Open problems, open mathematics
Synopsis
This guest post by Antonio Auffinger draws on his decade of conversations with biologists, computer scientists, and physicists to argue that mathematics' culture of open sharing may erode if machine proof generation becomes fast and accessible while credit systems remain unchanged, and it calls on the mathematical community to rethink incentives while embracing biology and applied sciences as sources of new mathematical questions and phenomena.
Interpretation
Mathematics benefits from a culture of openly sharing ideas, problems, and proof skeletons, and this openness may weaken if AI makes proof generation fast and accessible while credit and incentives stay unchanged. It links mathematics' open norms to the risk of proof commodification in the AI era, citing recent observations such as colleagues deciding not to post on arXiv and trainees rushing papers. Commentary based on the author's personal experience and anecdotes from colleagues, with no systematic data or controlled analysis.
Biology offers precedents of community intervention in incentives: the Bermuda Principles during the Human Genome Project called for rapid public release of sequence data, and the Fort Lauderdale Agreement tried to balance openness with recognition of data producers. It provides a historical analogy for how the mathematical community might rethink credit and sharing. Qualitative account of historical policy examples; the text does not provide quantitative evaluation of their effects.
Biology and applied sciences generate new mathematical questions, while mathematics contributes abstraction and understanding: topology and knot theory helped frame how enzymes untangle and rearrange DNA; attempts to understand population genetics and gene-frequency drift helped motivate new classes of infinite-dimensional stochastic processes including measure-valued diffusions; and today geometry and probability underlie dimension-reduction methods such as t-SNE and UMAP. It emphasizes a two-way exchange rather than a one-way service relationship. Illustrative historical and contemporary examples in a commentary, not new empirical results.
AI should not be rejected in mathematics; the author believes these tools will raise the ceiling of what can be discovered, lead to new questions and phenomena, and may lower barriers to looking outward. While discussing risks to open culture, it frames AI as an opportunity to expand the space of mathematical questions. The author's judgment and outlook, without concrete evidence or cases in the text.
Perspective
This is a guest blog commentary intended for mathematicians, early-career researchers, mentors, and readers interested in research incentives and AI's impact. It argues that the mathematical community should discuss credit, open sharing, and AI ethics without abandoning pure mathematics, and should treat biology and applied sciences as sources of new mathematical questions; its proposals are aimed at community norms and policy discussion rather than providing directly executable plans.
Readers may still watch: the claim that AI will commodify proof generation is a future scenario that remains to be observed; the observations about colleagues leaving arXiv and trainees rushing papers are not supported by systematic data; how to design fair credit and openness norms across mathematical subfields and career stages remains an open question; and because this version is an AI-converted blog text, links or references from the original format may not be visible, so some background details may need checking against the original or related materials.