions, m ≥ n since m is largest and n≥m since n is largest, so n = m remains only solution 3. Euclidean algorithm: a_0= y, a_1 = rem(x,y), a_{i+1} = rem(a_i;a_{i-1}) ...... Begins to scratch head ...... okay a_i exists such that x/a_i and y/a_i are integers .... or does it? Vsauce music starts playing

This reminds me of the golden ratio If you have a golden ratio number of dots in a circle and you you skip 1/golden ratio of that number you can get to any dot. Neat

GradeAunderA vibes

what are you foundational operators, and why should you care, only one is good

If one move in space time move against it and one move in time then space move against it too. Just like one expand toward infinity the negative infinity move backward so like breathing lung infinity is the same with small variation

Yooo Martie weissman taught my abstract algebra undergrad class. Great teacher, but unfortunately it was the first quarter of covid lockdown so he was forced to teach it online on short notice. I think he did a great job but it would’ve been nice to have some classroom time from him.

Dude, this is awesome. I'm a 4th grade teacher and can see playing around with these ideas with my higher math kids. More uploads! Can't wait!

0:30 Why do many American mathematical KZbinrs, say such things as "negative 6x"? -6x may or may not belong to the set of odd numbers. -6x may or may not belong to the set of even numbers. You do not say "negative even six" - why not? So, why use a set-descriptive adjective ("minus") when referring to a number, but no other set-descriptive adjectives such as "even"? You refer (1:43) to Andrew Wiles, and he refers (kzbin.info/www/bejne/q4LKlKOwgKZooM0) to "plus of minus five", not "positive or negative five". Nowhere does he use "negative" as an adjective for a number, but does use "minus". Is there a good reason that American usage differs from the usage of the person who proved Fermat's Last Theorem?

This is great video sir. Please make more.

YEah, you got my sub. Super interesting!

Have I just stumbled upon the beginnings of the next big math channel? Hope so...

Are you chewing mint gum?

is there a word for a an alternative numbering scheme where numbers are written as a list of its factors and only the primes are given symbols?

New subscriber, looking forwards to more content here! Regardless of how many weeds may or may not be growing in your garden, this was a very nice, clean discussion.

Yes! Weissman's book is fantastic.

It's a most obfuscated way ever to explain the Euclidean Algorithm.

Europe's hegemony . Diaphanous was great , no doubt. He never told integer solution in linear programma. He made rational solution. First positive integer generalised theory was given by Arya bhatta 1 . See verses 32 and 33, Ganita pada of Aryabhatiya. Except , one or two poems ( ser D E Smith ) on Euclid, Europe vehemently opposed infinity and zero, did not allow number system.. Decarte and Leibnitz were under constant threat for considering 0. Bruno was burnt alive. on 1600 AD. There was no mention of Euclidean algorithms in any book or paper of Algebra before 1950. Now , everything is called Euclidean algorithm.. What name, you suggest for LC M, then you come for name of addition, su traction echt. You find out how Christians hooligans murdered Hypatia ( Theon' s daughter), in 415 AD. My reaction is for your saying diaphantine integer and Euclidean algorithm.

Thanks for giving homework. Be back soon....

great video ! Keep it up !

1:59 it was shown by Euler mostly but first correct one was Kausler (1802), then by Legendre (1820s) etc. Wiles proved for all n that we hadn’t already solved by the

Euler had already solved n=3.

Nice work

8:50 The Hasse lattice section needs more work, I think, especially some animation to make the concept of 'multiplying in the direction of' clearer.

Aryabhatta didn't invented 0 just so you can become one yourself .

It's great for a basis and understanding of integers. Great video 👍

👍

I don't find your challenge questions interesting as these were all covered in math class. The video was good though.

Rather than the hasse diagrams, instead showing how prime factors cancel to reach GCD would be helpful. That’s how I learned to solve GCD anyways.

I admit I struggled with this algorithm so it is nice to see it explained visually. Very helpful.

Was it realy Andrew Wiles? Or was it Leonhard Euler 300 years before A. Wiles?

8:06 I was just going to mention that 2 and 4 will not reach 1, they can only reach their gcd of 2. Now it looks as though that's coming!

Hold on, at 7:30 you claim that whenever you have a list of numbers that decreases and is non-negative you'll always reach 0, but I think it's important to emphasize that this is only true for integers. If you allow for any real number (which is not the case for the problem in the video), calculus quickly shows us that it is indeed possible for a sequence to get smaller and smaller without ever approaching zero, but have it's limit at a non-zero positive number like 1, 2 or 3/2. Either way, you just got yourself a new sub, hope to see more of you in the future.