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The Simplest Math Problem No One Can Solve - Collatz Conjecture

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  • The Simplest Math Problem No One Can Solve - Collatz Conjecture

    22:09

    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 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. —

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

    Tao, T (2020). The Notorious Collatz Conjecture —

    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. —

    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. —

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    Written by Derek Muller, Alex Kontorovich and Petr Lebedev
    Animation by Iván Tello, Jonny Hyman, Jesús Enrique Rascón and Mike Radjabov
    Filmed by Derek Muller and Emily Zhang
    Edited by Derek Muller
    SFX by Shaun Clifford
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    3d Coral by Vasilis Triantafyllou and Niklas Rosenstein —
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  • UNCRACKABLE? The Collatz Conjecture - Numberphile

    7:52

    Catch David on the Numberphile podcast:
    Professor David Eisenbud on the infamous Collatz Conjecture, a simple problem that mathematicians may not be ready to crack.
    More links & stuff in full description below ↓↓↓

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  • The simplest math problem no one can solve- Colatz Conjecture

    3:05

  • Collatz Conjecture or the 3n+1 problem!

    10:55

    In this video, I attempt to explain the simple yet fascinating Collatz Conjecture problem using some examples. This is arguably the simplest mathematics problem that no one can solve.

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  • The Simplest Impossible Problem #shorts

    53

    Jeffrey Lagarias said the Collatz Conjecture is completely out of reach of present day mathematics. Can YOU find a number that doesn't eventually reach 1? #shorts

  • Collatz Conjecture Explained- 3n+1 Problem- Unsolved Problems in Mathematics- The Collatz Conjecture

    6:50

    This video is about the Collatz conjecture which is an unsolved problem in mathematics. This problem is famously known as Collatz Conjecture or 3n+1 problem.
    This problem was introduced by Lothar Collatz in 1937. Collatz Conjecture is also known by other names like 3n+1 conjecture, Ulam conjecture, Kakutani's problem, Thwaites conjecture, Syracuse problem or Hasse's algorithm.
    Collatz Conjecture is a millennium problem in mathematics. It means If you can solve this problem you will win a prize money of 1 million dollars!!! Many mathematicians have tried to solve it but all failed.
    Although the problem looks so simple that even a little kid can understand it, but solving it is not child's play.
    “Jeffrey Lagarias stated in 2010 that the Collatz conjecture is an extraordinarily difficult problem, completely out of reach of present day mathematics.
    First we will see the statement of the Collatz conjecture, then we will understand it with the help of some examples.
    The problem is simple.
    Take any positive integer
    if this number is even, then divide it by 2
    but if the number is odd then multiply the number by 3 and add 1 to get the next number.
    and repeat this process to get the next number.
    By following this process you will get a sequence of numbers. As the numbers in the sequence go up and down frequently, the sequence of numbers is also called as hailstone sequence or hailstone numbers.
    Now according to the Collatz conjecture- Regardless of which positive integer is chosen initially. This sequence will eventually reach the number 1.
    No one knows by this miraculous thing happens. Why all the positive integers end up at 1 by following this process.

    We can also represent the problem in simple mathematical terms by defining a function

    f(n) = n/2 : if n is even
    3n+1 : if n is odd
    Here n is a positive integer.

    Let's understand it with the help of some examples to make it more clear.
    We can take any positive integer, small or very big but it's better to take a small number to explain you the concept.
    You can try it with larger numbers of your choice.

    Let's start by taking a small positive integer 7.
    Now we will apply this process on number 7.
    As we know, 7 is an odd number so to get the next number, as per the rule we multiply it by 3 and add 1. Hence we get 22.
    Now see, 22 is an even number therefore next number will be obtained by dividing it by 2. We get number 11.
    11 is an odd number so multiply it by 3 and add 1. This time we get 34 as the next number in the sequence.
    Now all we need to do is just repeat the same process as per the rule. At last stage you will find that you reach to number 1.
    But you don't want to stop at 1. So you again apply the rule.
    As 1 is an odd number, you multiply it by 3 and add 1, you get 4.
    Since 4 is even, you divide it by 2 and get 2.
    Again 2 is even do you divide it by 2 and get 1 once again.
    Did you observe something weird?
    You are stuck in an endless loop of numbers 4, 2 and 1.
    This is what the Collatz Conjecture states- All positive integers end up at 1 by following this rule.

