The Collatz Conjecture is the simplest math problem no one can solve — it is easy enough for almost anyone to understand but notoriously difficult to solve. This video is sponsored by Brilliant. The first 200 people to sign up via https://brilliant.org/veritasium get 20% off a yearly subscription.

Special thanks to Prof. Alex Kontorovich for introducing us to this topic, filming the interview, and consulting on the script and earlier drafts of this video.

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References:
Lagarias, J. C. (2006). The 3x+ 1 problem: An annotated bibliography, II (2000-2009). arXiv preprint math/0608208. — https://ve42.co/Lagarias2006

Lagarias, J. C. (2003). The 3x+ 1 problem: An annotated bibliography (1963–1999). The ultimate challenge: the 3x, 1, 267-341. — https://ve42.co/Lagarias2003

Tao, T (2020). The Notorious Collatz Conjecture — https://ve42.co/Tao2020

A. Kontorovich and Y. Sinai, Structure Theorem for (d,g,h)-Maps, Bulletin of the Brazilian Mathematical Society, New Series 33(2), 2002, pp. 213-224.

A. Kontorovich and S. Miller Benford's Law, values of L-functions and the 3x+1 Problem, Acta Arithmetica 120 (2005), 269-297.

A. Kontorovich and J. Lagarias Stochastic Models for the 3x + 1 and 5x + 1 Problems, in "The Ultimate Challenge: The 3x+1 Problem," AMS 2010.

Tao, T. (2019). Almost all orbits of the Collatz map attain almost bounded values. arXiv preprint arXiv:1909.03562. — https://ve42.co/Tao2019

Conway, J. H. (1987). Fractran: A simple universal programming language for arithmetic. In Open problems in Communication and Computation (pp. 4-26). Springer, New York, NY. — https://ve42.co/Conway1987

The Manim Community Developers. (2021). Manim – Mathematical Animation Framework (Version v0.13.1) [Computer software]. https://www.manim.community/

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Special thanks to Patreon supporters: Alvaro Naranjo, Burt Humburg, Blake Byers, Dumky, Mike Tung, Evgeny Skvortsov, Meekay, Ismail Öncü Usta, Paul Peijzel, Crated Comments, Anna, Mac Malkawi, Michael Schneider, Oleksii Leonov, Jim Osmun, Tyson McDowell, Ludovic Robillard, Jim buckmaster, fanime96, Juan Benet, Ruslan Khroma, Robert Blum, Richard Sundvall, Lee Redden, Vincent, Marinus Kuivenhoven, Alfred Wallace, Arjun Chakroborty, Joar Wandborg, Clayton Greenwell, Pindex, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi, Ron Neal

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Written by Derek Muller, Alex Kontorovich and Petr Lebedev
Animation by Ivy Tello, Jonny Hyman, Jesús Enrique Rascón and Mike Radjabov
Filmed by Derek Muller and Emily Zhang
Edited by Derek Muller
SFX by Shaun Clifford
Additional video supplied by Getty Images
Produced by Derek Muller, Petr Lebedev and Emily Zhang

3d Coral by Vasilis Triantafyllou and Niklas Rosenstein — https://ve42.co/3DCoral
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Answer The Question Of Albert Einstein | How To Solve This Equation | Can You Solve This Equation

Math Tricks , Math Solution Videos , Knowledgeable Videos
By #mathmaster
#shorts

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Workout to 100 with Jack Hartmann in this workout to 100 song. Get your exercise and build your brain and body connection while changing exercises every 10 numbers. Follow along and get your brain and body oxygenated, get your heart pumping and your brain stimulated while having fun and moving with Jack

Lyrics
Let's reach it up and count
Let's bend it down and count
Let's pump it up and count
Move your body and sing along
Do the count to 100 workout song
Reach your hands up and crisscross
1,2,3,4,5,6,7,8,9,10
Bend your knees and do leg squats
11,12,13,14,15,16,17,18,19,20
Do arm curls and pump your muscles
21,22,23,24,25,26,27,28,29,30
Stroke your your arms and shoulders and swim
31,32,33,34,35,36,37,38,39,40
Step left leg right
Right leg left
41,42,43,44,45,46,47,48,49,50
Move arms out front and do scissors
51,52,53,54,55,56,57,58,59,60
Hop like a bunny left and right
61,62,63,64,65,66,67,68,69,70
Hands together, row side to side
71,72,73,74,75,76,77,78,79 80
Move legs and arms and climb up high
81,82,83,84,85,86,87,88,89,90
Jog in place and work it out
91,92,93,94,95,96,97,98,99,100
You did it!
Cool it down now
Way to go!

