Knowledge Work

Mathematics has a management problem. That sounds less romantic than saying it has a reasoning problem, but romance is not usually where bottlenecks hide. A proof can be brilliant, a referee can be diligent, and still the verification system can fail for the boring reason that nobody has enough time to check everything line by line. The paper Automatic Textbook Formalization takes that bottleneck seriously and then does something unusually concrete: it reports a multi-agent system that formalized a 500-plus-page graduate algebraic combinatorics textbook into Lean, with all 340 target definitions and theorems proved, in about one week.1 ...

A customer-support bot fails in the most ordinary way. It retrieves the right policy document. It identifies the right customer case. It even quotes the correct refund condition. Then, somewhere between retrieval and answer synthesis, it forgets that the customer bought the product through a reseller, not directly from the company. The final answer is plausible, polite, and wrong. The system did not lack information. It lacked coordination. ...