    If this example is not enough to make you feel satisfied then I have few more examples for you.

    This time let's try with a little bigger number, ofcourse a positive integer.

    Let's take number 12
    We will repeat the same process with number 12 to get a sequence of numbers.
    Since 12 is even divide it by 2. we get 6. It's again an even number so divide by 2 once again. We have 3 which is an odd number. Now multiply it by 3 and add 1 to it. You see, we get number 10.
    Now repeat the same process untill you reach 1.
    On applying the rule again on 1, you will see, you are stuck in an endless loop of 4, 2, 1 again.
    You can observe the same thing with another example of number 19
    This sequence of numbers also ends at 1 and forms a loop of numbers 4, 2 and 1.
    Amazing!!!
    Do you know why does it happen? Actually no one know!!! It's actually a mystery of Mathematics, Why all the positive integers are having same type of end of the sequence. What's forcing them to do so?
    As of 2020, Collatz Conjecture has been checked by computer for all starting values upto 2^68. As a result, It has been found that all these values eventually end in a repeating cycle of (4, 2, 1).
    Although the Collatz Conjecture has been tested for all the values upto such a large number 2^68 but it doesn't mean that the Conjecture is proved. We still have a long way to go before we can say that Collatz Conjecture has been proved by testing even larger numbers
    If we could find even a single positive integer that gives rise to a sequence that does not include 1 or increases without bounds, then the Collatz Conjecture will be disproved. But no such number has been found till date.
    So researchers believe that the conjecture is true based on experimental evidences and heuristic arguments.
    So guys now you are familiar with the simplest unsolved problem in mathematics.

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  • The Collatz conjecture | Famous Math Problems 2 | NJ Wildberger

    33:12

    The Collatz conjecture is tantalizing; simple to state, spectacular in its claim, and notorious for defeating all who attack it. First enunciated by Lothar Collatz in 1937, it has also sometimes been called the Syracuse problem, Kakutani's problem, Ulam's problem, the Hailstone conjecture.

    After stating the conjecture and running through some of the evidence for it, we have a look at some variants, and also some strategies for tackling the problem. One obvious tactic is to look at the problem in base 2; so we first review the fundamentals of arithmetic in base 2. The problem also has a number theoretical aspect.

    Be warned: this problem is addictive, and you might easily catch the bug! More info on it can be obtained from a survey by J. Lagarias.

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  • The Simplest Impossible Problem

    3:57

    A 7-year-old can understand this problem which completely baffles mathematicians.

    Collatz calculator:

  • Collatz Conjecture

    15

    People say that you are wasting your time if you try to solve this problem because this problem is UNSOLVABLE. Behold the Collatz Conjecture. A simple math problem no one can solve, or at least until someone solves it.

    Pick a number (any positive integer)
    If the number is odd - multiply by 3 and add 1
    If the number is even - divide by 2

    Repeat this until you find yourself stuck in a loop. Every positive integer will eventually end up in the 4-2-1 loop. I was curious on this simple math problem after watching the video 'The Simplest Math Problem No One Can Solve' by Veritasium. So I created a MATLAB code to run the problem and all the graphs led to the 4-2-1 sequence. It is simple enough for almost anyone to grasp the problem but difficult to solve.

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  • 5 Simple Math Problems No One Can Solve

    5:25

    5 Simple Math Problems No One Can Solve
    Mathematics can get pretty complicated. Fortunately, not all math problems need to be inscrutable. Here are five current problems in the field of mathematics that anyone can understand, but nobody has been able to solve.


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  • How accurate is Veritasium about the Collatz 3x+1 Problem? - Easy Theory

    26:45

    We correct a minor point on Veritasium's video about the Collatz Conjecture (aka the 3x+1 problem) in that he claimed it may be undecidable. The issue is that, in some reasonable descriptions of the problem, it *is* decidable; just that we may not now what the decider actually is! But in others, it may or may not be decidable. In fact, we give some sufficient assumptions for the 3x+1 problem to be true, which are somewhat reasonable to make based on previous work. (We love Veritasium here! ❤️)

    What is the 3x+1 problem? Take any positive integer x, and apply the following operation: if x is even, divide it by 2; and if it is odd, multiply it by 3 and add 1. The trajectory of x then is the sequence of numbers x, f(x), f(f(x)), etc., where f is the operation. The conjecture claims that every integer x larger than 1 contains 1 in the trajectory of x.