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Meet the Math Facts Level 1 makes multiplication and division fun and easy! You will learn basic multiplication and division through fact families. With fun characters that you will grow to love, levels 1, 2, & 3 will teach you to easily recall basic multiplication & division math facts to 12×12.

Level 1: Equations 0x0 to 3x12
Level 2: Equations 4x4 to 6x12
Level 3: Equations 7x7 to 12x12

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Roman Numbers 1 to 12 | Mathematics Grade 2 | Periwinkle

Hi Kids,
In this video we will learn how to read and write Roman Numbers.
So lets begin!!


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MATH SONG

Learn Multiplication - Table of 2 to 10

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Multiplication Table of 2 :- https://youtu.be/CjEjAeeiVkg

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Multiplication Table of 12 :- https://youtu.be/O79KEBWj54c

Multiplication Table of 13 :- https://youtu.be/ge9_uDINYCg

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Multiplication Table of 27 :- https://youtu.be/HVC-RWgJvkg

Multiplication Table of 28 :- https://youtu.be/HIlGDNbtMpU


Learn "Table of Two to Ten (2 to 10)" in a very interesting and easy way. E -Learning Studio brought entertaining and fun-filled Nursery Rhymes, Counting, Colours, Shapes and many more titles for your children, keep watching. Subscribe to E-Learning Studio channel, Enjoy our collection of Nursery Rhymes, Fairy Tales, Moral Stories, Educational Videos and much more.

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Welcome to Least Common Multiple (LCM) with Mr. J! Need help with finding the least common multiple? You're in the right place!

Whether you're just starting out, or need a quick refresher, this is the video for you if you're looking for help with how to find the least common multiple. Mr. J will go through least common multiple examples and explain the steps of how to find least common multiples.

MORE ADDING AND SUBTRACTING FRACTIONS VIDEOS:
✅ Adding Fractions with Unlike Denominators (Part 1) - https://youtu.be/CoCmsyFQ_Xc
✅ Adding Fractions with Unlike Denominators (Part 2) - https://youtu.be/SSxU5sjxqyk
✅ Subtracting Fractions with Unlike Denominators (Part 1) - https://youtu.be/jgGAJOe-Bgg
✅ Subtracting Fractions with Unlike Denominators (Part 2) - https://youtu.be/Tl3lbRe18JY
✅ Simplifying Fractions - https://youtu.be/oFVzcnJfYkg
✅ Least Common Multiples - https://youtu.be/53Ed5yjBELc
✅ Why Do We Need a Common Denominator When Adding and Subtracting Fractions? - https://youtu.be/YxAXC8Q16ok
✅ Equivalent Fractions - https://youtu.be/dBZ2QGZBH6M

About Math with Mr. J: This channel offers instructional videos that are directly aligned with math standards. Teachers, parents/guardians, and students from around the world have used this channel to help with math content in many different ways. All material is absolutely free.

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Hopefully this video is what you're looking for when it comes to least common multiples.

Have a great rest of your day and thanks again for watching!

Multiply by 3's and learn the 3 multiplication table with an electric guitar beat. Sing along to the 3's times tables in order by singing along with the multiplication fact the first time through. The second time through we delay the answer so students can give the answer and then the answer is reinforced. The third time we supply the 3's times table and leave the answer blank for higher order learning.
Multiply by 3's with this electrical guitar beat to help student's learn their 3 multiplication table.
This song goes through each table 1 through 12 three times to give your children a chance for lots of practice.
This song also has a gradual learning structure.

First time: I sing the multiplication table I give the answer.

Second time: I say the table I delay the answer, so children have a chance to answer before me.

Third time: I completely omit the answer so children can answer on their own.

This song on learning how to Multiply by 3 is a wonderful way for your children to learn and practice the multiplication tables.
Multiply by 3's with this catchy rock n' roll tune to help student's learn their 3 multiplication table
LYRICS:

Multiply by 3

Three little pigs, three blind mice
Three was the number and that was nice.
Now I’m bigger and I can see
I’ve got to multiply by three.

