Don’ts 1. Don’t Trust Blindly : Never accept AI mathematical outputs without verification. 2. Don’t Outsource Understanding : Use AI to augment your thinking, not replace it. 3. Don’t Skip Steps : Even if AI produces an answer, work through the derivation yourself. For steps that AI skipped, either carry them out yourself or ask them to provide the details and then check. 4. Don’t Ignore Errors : When you find errors in AI output, use them as learning opportunities about failure modes. 5. Don’t Publish/Accept Without Verification : Ensure every theorem, proof, and claim has been independently verified by qualified humans. BROADER IMPLICATIONS My limited experience suggests several broader implications for AI in scientific research: 1. AI as an Amplifier, Not a Replacement: AI tools amplify human capability but cannot replace domain expertise and judgment. 2. Verification is Essential: The ease of generating content makes verification more critical, not less. 3. New Skills Required: Researchers need to develop skills in prompting and strategic directions, verification, and critical assessment of AI outputs. 4. Transparency Matters: Academic culture should encourage, not discourage, transparency about AI assistance. 5. Education Must Adapt: We must teach students both how to use AI tools and, critically, how to work without them productively and responsibly. ANSWER TO THE TITLE QUESTION Is human-centered AI-assisted creative scholarly work in mathematics productive collaboration or perilous shortcut? My personal answer: it depends entirely on how you use it. With proper safeguards—expert human verification, clear division of responsibilities, appropriate skepticism, and rigorous testing—AI assistance can meaningfully accelerate mathematical discovery and verification while enhancing understanding. We completed in weeks what might have taken months without AI assistance. However, without these safeguards, AI assistance becomes a liability. The risk of subtle errors, the atrophy of mathematical thinking, and the false confidence in unverified results can lead researchers astray. The technology is neither inherently good nor bad. The outcomes depend on human choices about implementation and oversight. SHOULD WE ENCOURAGE HUMAN-CENTERED AI-ASSISTED SCHOLARLY WORK? This is clearly debatable (and even controversial). Some of us may disapprove of the idea, while others will embrace it. Historically, scholarly work has been human–human collaboration, and that has been the default model. We have long accepted citing mathematical software and computer algebra systems like Mathematica , MATLAB , or Maple when they perform symbolic manipulations. These tools execute algorithms with precise syntax and problem encoding programmed by humans, yet we don’t credit them as coauthors. Why? Because they are traditionally deterministic tools executing known procedures. LLMs are fundamentally different. They offer natural language interaction and can suggest solution strategies, but could make computational errors. They generate novel strategies, explore unexpected proof directions, and sometimes produce insights that surprise even expert users. The distinction between "tool" and "collaborator" becomes murky in this case. If we credit a human research assistant under supervision, why not credit an AI assistant performing the same function, as long as new knowledge or findings have been developed? In other words, as far as advancing knowledge and the state-of-the-art is concerned, should it matter if a scholarly work is a human-human or human-AI collaboration? However, I acknowledge the counterarguments: • AI lacks intent, understanding, and responsibility. • AI cannot defend its contributions or verify correctness. • Coauthorship implies accountability that AI cannot bear. • There are practical issues with copyright and legal responsibility Perhaps the solution is a new category: "AI Research Assistant" in acknowledgments, with detailed specification of contributions. This preserves transparency without granting full coauthorship status. LIMITATIONS OF THIS STUDY This case study has several limitations that readers should consider: 1. Single Domain : Our experience is limited to mathematical proof development. Results may not generalize to experimental science, data analysis, or other forms of scholarly work. 2. Expert User : As a professor with extensive mathematical training and experience, I could quickly identify AI errors. Less experienced researchers might struggle with verification. 3. Specific Problem Type : The algebraic nature of our problem played to AI strengths. More conceptual or geometric problems might yield different results. 4. Time Snapshot : AI capabilities are rapidly evolving. This study reflects systems available in late 2025. 5. Selection Bias : We document a successful collaboration. Failed attempts at AI-assisted research may have different patterns we didn’t observe. While broader methodological studies across multiple problems would enhance generalizability, we believe detailed transparency about one case offers practical insights appropriate for illuminating controversies. COMPARISON WITH SPECIFIED TOOLS LLMs vs. Search Engines for Literature: LLMs can synthesize patterns across papers and identify conceptual connections that keyword search might miss. However, they sometimes hallucinate citations or misattribute results. My recommendation is to use LLMs for initial literature mapping, then verify all citations manually using traditional search and human verifications. LLMs vs. Computer Algebra Systems: CAS (like Mathematica and Maple ) excel at deterministic symbolic computation but require precise syntax and problem encoding. LLMs offer natural language interaction and can suggest solution strategies, but could make computational errors. The ideal workflow combines both: use LLMs for strategy exploration and problem setup, then CAS for verifications when applicable. General LLMs vs. LLEMMA and Minerva : This requires an in-depth, comprehensive, and systematic comparison, which is beyond the scope of this paper. However, the general LLMs (such as GPT-4 , Claude ) proved surprisingly capable when properly prompted for our mathematical derivation tasks. This suggests that for many applications, accessibility and ease of use may matter more than mathematical specialization. CONCLUSION We have provided empirical evidence that human-AI collaboration in mathematics can produce rigorous, novel results when properly structured. Our work on Hermite quadrature demonstrates both the potential and the limitations of current AI systems. The key insight is not that AI can do mathematics—it cannot, at least not reliably—but that it can assist mathematicians in specific, well-defined ways under appropriate supervision. The human must remain firmly in control, providing intuition, strategic directions, verification, and judgment. As AI capabilities continue to advance, the research community must develop best practices for responsible use. We hope this detailed account of our experience contributes to that ongoing conversation by providing concrete evidence of what works, what doesn’t, and what safeguards are essential. The future of mathematics may well involve human-AI collaboration. Our results suggest this future can be productive, if we proceed thoughtfully, responsibly, and maintain appropriate skepticism. ACKNOWLEDGMENTS The author would like to thank his students, Giancarlo Villatoro and C.G. Krishnanunni for their initial work without AI assistance in [ 7 ] . The author also would like to acknowledge the contributions of Claude (Anthropic) and ChatGPT (OpenAI) as AI research assistants in this work. All final collaborative mathematical results were verified by the author. We thank the Associate Editor and all reviewers for their constructive feedback, which has significantly improved the manuscript. This work is partially funded by the National Science Foundation award NSF-OAC-2212442, and by the Department of Energy award DE-SC0024633. Examples of prompts and outputs