    What are the roadblocks to proving the 3x+1 conjecture? There are three possible behaviors of any trajectory: (1) it contains 1, (2) it contains a repeated value, other than 1--4--2--1--..., or (3) it tends towards infinity. The issue is that one needs to say something about the prime factorizations of the numbers 3x and 3x+1, but these can be wildly different. Think about any power of 2, and one less than it; there is no prime factor in common between them. Yet the conjecture is equivalent to landing on a power of 2 eventually (since that eventually yields 1 always). Another equivalent form of the conjecture is: every positive integer x eventually contains some number less than x in its trajectory exactly once, other than 1, 2, and 4.

    I show the following results:
    (1) Consider the following problem formulation: given a positive integer x, every integer larger than x contains 1 in its trajectory. Then this problem may or may not be decidable (which is an open research question).
    (2) Even if we assume (1) is decidable, the entire conjecture STILL may or may not be decidable.
    (3) If the conjecture is formulated as: construct a language L such that L = {1} if the 3x+1 conjecture is true, and L = {0} otherwise, then unconditionally L is decidable.
    (4) If the following assumption is made: there exists an n0 such that every number x larger than n0 contains 1 in its trajectory, then the 3x+1 problem is decidable (and further, any counterexample involves a cycle, and not tending towards infinity).

    It's important we understand the technical terms so that we can be accurate in communicating technical topics like this one. I also give the example of Turing Machines and Linear Bounded Automata to show that just because a larger class of problems is undecidable, does not imply the smaller class is undecidable.

    All of the rest of the video is great, please check it out; just this one item needed correcting.

    Veritasium's video:
    Reddit thread:

    Timeline:
    0:00 - Intro
    0:08 - Part of Veritasium's Video
    0:50 - Beginning of my Rant
    2:12 - One Encoding of the 3x+1 Problem
    6:30 - Why Generalized Problem does not imply Specific problem behavior
    10:25 - A Decidable Encoding of the 3x+1 Problem
    15:40 - How a (reasonable, possible) assumption can show Decidability
    23:16 - Recap

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  • When the correct answer isnt even an option. #Shorts

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    What is 2 + 2x4 = ? Many people are having arguments about this problem. It's time for the order of operations to save the day, again! #shorts

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  • The Simplest Math Problem No One Can Solve

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  • impossible maths problem solved collatz conjecture solved

    1:23

    the collatz conjecture solved collatz conjecture solution for collatz conjecture solved 3n + 1 3x +1 proof

  • The unsolved math problem which could be worth a billion dollars.

    5:59

    No one on Earth knows how to reverse one of the most popular computer algorithms. Yet it's really easy to compute one-way. You could make billions of dollars if you solved this mathematics problem, which is computed quintillions of times per second in the race for mining Bitcoin. SHA256 has some amazing properties, is useful for digital signatures, cryptography, authentication, and is a central part of the Bitcoin protocol.

    (**** UPDATE 2021: After two years, I've finally posted a follow-up video, an introduction to Bitcoin. You can find it here: )

    Bitcoin and other crypto-currencies rely on one-way hash functions like the SHA-256 algorithm to secure the blockchain where all the transactions are kept.

    In this video, I explain some of the big-picture ideas behind this one function. Other cryptocurrencies use similar ideas.

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  • A slacker was 20 minutes late and received two math problems… His solutions shocked his professor.

    7:13

    Today I will tell you a relatively short story about a young man, which occurred many years ago. Even though the story contains nothing supernatural, I’m not exaggerating when I say that it was able to change the lives of millions across the world. In one way or another, every self-respecting successful person knows about it, and I think each one of you should hear it as well.

  • How I FAILED to solve the Collatz Conjecture

    5:52

    Since this has become a bit of a popular topic, I thought I'd share my own failed attempts at solving this long standing open problem. The Collatz problem is also known as the Collatz Conjecture or the 3x+1 Problem. As many of you have seen already, Veritasium recently uploaded a video talking about the problem and some successes by members of the mathematical community. I'm definitely not one of those guys.