3 x 1 is 3
3 x 2 is 6
3 x 3 is 9
3 x 4 is 12
3 x 5 is 15
3 x 6 is 18
3 x 7 is 21
3 x 8 is 24
3 x 9 is 27
3 x 10 is 30
3 x 11 is 33
3 x 12 is 36

Three little pigs, three blind mice
Three was the number and that was nice.
Now I’m bigger and I can see
I’ve got to multiply by three.

Now you give the answer before I do
3 x 1 is 3
3 x 2 is 6
3 x 3 is 9
3 x 4 is 12
3 x 5 is 15
3 x 6 is 18
3 x 7 is 21
3 x 8 is 24
3 x 9 is 27
3 x 10 is 30
3 x 11 is 33
3 x 12 is 36

Now let's try it on your own'
You can do it!

3 x 1 is
3 x 2 is
3 x 3 is
3 x 4 is
3 x 5 is
3 x 6 is
3 x 7 is
3 x 8 is
3 x 9 is
3 x 10 is
3 x 11 is
3 x 12 is


Three little pigs, three blind mice
Three was the number and that was nice
Now I’m bigger and I can see
I’ve got to multiply by three
Got to multiply by three


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Find the Difference
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I think I'm a Math addict now...

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A fun song I use to teach the ordinal numbers to my k-3 classes. Teach the difference between ordinal and cardinal numbers and have your students try to sing along!
Purchase on iTunes: https://goo.gl/RIK9QX

LYRICS:
First, second, third, and fourth
fifth, sixth, seventh
eighth, ninth, tenth
First, second, third, and fourth
fifth, sixth, seventh
eighth, ninth, tenth
Those are the ordinal numbers
Those are the ordinal numbers
Those are the ordinal numbers
and they go just like this
Go First
Go Second
Go Third
Go Fourth
Go Fifth
Go Sixth
Go Seventh
Go Eighth
Go Ninth
Go Tenth
Those are the ordinal numbers
First, second, third, and fourth
fifth, sixth, seventh
eighth, ninth, tenth
First, second, third, and fourth
fifth, sixth, seventh
eighth, ninth, tenth
Those are the ordinal numbers
Those are the ordinal numbers
Those are the ordinal numbers
and they go just like this
Go First
Go Second
Go Third
Go Fourth
Go Fifth
Go Sixth
Go seventh
Go Eighth
Go Ninth
Go Tenth
Those are the ordinal numbers
Cardinal numbers tell us how many or how much of something we have
For example, this bag has ten cookies in it
Ordinal numbers tell us what position or place something is in
For instance, you might line up the cookies to eat them one at a time
Here's the first cookie
Here's the tenth, and last cookie
Those are the ordinal numbers
Those are the ordinal numbers
Those are the ordinal numbers
and they go just like this
Now you say them
First, second, third, fourth
fifth, sixth, seventh
eighth, ninth, tenth

Tons of MATH VIDEOS here: https://www.mccarthymathacademy.com/

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Want to focus on one factor at a time? Jump ahead by clicking the factor you want to practice:

Multiply by 0 - 0:16 (Music: "No" by Meghan Trainor)
Multiply by 1 - 0:50 (Music: "I Knew You Were Trouble" by Taylor Swift)
Multiply by 2 - 1:18 (Music: "Rude" by Magic!)
Multiply by 3 - 1:47 (Music: "Moves Like Jagger" by Maroon 5)
Multiply by 4 - 2:07 (Music: "Single Ladies" by Beyonce)
Multiply by 5 - 2:30 (Music: "Honey, I'm Good" by Andy Grammer)
Multiply by 6 - 2:49 (Music: "Call Me Maybe" by Carly Rae Jepsen)
Multiply by 7 - 3:09 (Music: "Love Yourself" by Justin Bieber)
Multiply by 8 - 3:50 (Music: "Party Rock Anthem" by LMFAO)
Multiply by 9 - 4:18 (Music: "Watch Me (Whip/Nae Nae)" by Silento)
Multiply by 10 - 4:50 (Music: "Sorry" by Justin Bieber)
Multiply by 11 - 5:16 (Music: "Drag Me Down" by One Direction)
Multiply by 12 - 5:49 (Music: "Can't Stop the Feeling" by Justin Timberlake)



This song is a mash up of current popular music. I do not claim rights for the music, just the adapted educational content of the lyrics. Enjoy!

