Will the Collatz Conjecture be proved true by December 2024? | Manifold

Will the Collatz Conjecture be proved true by December 2024?

7

270Ṁ988

resolved Oct 13

ResolvedN/A

0.2%

Yes, and the Japanese $1M prize will be won.

0.2%

Yes, and the Japanese $1M prize will not be won.

92%

No

6%

Yes

1.4%

Yes, but there will be a disagreement among mathematicians as to whether the proof is correct or not.

0.2%Other

A proof has been suggested on Quora for "the nth terms of convergence of the Collatz map".

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 \(1\). \[ f(x) = \left \{ \begin{array} \\ x \mathbin{/} 2 & (x \equiv 0 \pmod 2) \\ 3 x + 1 & (x \equiv 1 \pmod 2) \end{array} \right. \]

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