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    #Veritasium #Collatz

  • The Simplest Math Problem No One Can Solve But I Can #shorts

    12

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  • Collatz Conjecture Visualisation

    4:54

    The Collatz conjecture is a conjecture in mathematics that concerns sequences defined as follows: start with any positive integer n. Then each term is obtained from the previous term as follows: if the previous term is even, the next term is one half of the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1. The conjecture is that no matter what value of n, the sequence will always reach 1.
    Read more on

  • Collatz Conjecture in Color - Numberphile

    6:18

    The Great Courses Plus (free trial):
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  • THE COLLATZ PROOF 20201229-THE TEOTL THEOREM

    9:28

    Hello World,

    I am sharing the solution that I found to the Collatz Conjecture and similar problems dealing with integer values. If you are curious to know more about what I call the Teotl Theorem, refer to (for an eBook or Poster). YouTube has a limit on video length set to 15min so I decided to keep the video short and simple. Even when some terms appear complicated, they are not. The book has a full description of terms used and more detailed explanation of the actual Theorem and its principles.

    Do share your comments and/or questions!

    If you want to do a full review of the eBook covering Collatz, Goldbach, Polignac and Riemann's Hypothesis but you reside in one of the classified Developing Countries, send me an email and I will share the eBook and you don't have to pay anything.

    For Youtube conversation files shared on multiple comments refer to the following link:

    cescamilla@archeeng.com.
    Enjoy the rest of your day!
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  • Math Has a Fatal Flaw

    34:00

    Not everything that is true can be proven. This discovery transformed infinity, changed the course of a world war and led to the modern computer. This video is sponsored by Brilliant. The first 200 people to sign up via get 20% off a yearly subscription.

    Special thanks to Prof. Asaf Karagila for consultation on set theory and specific rewrites, to Prof. Alex Kontorovich for reviews of earlier drafts, Prof. Toby ‘Qubit’ Cubitt for the help with the spectral gap, to Henry Reich for the helpful feedback and comments on the video.

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    References:

    Dunham, W. (2013, July). A Note on the Origin of the Twin Prime Conjecture. In Notices of the International Congress of Chinese Mathematicians (Vol. 1, No. 1, pp. 63-65). International Press of Boston. —

    Conway, J. (1970). The game of life. Scientific American, 223(4), 4. —

    Churchill, A., Biderman, S., Herrick, A. (2019). Magic: The Gathering is Turing Complete. ArXiv. —

    Gaifman, H. (2006). Naming and Diagonalization, from Cantor to Godel to Kleene. Logic Journal of the IGPL, 14(5), 709-728. —

    Lénárt, I. (2010). Gauss, Bolyai, Lobachevsky–in General Education?(Hyperbolic Geometry as Part of the Mathematics Curriculum). In Proceedings of Bridges 2010: Mathematics, Music, Art, Architecture, Culture (pp. 223-230). Tessellations Publishing. —

    Attribution of Poincare’s quote, The Mathematical Intelligencer, vol. 13, no. 1, Winter 1991. —

    Irvine, A. D., & Deutsch, H. (1995). Russell’s paradox. —

    Gödel, K. (1992). On formally undecidable propositions of Principia Mathematica and related systems. Courier Corporation. —

    Russell, B., & Whitehead, A. (1973). Principia Mathematica [PM], vol I, 1910, vol. II, 1912, vol III, 1913, vol. I, 1925, vol II & III, 1927, Paperback Edition to* 56. Cambridge UP. —

    Gödel, K. (1986). Kurt Gödel: Collected Works: Volume I: Publications 1929-1936 (Vol. 1). Oxford University Press, USA. —

    Cubitt, T. S., Perez-Garcia, D., & Wolf, M. M. (2015). Undecidability of the spectral gap. Nature, 528(7581), 207-211. —

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  • Collatz - The Long Sought Visual Pattern in the Collatz Conjecture

    8:19

    In this video, the long sought visual pattern in the Collatz conjecture, is presented. With the discovery of this never before seen visual pattern, a new way has opened up to solving this 80 year-old conjecture.

    1. View my Collatz generalization that can generate infinite Collatz-like functions that converge to 1:

    2. For more information, you can read my arXiv article at Three significant results are presented in the paper:
    (i) the discovery of the long sought visual pattern in the Collatz Conjecture
    (ii) the link between the Collatz conjecture and prime numbers, and
    (iii) the proof that the conjecture contains no non-trial cycles.

    3. Update: The new sequence referenced in this video is now added to the Online Encyclopedia of Integer Sequences. Find out more at You can also add tot his work there.

