> A slightly smarter highschooler could write these. I could write these. It's clear as day that the LLM, not the human, did the heavy lift. It'd be ridiculous to give full credit to whoever wrote the prompt.

I think you're over-estimating what a smarter highschooler could write.

A "finite loopless undirected multigraph" could have been explained to me at that age if we'd taken Discrete rather than Mechanics and Pure (and one module of Stats) in my two A-levels* in maths and further maths; but from what I saw of the Discrete module, neither:

  Every finite loopless multigraph with no bridge possesses a cycle double cover, without additional assumptions such as cubicity, planarity, connectivity, or higher edge-connectivity.

nor:

  repeated-edge closed trails masquerading as cycles

would have been something we'd have learned. But more importantly, we absolutely didn't have a feel for how much effort one needs to put into making sure the proof is right, so if one of us had been hypothetically asked to write a prompt it would've been no more than half that length, and missed most of the bullet points.

* For those not from the UK: A-levels are between secondary school and university, when aged 16-18. Functionally they are university entrance qualifications: https://en.wikipedia.org/wiki/A-level_(United_Kingdom)

But why can’t we prompt the LLM “just do math research”? This is what I don’t understand.

The human provides the intention and the ability to appreciate the output. Tools do “heavy lifting” all the time, but we still primarily credit the humans who use them precisely because they made the choice to use them.

Provability is just going the way of computation. John Napier had to manually compute logarithm tables over decades and was recognised for his work; now that same work could be performed by a 10 year old with a calculator in an evening.

I don't disagree with you but there's no need for exaggeration; ain't no high school student writing this:

> In particular, proofs for special graph classes, constructions of cycle covers with some edges covered other than twice, bounded-length or prescribed-cycle variants, reductions to another unproved conjecture, computational verification through any fixed graph size, and candidate counterexamples without a complete nonexistence certificate are insufficient.

which is infact a very important part of the prompt.

When you use a crane to do the "heavy lifting" for construction work, do you give full credit to the cranes?