The Collatz Conjecture: Easy Enough for a 3rd Grader, Hard Enough for Terry Tao

The Collatz Conjecture has been called the simplest math problem no one can prove. It has captivated mathematicians for two generations. In today's Math Minute (the fiftieth Math Minute!), I want to look at just what is so surprising about the Collatz Conjecture, and talk about a few ways it might eventually be proven true or false.

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randolph college is the best

[jackwijma]

Congrats on the 50th math minute, that’s like, almost an hour!!

[ImperfectKingdomSeeker]

I think some numbers are landmines i.e. they hit a power of 2 and it's obvious they immediately go down to 1.

I think other numbers are sneaky - they might not necessarily hit a power of 2 but rather take a long time getting down to 1 with lots of ups and downs.

[olezhekt]

In the description for this video you wrote you would talk about a few ways this conjecture might eventually be proven true or false. I do not think you have mentioned a single way (obviously, simply keeping checking larger and larger numbers by brute force is a futile approach).

[thegamehunter]

The funny thing is that I have already tried to solve this conjecture last year, with the knowledge of the 9th grade math😂😂, and as expected, I couldn't do too much than overcomplicate. But there must be a way to do it, it's pure logic...

[speedycpu]

I've tested numbers to in various chunks (not ALL numbers, obviously), but the many millions I did test always went back to 1. It would take many millions of iterations to get there, but they do.

[TymexComputing]

Answering the question i think it will not become proved nor disproved.

[soufianehemza]

I am working on collatz for 4 months
I have proved it with 6 different ways
IT has a fixed pattern
I can now calculate the far away number in sequence directly even if it's the or greater
2 additinal ways to represent the function
a cooming book about that this month

[jamestagge]

So, it is obvious that if any odd number is multiplied by 3, the result will also be odd, e.g., 3 x 3 = 9 and 3 x 9 = 27, etc. This is simply because the last digit in the multiplication which is odd, multiplied by an odd number, structurally cannot be but odd. It follows then, logically that the addition of 1 will make it even, i.e., it changes the last digit (or the only digit if a one digit number) to an even number. Then the division by 2 will always be possible because the number being divided, as per the above, is always going to be even. The problem then arises when dividing an even number which can result in two odd numbers of equal value such as in 10/2 = 5. If then there is a particular structure in the application of this process, it should be predictable.
Note an example of a structure…….in each column the black numbers are increments of 10 as would be expected. The red numbers in the columns are separated each by 30. The columns of black numbers each of which is the product of halving the even numbers are separated each by 5. The red numbers in rows are separated by 6. The black numbers in rows, the divided product of the numbers above are separated by 1. I believe that given this structure, it should be understood that the progression would have to always come back down to 1 and loop.
1 2 3 4 5 6 7 8 9 10
4 1 10 2 16 3 22 4 28 5

11 12 13 14 15 16 17 18 19 20
34 6 40 7 46 8 52 9 58 10

21 22 23 24 25 26 27 28 29 30
64 11 70 12 76 13 82 14 88 15

31 32 33 34 35 36 37 38 39 40
94 16 100 17 106 18 112 19 118 20

41 42 43 44 45 46 47 48 49 50
124 21 130 22 136 23 142 24 148 25

51 52 53 54 55 56 57 58 59 60
154 26 160 27 166 28 17 29 178 30

31 32 33 34 35 36 37 38 39 40
94 16 100 17 106 18 112 19 118 20

41 42 43 44 45 46 47 48 49 50
124 21 130 22 136 23 142 24 148 25

[kadersalah]

ما رأيك في تمديد حدسية كولاتز على جميع الاعداد الصحيحة وذلك بتغير العبارة 3n+1 إلى 3n+1_ حيث نحصل على متتاليات اعداد فيها مزيج من الاعداد الفردية الموجبة والسالبة وكلها تتقارب نحو الواحد

[gabenuss]

When you ask "Will it be proven or disproven in a certain amount of time?", you assume that it can definitively either be proven or disproven. Kurt Gödel would not approve! JK😂

[TheGuyCalledX]

Technically you'd never end up with less than $4 because you could always play until you had $4

[blair]

Someone needs to invent a new math to tackle this problem. Mathmeticians and/or novices need to quit trying to prove the conjecture with existing math which is apparently not useful.

[sergiopaganoti]

So was Paul Erdos right?
Maybe in a year or in centuries...

[Tabu]

Is this secretary the haulting problem?

[Loots]

its not all numbers, its all positive integers, big difference

[farahabdullahi]

I’m a third grader but this is my moms Chanel

[martinkotze]

Is it so difficult to prove because of the "if" before each operation?

[alikaperdue]

There are no special numbers that go on forever or loop. The conjecture is true. I can prove it in a way that I have not seen yet. I'm searching for someone else who said what I am thinking. You didn't touch it on this video. Maybe I have something.

[gobyg-major]

Actually 3 times any even number makes an odd number, not any odd number…..

[patrickwithee]

The fact you make this about investments makes me sick.