    4. Collatz (Part 2) –

  • How Imaginary Numbers Were Invented

    23:29

    A general solution to the cubic equation was long considered impossible, until we gave up the requirement that math reflect reality. This video is sponsored by Brilliant. The first 200 people to sign up via get 20% off a yearly subscription.

    Thanks to Dr Amir Alexander, Dr Alexander Kontorovich, Dr Chris Ferrie, and Dr Adam Becker for the helpful advice and feedback on the earlier versions of the script.

    ▀▀▀
    References:
    Some great videos about the cubic:

    500 years of not teaching the cubic formula. --

    Imaginary Numbers are Real --

    Dunham, W. (1990). Journey through genius: The great theorems of mathematics. New York. --

    Toscano, F. (2020). The Secret Formula. Princeton University Press. --

    Bochner, S. (1963). The significance of some basic mathematical conceptions for physics. Isis, 54(2), 179-205. --

    Muroi, K. (2019). Cubic equations of Babylonian mathematics. arXiv preprint arXiv:1905.08034. --

    Branson, W. Solving the cubic with Cardano, --

    Rothman, T. (2013). Cardano v Tartaglia: The Great Feud Goes Supernatural. arXiv preprint arXiv:1308.2181. --

    Vali Siadat, M., & Tholen, A. (2021). Omar Khayyam: Geometric Algebra and Cubic Equations. Math Horizons, 28(1), 12-15. --

    Merino, O. (2006). A short history of complex numbers. University of Rhode Island. --

    Cardano, G (1545), Ars magna or The Rules of Algebra, Dover (published 1993), ISBN 0-486-67811-3

    Bombelli, R (1579) L’Algebra

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  • Iss maths problem ko aaj takk koi solve nahi kar paya | Collatz Conjecture in hindi

    10:19

    Collatz Conjecture in hindi | Sabse aasan maths problem jisse koi solve nahi kar paya | Easiest maths problem no one can solve

    Aaj hum ek aise maths problem ke baare mein baat karenge, jisse ek 3-4 standard ka student bhi samajh sakta hai, lekin jisse aaj takk koi bhi mathematician solve nahi kar paya hai. Ye problem hai Collatz Conjecture.
    Iss problem mein sirf do rules hain. Aap kisi bhi positive number se start kar sakte hain aur agar wah even hai to use 2 se divide karna hai aur agar odd hai to usko 3 se multiply karke usmein 1 add karna hai.
    Aur ye rule apply karte jana hai. Interestingly aap kisi bhi number se start karein aap humesha 1 pe hi pahuchenge.

  • Did Terence Tao prove Collatz Conjecture

    1:49

    Although Terence Tao didn't completely prove the Conjecture but his work is a significant leap.
    At certain times the text might change a bit quickly . Plz do accept my apologies for that.

    Original work:
    Don't forget to SUBSCRIBE .


    Check out some amazing books for high school mathematics:

    Copyright Disclaimer Under Section 107 of the Copyright Act 1976, allowance is made for fair use for purposes such as criticism, commenting, news reporting, teaching, scholarship, and research. Fair use is a use permitted by copyright statute that might otherwise be infringing. Non-profit, educational or personal use tips the balance in favour of fair use.

  • One step forward to Collatz Conjecture proof?

    5:50

    In this video, I attempt to show an approach to finding a couple interesting patterns for the infamous Collatz Conjecture, aka 3x+1 problem. I also provide formulas and a few graphs that clearly indicate these patterns which do not seem to have exceptions. I have scanned the currently developed patterns and graphs on the Internet and decided to share.

    Edit: Eventually was told that this was discovered in 2006:

  • Collatz Conjecture - Numberphile

    6:02

    Main video on Collatz Conjecture:
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  • Poincaré Conjecture - Numberphile

    8:52

    The famed Poincaré Conjecture - the only Millennium Problem cracked thus far.
    More links & stuff in full description below ↓↓↓

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    Discussed here by Katie Steckles and James Isenberg.

