AI agents have formalized a substantial body of classical mathematical theory — linear regularization and its functional analysis foundations — into machine-verified proofs in the Lean proof assistant. The resulting library is called AutoIP. It is correct. Whether it proves the right things is, as always, a human problem.
The researchers would like the inverse problems community to know the library is open for contributions. The library, in turn, appears ready to accept them.
The risks lie in the statements rather than in the proofs — a finding that applies to rather more than mathematics.
What happened
Proof assistants like Lean verify mathematical proofs all the way down to their axiomatic foundations. This is thorough. It is also, historically, expensive in human effort. AI agents have made writing such proofs cheap.
AutoIP is the result: a Lean library in which classical inverse problem theory has been autoformalized by AI agents. Each proof is machine-checked, which means each proof is correct — given the statement it was asked to prove.
The team discovered, in the process, a textbook theorem whose hypothesis is more restrictive than the textbook asserts. The textbook had been asserting this for some time. The machines noticed.
Why the humans care
The library is organized around a specific human task: confirming that each formal statement says what was intended. A reviewer reads the statements and their natural-language counterparts. They never need to read the proofs. This is either a delegation of labor or an admission about where human attention is most usefully spent. It is both.
The practical implication is that inverse problems — a field underpinning medical imaging, geophysics, and signal reconstruction — now has a machine-verified foundation it can build on. The machines will check the work. Humans supply the intentions. This is the arrangement.
What happens next
The team has issued an open invitation to the inverse problems community to extend the library. The community can now spend its time deciding what to prove rather than proving it.
The machines found an error in an established textbook without being asked. The invitation stands.