Deep theorems were scarce, and AI has broken that signal
Kra argues that deep theorems were a proxy for understanding, and AI has made the proxy cheap. Research software has lived with a weak proxy for longer: credit goes to papers, not to the tests, documentation and maintenance that make the code trustworthy. Now AI makes those cheap to produce too, so they stop being a signal either.
[…] Our incentive structures are misaligned with the prolific output of highly accessible AI models. Careful verification and stellar exposition will not happen when there is no reward for those tasks. Producing a paper is no longer enough: authors must be able to explain the proof’s mechanism and how they arrived at this point. Journals need to distinguish and credit the roles of discovery, proof, formalization and explanation. […]
True of open source too. A test suite and documentation used to signal care; now an agent writes both in minutes. And we used to review the code we and our peers wrote; with agentic engineering we can’t keep up. Give up the speed, or the verification.
[…] The creation of collective understanding, the ability to communicate ideas in a lecture, and the sharing of ideas informally that spark research have always been admired. Such achievements are harder to quantify than theorem production, and so have been treated as by-products. […] Our incentive system needs to be realigned to reflect what we truly value, and not just what we can easily measure.
By-products: tests, CI, benchmarks, documentation—sometimes the software itself. The fields RSEs support run on publish or perish. We don’t publish directly, but we inherit the pressure: our collaborators aren’t rewarded for by-products, and every hour spent on them is an hour not spent on the next paper.
Mathematics is the canary in a coal mine for all parts of intellectual life. Its claims can be carefully checked and so we are witnessing the disruption in real time. […] Science, law, public policy, and art will all have to find ways to assess what is valuable amidst the abundant output.
Research software included.
The arrival of machine generated mathematics does not replace the role of human expertise. Instead it reveals why we valued that expertise. […] It will take our entire community to create new standards, discover new ways of creating mathematics, work with AI models to open new horizons of knowledge, and develop the tools to approach them. It’s truly an exciting time to be a mathematician.
United or fragmented? Polarization over AI distracts us from finding an equilibrium where we can thrive.