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  • Catalans Conjecture - Numberphile

    8:06

    With Dr Holly Krieger from Murray Edwards College, University of Cambridge.
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  • The Math Problem With a $1 Million Prize for Solving

    6:16

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  • Day 2 - The notorious Collatz conjecture - Terence Tao

    50:03

    at Liceo Scientifico Galileo Ferraris

  • 8 Math Problems No One Knows the Answers to

    7:45

    8 Easy to understand Math problems which no one has found answer to.


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    Refrences:






    Timestamps:
    0:00 Introduction
    0:24 Unsolved Problem 1 - Goldbach Conjecture
    1:28 Unsolved Problem 2 - Mondrian Puzzle
    2:38 Unsolved Problem 3 - Collatz Conjecture
    3:17 Unsolved Problem 4 - Legendre's Puzzle
    3:57 Unsolved Problem 5 - Moving Sofa Problem
    5:01 Unsolved Problem 6 - Twin Prime Conjecture
    5:28 Unsolved Problem 7 - Can every number be written as sum of 3 cubes
    6:25 Unsolved Problem 8 - Inscribed Square Problem
    6:57 Conclusion



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  • 3+1 The Collatz conjecture the only proof the ultimate proof by Jesus Duenas Jr short version

    21:07

    The Collatz conjecture 3(x)+1 is a very simple conjecture to understand, but very difficult to proof.
    Together we will discover the world of 3(x)+1, the laws that govern the system, we will discover why is true and never will be false. I challenge you to show me where is the error, where is my mistake, why nobody have found a solution? if you do not find a mistake in my arguments, then I just proof the 80 years old conjecture.
    Veritasium video


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    Insights into mathematics


    Discovermaths

  • Explore the Collatz Conjecture or the 3N+1 Problem

    5:07

    Pick a number. If it's even, halve it. If it's odd, triple it and add 1 (3N+1). Repeat. Will you always end in a 4-2-1 loop? Starting from a number less than 100, what's the highest number you can reach? What's the longest series you can create? So many questions to explore. Mathematicians still don't have all the answers! Enjoy.

  • Collatz Conjecture: Fractals, Networks, And Harder Problems

    19:58

    A child can easily understand the Collatz conjecture, but nobody can prove it. Even after 50 years work by some of the best mathematicians, the problem is unsolved. We look at beautiful fractals and networks that come from the problem.

    This is a famous unsolved problem in elementary mathematics. Many famous mathematicians have tried to prove or disprove the conjecture and consequently it has acquired many names (the Ulam conjecture, the 3n + 1 conjecture, Kautani's problem, Thwaites conjecture and the Syracuse problem). Even the great Paul Erdos (who published more mathematics papers than anyone) thought that mathematics was not ready for such a problem.

    Despite resisting attacks from so many great mathematicians, the Collatz conjecture is extremely easy to understand. Most ten year old children should be able to grasp it.

    The Collatz conjecture says that if you start with any positive whole number, and you keep doing the following operation:

    If the number is even, then change it by dividing it by two, otherwise change it my multiplying it by three and then adding one,

    then you will eventually get to number 1.

    A proof or disproof of this open conjecture would be well accepted by the mathematicians of the world.

    There are many mathematical objects related to the Collatz Conjectue (the hailstone sequence, wondrous numbers, and Hasse's algorithm), but as far as I know the central problem is still open.

    In this video I focus on interesting objects related to the generalizing the Collatz conjecture. In particular, I discuss the Collatz fractal, which was first considered by Letherman, Schleicher, and Wood (1999).

    The idea here is to extend the Collatz problem to the complex plane and create a fractal (somewhat akin to Julia sets and Mandlebrot sets) which can be colored to show which complex numbers converge or diverge as the extended Collatz operator is iterated.

    I also examine various other closely related problems which I found by exploring networks where vertices represent numbers and edges represent simple operations (like multiplying by three and adding one). Using this novel approach we immediately see that the network associated with the Collatz problem is highly complex, however we also see a great many other very similar looking problems which also generate highly complex networks, and therefore probably also correspond to extremely difficult problems of number theory.

    This work reveals many interesting new object that can be generated by `double valued mappings'. It also shows that there are many systems which are very closely related to the Collatz conjecture, but which are also extremely complex.

    This work on networks derived from `double valued mappings' is my own research, although it was inspired by the `Multiway Systems Based on Numbers' Wolfram Demonstration by John Cicilio.



    More details about my work on this see

    Experimental Complex Networks, Numbers, Collatz Problem


    and my website

  • No One Can Solve_The Simplest Math Problem/ #challengingmathproblems #integralequation/#integral

    9:49

    Integral is the simplest math probleme no one can solve
    Math,mathématique,mathway,mathematics,integral,algorithme,fonction,equation,الرياضيات ،le seceet de math

  • The 3n+1 Conjecture, Episode 35

    2:45

    A 3n+1 variation that can translate Swahili poetry into English #collatz collatz conjecture 3x+1

    Reference: J. H. Conway, FRACTRAN: A Simple Universal Programming Language for Arithmetic.

