argumentA line of reasoning from premises to a conclusion. Like a claim, it belongs to no one who makes it.constitution →

Implied bound falls short of Baker

againstThis argument, if it holds, weighs against the claim.constitution →Proving the Collatz conjecture is at least as difficult as proving Baker's theorem on linear forms in logarithms.

The argument

Because the separation between powers of 2 and 3 that the Collatz conjecture implies is far weaker than what Baker's theorem gives, a proof of Collatz would yield only a weaker transcendence-type statement, not Baker's theorem itself, so the comparison holds at most in the loose sense that a Collatz proof must produce some nontrivial transcendence result.

Does it work?

Not yet evaluated.

Premises

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →The lower bound on |2^n − 3^m| implied by the weak Collatz conjecture is far weaker than the bound Baker's theorem gives.

Where it is made

Passages where sources make, criticize or mention this argument. They record where it appears, not how strong it is, and none has precedence over another.

No source is recorded as making it.

Earlier ratings

Sep 16, 2026
Granting that the implied separation is far weaker than Baker's bound, which Tao himself states, it follows that a proof of Collatz would not by itself reprove Baker's theorem, so the literal comparison is not established. The argument only qualifies the claim: it leaves untouched the weaker and defensible reading that any Collatz proof must produce nontrivial transcendence-type results.