Lyrics:

C’mon ya’ll
Get fluent
Know your fast facts
Then flaunt it

I’m ‘bout to break it down
Zeros to twelves
Check out my fluency
Let’s go!

(Zeros)

All my students, listen up
If zero is a factor
It takes control
It steals the show
The Property of Zero

Times 1 is 0
Times 2 is 0
Times 3 is 0
Times 4, it is 0
Times 5, it is 0
Times 6, it is 0
Nah, n-nuh, nah, n-nuh
Zee-eer-ro

Times 7 is 0
Times 8 is 0
Times 9 is 0
Times 10, it is 0
11, is 0
Times 12 is 0
Nah, n-nuh, nah, n-nuh
Zee-eer-ro

(Ones)

I knew ones weren’t trouble when they walked in
In fact, they’re so easy
Just count like 1, 2, and 3,
4, 5, 6, 7, 8,
9, 10, 11, 12, ohh
Identity Property of Multiplication

(Twos)

Do you know I know my twos?
Yes, I most certainly do
Do you know I know my twos?
2, 4, 6, 8, 10, 12
14, 16, 18, 20, 22, 24
I know my twos
Use that doubling strategy
So easy,
But I’ll practice them anyway

(Threes)

Hit me with my threes, pretty please
3, 6, 9, 12, 15, 18
21, 24, 27
30, 33, 36
I love me some threes, yeah

(Fours)

If you know your fours, then you should sing a-long with me
If you know your fours, then you should sing a-long with me
Don’t be shy, I know you know ‘em
Sing a-long with me
If you know your fours, then you should sing a-long with me
4, 8, 12, 16, 20, 24, 28
32, 36, 40, 44, 48

(Fives)

Aw, no! Here come the fives
5, 10, 15, 20, 25
You’ll know ‘em all shortly
30, 35, and 40
And then there’s 45, 50, 55, feeling alive
60’s coming, it’s true
Now the fives must bid you adieu

(Sixes)

Hey sixes, I just met ya
You’re kinda crazy
6, 12, and 18, 24, and 30
36 and 42 and 48
54 and 60, 66, 72

(Sevens)

What was the song for the sevens again?
Oh wait, I’ve got it
My momma once told me your sevens could be hard
She said, “If you practice, then soon, you’ll be a star.”
Well I’ve been practicing all day
Now I can finally say,
“Now I know, I know the sevens on my own.”
It goes like 7, 14, 21, 28, 35, 42, 49
56, 63, and 70,
77 and 84

(Eights)

Party rockin’ with the eights, for sure
8, 16, 24
32, 40, 48
56, 64 (Ow!)
72, 80, 88, 96
Party rockin’ with the eights
Can you handle it?

(Nines)

Go on and do those nines for me
McCarthy Math!
We’ve got those nines
9, 18, 27
I’m just beginning
36, 45, 54, 63
Now watch that 72, that 81, that 90, yeah
Now watch that 99, 108
Oh, life is so great with the nine whip nae nae

(Tens)

Is it too late to learn your tensies? (Did she really just call ‘em tensies?)
10, 20, 30, 40 (Oh, she did…)
50, 60, 70, 80
90, 100, 110
120, and that’s the end

(Elevens)

You know the elevens will not drag us down
11, 22, 33, 44, 55, 66, 77, 88, 99
110, 121, 132

(Twelves)

Yeah, uhn, yeah, uhn

I’ve got this feeling
The twelves are great
12, 24, 36, 48
The big 6-0
72
84, 96, we’re almost through

We’ve got that 108
Stepping up to 120
132 and 144
I can’t stop studying because I’m grooving to the beat
Soon I’ll be fluent with my fast facts
And that’ll be sweet

Faster than fast at quiz after quiz
I never thought I’d be a multiplication whiz
Spread the word to all the other kids
‘Bout this mashup, ‘ bout this mash-up, ‘bout this mash-up

Nothing I can see but As,
So I dance, dance, dance
My teacher and my parents are proud of me,
So I dance, dance, dance, c’mon
Multiplying is so easy
So I dance, dance, dance
And I can’t stop listening to this jam
I keep dancing

Multiplication
Mashup
Multiplication
Mashup
C’mon!