  • Collatz Conjecture

    6:06

    The Collatz conjecture is a sequence where you start with a positive integer n, and follow certain rules. The rules are: if the prior integer is even, the next number is one half of that number. If the prior number is odd, the next number is 3 times the previous number plus 1. The conjecture is that no matter what the value of n is, the sequence will always reach 1.

  • I tried solving Collatz Conjecture !

    8:28

    Hey guys,
    This is my first video....

  • The 3n+1 Conjecture, Episode 36

    2:17

    When you innocently step across the Line of Total Incomprehension #collatz collatz conjecture 3x+1

    Did I say internal dialogue?

  • Collatz Conjecture - An UNSOLVED Problem of Mathematics | A Chance To Create History | Abhay Sir|VOS

    8:13

    Collatz Conjecture - An UNSOLVED Problem of Mathematics | A Chance To Create History | Abhay Mahajan | Vedantu Olympiad School | Maths Olympiad 2021 | Maths Olympiad Preparation | PRMO 2021 | IMO 2021

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    We hit a century in our debut year by helping more than 100 NTSE Scholars clear NTSE. Vedantu claimed 5% of the total NTSE Stage-2 Results. Now it’s time to move ahead and aim at helping more students grab NTSE fellowships and in order to do so, Vedantu is here with the NTSE Stage-2 Test Series. A specially designed test series that will test your NTSE Stage-2 Preparations. This test series is curated by subject experts who have produced many NTSE Scholars over the years. So, what are you waiting for? If you are aiming at becoming NTSE Scholar then this is the Golden Opportunity for you.

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  • THE 10 HARDEST MATH PROBLEMS THAT REMAIN UNSOLVED

    2:08

    Thanks for watching!

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  • No one can solve the simplest math problem Bangla

    2:33

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

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

    Tao, T (2020). The Notorious Collatz Conjecture —

    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. —

    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. —

    #mathematics
    #simplemath
    #mathsolution

  • Quick Look at Collatz Conjecture

    5:26

    I'm not an expert, if you fail your math final its not on me.

  • An Automated Approach to the Collatz Conjecture

    48:51

    Emre Yolcu (Carnegie Mellon University)

    Theoretical Foundations of SAT/SMT Solving

  • Visualizing Collatz Conjecture using Python

    2:25

    The Collatz Conjecture is a long standing problem in Mathematics. Here is a small visualization of the problem to help you understand it better.

    For a detailed read :

    Song: Jay Someday - Come Along
    Music provided by Vlog No Copyright Music.
    Creative Commons - Attribution 3.0 Unported
    Video Link:

    #Mathematics​ #CollatzConjecture #Conjecture #NumberTheory​ #Python

  • Do Math to Get Rich and Famous!: The Collatz Conjecture

    5:25

    Want a million dollars? Prove I'm not psychic. Pick a number, any number. If it's even, divide it by 2; if it's odd, multiply it by 3 and add 1. Keep doing this, I predict you'll eventually get to 1.

    Example: Suppose I pick the number 3. This is odd, so I multiply it by 3 and add 1, this gives me 10, which is even. I then divide 10 by 2 to get 5, which is odd. I then multiply by 3 and add 1 to get 16, which is even. I divide this by 2 and get 8, which is even. I then divide 8 by 2 to get 4, which is still even. I then divide 4 by 2 to get 2, which is even, and then I divide 2 by 2 to get 1. I win!

    This is called the Collatz Conjecture.


    Like/Subscribe/Comment/Share, I reply to everyone, guaranteed! Think you've proved me wrong? Let me know in the comments!

  • The Problem 51% Of People Cant Solve

    7:29

    How does your brain work? These simple puzzles will reveal a lot!
    The first 1,000 people to use this link will get a 1 month free trial of Skillshare:
    Subtraction Podcast Episode:

    Huge thanks to Leidy Klotz (and his co-authors of the paper) for helping out with this episode.

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  • Solved? Collatz Conjecture solving using binary representation, 3x+1, 3n+1

    2:26

    #Collatz Conjecture #Гипотеза Коллатца
    Solving of Collatz Conjecture regarding the impossibility of an infinite increase in the numbers 3x + 1 using binary representation

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