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Simple answer: of course there is. The real challenge is finding such strings.

If I wanted to know the answer to that question, I'd first search some precomputed rainbow tables to see if anybody's gotten lucky:

http://project-rainbowcrack.com/table.htm

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The discussion on security.SE seems to imply it's unknown: https://security.stackexchange.com/questions/107081/does-eve... so if you have a proof of your simple answer, I'm sure they'd welcome it

My statement is one of statistically-informed confidence. A physicist's proof, not a mathematician's. As I said, proving it is where the challenge lies.

I believe proof-by-induction is still a mathematically valid proof. Just one to be suspicious of/can be overridden by more rigid proofs.

Induction is a mathematical tool. Overwhelming statistics is the physicist's.

The linked answer on SE basically says statistically there's a near-100% chance that there's a string where md5(string) is 0xfffffff... but there's no concrete proof.

Which is basically the same thing the GP says.

Do you mean just that it is very very likely that there is, or is there some argument that the MD5 function must be surjective?

It is not known to be surjective.

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