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MANIFOLD
Will the Collatz Conjecture be proved true by December 2025?
40
Ṁ1.4kṀ4.4k
resolved Jul 24
Resolved
YES
No
Resolved
NO
Yes, and the Japanese $1M prize will be won.
Resolved
NO
Yes, and the Japanese $1M prize will not be won.
Resolved
NO
Yes
Resolved
NO
Yes, but there will be a disagreement among mathematicians as to whether the proof is correct or not.
Resolved
NO
There will be a third, and final, proof

A proof has been suggested on Quora for "the nth terms of convergence of the Collatz map". (I am restarting this market as multiple choice, now Manifold has that option.)

There are two parts to the proof:

A general statement of the theorem, https://qr.ae/pyD8Nk, and an inductive proof of that theorem, https://qr.ae/pKRv1A. 

The ambiguity is whether or not proving convergence of the nth terms is the same as proving all sequence Ns converge on 1.

A third, generalized, proof may be published on Quora. 

If you want to learn about the conjecture and its place in contemporary mathematics, watch the Veritasium video on YouTube: https://youtu.be/094y1Z2wpJg

About the prize: https://mathprize.net/posts/collatz-conjecture/

Collatz conjecture Prize 120 million JPY
A prize of 120 million JPY will be paid to those who have revealed the truth of the Collatz conjecture. The conjecture is also known as the \(3x + 1\) problem or the \(3n + 1\) problem. 120 million JPY in USD Collatz conjecture Repeatedly applying the function \(f(x)\) defined below to any positive integers will eventually result in \(1\). \[ f(x) = \left \{ \begin{array} \\ x \mathbin{/} 2 & (x \equiv 0 \pmod 2) \\ 3 x + 1 & (x \equiv 1 \pmod 2) \end{array} \right. \]
Market context
Math
Science
Unsolved Problems
Collatz
Conjecture
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@creator I see this is unlisted, do you still intend to resolve it or do you want it to be N/A'd?

Hi @michelangelo - I’m confused about the resolution criteria for your market, as have traders for months (as can be seen from scrolling down). Since I’m worried that people will bet on things they don’t realize they’re betting on, or will misinterpret probabilities, I’ve decided to unlist your market until you provide greater specificity. Thanks!

I didn't like the papers. Not enough words, unreadable. He throws numbers around, instead of showing how from a set of statements A follows that some statement B has to be true.

If the proof had any hope of being real, it wouldn't be suggested on Quora.

@TimothyJohnson5c16 the proof is obviously wrong but we're betting on the market creator's resolution 😅

Lol, have fun! I'm not touching this one.

WTF is this market? Caveat emptor indeed.

Wait a second. The author of the claimed proof made a market and is betting on "Yes, but there will be a disagreement" and didn't exactly specify resolution criteria? I'm a moron for even touching this market.

@MichaelMRoss yep, some detailed criteria would be nice, especially for the "yes, but no prize" and "yes but controversy" options.

@EvanDaniel These things never go exactly according to plan. Look up the history of Andrew Wiles proof of Fermat's Last Theorem. As for the prize, look at the fine-print in order to win.
If I was clairvoyant, I wouldn't be asking the question!

Will you do like Wiles did and accept it if your proof is shown to be wrong? He had to work a couple more years after the first proof attempt was shown to be flawed.