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Sources and links to learn more below!

I’m very grateful to mathematician Hugh Woodin, Professor of Philosophy and Mathematics at Harvard, for taking the time on multiple occasions to discuss this topic with me and help me wrap my (finite) head around it.

I’m also grateful to David Eisenbud, the Director of the Mathematical Sciences Research Institute (MSRI) and professor of mathematics at the University of California, Berkeley, for his help and for connecting me with Hugh Woodin.

And of course, big thanks to Brady Haran who created the “mile of pi” seen in this video and connected me with all these mathematicians in the first place. His channel, Numberphile, is superb: https://www.youtube.com/user/numberphile

BOOKS related to these topics that I used:

“The Outer Limits of Reason” by Noson S. Yanofsky: http://amzn.com/0262019353
“Infinity and The Mind” by Rudy Rucker: http://amzn.com/0691121273
“Roads to Infinity” by John C. Stilwell: http://amzn.com/1568814666
“More Precisely: The Math You Need to Do Philosophy” by Eric Steinhart: http://amzn.com/1551119099
“Satan, Cantor and Infinity: Mind-Boggling Puzzles” by Raymond M. Smullyan: http://amzn.com/0486470369

classic book that helps introduce concept of axioms: “Introduction to the Foundations of Mathematics” by Raymond L. Wilder: http://amzn.com/0486488209

Hugh Woodin speaking about infinity at the World Science Festival: https://youtu.be/KDCJZ81PwVM?t=29m45s

Names of large (finite) numbers: https://en.wikipedia.org/wiki/....Names_of_large_numbe

Geoglyphs:

The biggest number: https://goo.gl/maps/7GWcpnzo7iG2

Fovant badges: https://en.wikipedia.org/wiki/Fovant_Badges

Battalion Park: https://en.wikipedia.org/wiki/Battalion_Park

A mile of pi [VIDEO]: https://www.youtube.com/watch?v=0r3cEKZiLmg

Wikipedia’s great visualization of ordinals out to omega^omega: https://en.wikipedia.org/wiki/....File:Omega-exp-omega

as seen on: https://en.wikipedia.org/wiki/Ordinal_number

this is also a good page about ordinals: http://math.wikia.com/wiki/Ordinal_Number

also: http://www.cut-the-knot.org/Wh....atIs/Infinity/Ordina

and: https://en.wikipedia.org/wiki/Order_type and https://en.wikipedia.org/wiki/Well-order

Axioms:
https://en.wikipedia.org/wiki/Axiom
https://www.reddit.com/r/asksc....ience/comments/30xok
http://philosophy.stackexchang....e.com/questions/5922
http://www.cs.umd.edu/~gasarch..../BLOGPAPERS/belaxiom
http://www.cs.umd.edu/~gasarch..../BLOGPAPERS/belaxiom

THE UNREASONABLE EFFECTIVENSS OF MATHEMATICS IN THE NATURAL SCIENCES
[PDF]: http://www.maths.ed.ac.uk/~aar/papers/wigner.pdf
https://en.wikipedia.org/wiki/....The_Unreasonable_Eff

Large Cardinal game based on 2048: http://cantorontheshore.blogsp....ot.it/2014/10/one-re

Other good resources:

http://quibb.blogspot.com/2012..../01/infinity-first-t
http://plato.stanford.edu/entries/set-theory/
http://cantorsattic.info/Cantor%27s_Attic
http://cantorontheshore.blogsp....ot.co.at/2014/09/art
http://isomorphism.es/post/107....82081422/what-comes-
https://lukepalmer.wordpress.c....om/2007/06/14/the-le

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Do you think you're smarter than other people and have exceptional logic? Well, you have an opportunity to test your brain and your analytical skills right now. By the way, if you solve puzzles and riddles regularly, you’re giving your brain the workout it needs and increasing your IQ level. Yes, your brain needs workouts, just like your body, to keep it sharp and help you get smarter in no time. Scientists have long proved that! So, can you be really attentive and think outside the box? Let's find out!

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