Search arXivSearch

arXiv · 2608.29401

Explanations, Prompts, and Formalizations: Arguments for New Norms in LLM-Enabled Mathematical Research

Abstract

As several mathematical conjectures have recently been settled using large language models (LLMs), the mathematical community has formulated norms and recommendations regarding the publishing of such results. These norms do not cover the disclosure of the prompts and precise software setup used to obtain those results, nor do they require that results be formalized in a manner that allows for machine verification. I argue that both of these are essential. In addition, since LLM-obtained results may be hard to understand, human authors have the responsibility to invent intuitive explanations.

Explore related subjects

Keep this discovery

BibTeXRIS

Axel Boldt. 2026-08-29. Explanations, Prompts, and Formalizations: Arguments for New Norms in LLM-Enabled Mathematical Research. https://arxiv.org/abs/2608.29401

Cite the original work for its findings. Save a collection to share your selection of sources.

Discover connections

Connections use source metadata and explicit phrase matches, not verified experimental comparisons.

KEEP EXPLORING

Related papers

On systematicity of linear function-correcting codes

The standard formulation of function-correcting codes uses systematic encodings. We study the redundancy cost of this constraint when both the prescribed function and the encoding are linear. We introduce the function-separation distance and show that several classical unequal error protection parameters are special cases. For linear functions and encodings, this distance is the first relative generalized Hamming weight of the code relative to the encoded kernel. We formulate free and systematic linear separation problems. We prove that the optimal free redundancy depends only on the rank of the function, and determine the optimal systematic redundancy for prescribed separations $d\leq3$.

cs.IT

Fundamental Mathematics in the Age of AI -- The Residue, the Journey, and the Ecology

Large language models have begun refuting long-standing conjectures and solving long-open problems. The introspection this has prompted about the future of mathematical discovery is well under way, and the anxiety accompanying it legitimate -- but both, we claim, are attached to the wrong loss. What machines now produce is the countable part of mathematics -- theorems, proofs, refutations -- which was always the work's residue, not its product. The distinction is old, and not economic: a result can be taken in its finished essence, or in the operations that engendered it. The product is human understanding: not a stock of results but a collective, hard-won way of deciphering the world and acting upon it. The two are arcs of a single loop: understanding tells us where to look; looking produces the residue; and taking it up again, one journey at a time, rebuilds shared understanding. Machines are strong on the countable arc, absent from the one that feeds it. The peril is to leave the loop open. AI did not create the confusion between residue and product; it has called a bluff long on the books, driving the cost of the residue towards zero and making the scarce thing visible at last. A new instrument makes a new way of working before it makes a new result. The pressing questions are therefore institutional: who can check an announced result, whoever announces it; what work and training become for the next generation of researchers; and whether the one thing that cannot be mass-produced -- the journey that nourishes a shared understanding -- continues to be funded. Mathematics, we argue, is uniquely placed among the sciences on the first -- a proof answers to no one's permission -- and uniquely exposed on the other two: teaching cannot go on as before, and no collective position yet exists; and the journey has never had a price our institutions knew how to pay. The decision is ours.

math.HO

Oculi: A Conversational Agentic Platform for Automated Credit Risk Analysis

Credit risk analysis in financial institutions traditionally requires analysts to manually write SQL queries, run statistical computations, and build visualization dashboards. This is a time-consuming workflow that limits exploration to familiar segments. We introduce \textbf{Oculi}, a conversational platform that transforms natural language questions into comprehensive credit risk analyses, complete with data queries, statistical testing, and interactive visualizations. Oculi employs a three-layer architecture that separates reasoning (LLM-powered agent), execution (Model Context Protocol tool servers), and presentation (agentic UI), enabling analysts to discover high-risk portfolio segments. Within Oculi, a new segment discovery pipeline is proposed that combines deterministic statistical methods with LLM-guided feature selection, leveraging LLM semantic domain knowledge alongside data-driven metrics to identify meaningful, actionable portfolio segments. Evaluated on a mortgage portfolio with 200+ features, Oculi demonstrates effectiveness in discovering material risk segments previously intractable through manual exploration, reducing time-to-insight significantly while maintaining auditability and statistical rigor.

cs.AI