Summer School 2026

Theory and Applications of Elliptic PDE

University of California, Irvine | August 17–21, 2026

The Role of AI in PDE Research

Panel Discussion — 2026 UCI PDE Summer School
As part of the summer school, participants, speakers, and organizers held an open discussion on the rapidly evolving role of artificial intelligence in mathematical research. The conversation focused on personal experiences with AI, its potential benefits and risks, and its possible impact on the future of mathematical research and graduate education.

Opening Survey

Participants were asked: “Overall, what is your current attitude toward the use of AI in mathematical research?”

A total of 37 participants responded.

Mostly negative: I prefer to avoid using AI in research 7 (19%)
Reluctantly open: I have concerns, but I am willing to use AI when it is helpful 13 (35%)
Cautiously positive: — I see significant potential, but think AI should be used carefully and critically 14 (38%)
Highly enthusiastic: I see AI as opening an exciting new era of mathematical discovery 3 (8%)

Discussion: Opportunities and Concerns

Participants were then invited to identify potential benefits and concerns. Their comments were collected on the board and used to guide the subsequent discussion.

Potential Benefits

  • A new dimension for understanding. AI may provide alternative viewpoints and new ways to approach mathematical questions.
  • A research companion or assistant. AI can serve as a readily available partner for exploring ideas, asking questions, and testing approaches.
  • Learning things faster. AI can help researchers enter unfamiliar areas and understand new material more efficiently.
  • More time to explore. By accelerating routine parts of research, AI may leave more time for exploration and creative thinking.
  • Easier movement between research areas. AI may make it easier to pick up, return to, or explore a new field.

Concerns and Risks

  • Reluctance to share unfinished ideas. Researchers may become more cautious about telling others what they are currently working on.
  • Changes in research evaluation. AI raises questions about how mathematical contributions should be evaluated in hiring, promotion, and publication.
  • Homogenization of ideas and approaches. Heavy reliance on similar AI systems could make mathematical thinking less diverse.
  • The future of graduate training. Participants expressed concern about how young mathematicians will develop independence and mathematical judgment in an AI-assisted environment.
  • Loss of collaboration. AI could replace some interactions that traditionally occur between mathematicians.
  • Loss of the joy of discovery. Some worried that rapid AI-assisted problem solving could reduce the satisfaction associated with struggling with and eventually solving a difficult problem.
  • Less excitement about new results. If results are produced much more rapidly, individual discoveries may feel less surprising or significant.
  • What do we ultimately gain? A broader concern was whether increased research speed necessarily leads to a better mathematical experience or a healthier research community.
The survey was an informal show-of-hands poll conducted during the panel discussion. Comments above are anonymous and have been lightly edited for clarity. They represent views expressed by individual participants and should not be interpreted as a consensus statement of the summer school or its organizers.