Last updated 10/12/2026
As AI continues to change the landscape of our world (and academia in particular), I feel that it is important as an academic to have a clear stance on the use of AI in my field. The purpose of this page is neither to persuade others of my beliefs nor to state that this should be the standard policy of any academic. Rather, this page is simply an outline of my personal beliefs and professional policies surrounding AI; it does not represent the views of any institution or organization. This should be understood to be a living document; as AI continues to develop, so too will this policy.
I hope that my writing is complete enough to be clear and concise enough to be approachable. I encourage my fellow academics to create policies of their own regarding AI usage. For this pursuit, I grant full license to copy, distribute, or reuse this page either in part or in full.
Section 1: The Purpose of Mathematics
To understand the appropriate use of AI as it applies to the field of mathematics, one must understand the overarching purpose of mathematics. Fundamental to the field of mathematics is the idea that, although our notations, definitions, and even axioms can be considered human constructions, mathematics itself is not. The question of whether our universe truly exists is something that can be (and has been) debated to no end; the existence of logic and mathematics is far more certain. Although human study of mathematics began as a way to formalize observations about the universe in which we live, it has evolved into a framework by which we may understand the abstract structures underlying any possible universe.
With this understanding, mathematicians must recognize that the work we do in our research is not to create new math, but rather to discover math that already logically follows from a chosen set of axioms. Since the answer to any problem we may attempt to solve is already determined before we observe it, the purpose of mathematics must lie in the process of discovery itself and in the communication of that discovery. Without an understanding of the logic that leads to the conclusion, one cannot truly claim to have made a discovery at all. Without clear communication of the logic and the conclusion, no progress in our collective understanding of mathematics can follow. If an answer does not exist in the consciousness of beings capable of understanding it, no progress has been made at all; this is simply the base state of the universe.
In the pursuit of this goal of understanding (and in the support of applications in science, engineering, and beyond), proper mathematical reasoning and problem-solving skills must be developed in those with the desire to see mathematics flourish. In the developing of this understanding, there is truly no substitute for the exercise, practice, and struggle of doing mathematics oneself. These difficulties in learning mathematics are not a roadblock to the success of the field; they are the very cornerstone upon which the field is built. Without this struggle, an individual cannot grow in understanding; without new individual growth in understanding, the field of mathematics cannot continue into the future.
Section 2: The State of AI
Unlike in mathematics, I am not an expert in artificial intelligence. This section should be viewed through that lens. Any information found here is simply my understanding of AI at this moment in time. As AI evolves or as my understanding changes, I expect that this section will change.
As it stands now, AI systems collect input data by some means and use that to produce an output. For most AI that is in widespread use, this means collecting large swaths of data from the Internet (among other sources), transforming it in some way, then using predictive models to construct an output that seems to follow from the input. One of the key ideas to this discussion is that, when an AI produces an output, neither the developer, nor the prompter, nor even the AI itself will necessarily understand exactly how and why the output was produced in the way that it was. Quite simply, a modern AI cannot truly understand its input and output.
In addition, it is important to keep in mind the realities of developing and running a modern large-scale AI. In order to be able to provide information on a wide array of topics and to have enough data to draw desirable conclusions, large-scale AI takes any and all data it can get. Since the output depends on this input in uncertain ways, an AI may plagiarize information from sources without properly citing them or include information from sources that cannot be trusted. Recently, AI have become more likely to provide citations for their claims (perhaps in response to this criticism), but often those citations are not completely correct. Source titles, author names, publication year, and any number of other pieces of information may be improperly provided, meaning that any information provided by these modern large-scale AI models can be considered suspect at best. A more cynical view might see this practice as intentional by the developers, a way to project an image of accountability without real substance behind it. Regardless of the intention of the developers, modern large-scale AI cannot be trusted to properly cite the sources it is using or the intellectual property it is coopting.
Beyond the concern of improper attribution is the fact that fast-paced AI development without proper oversight has allowed large-scale AI developers to provide AI services at the expense of both natural and human environments. This practice turns large swaths of land into data centers which drain the natural resources of the surrounding area. Even ignoring the impacts this has on local wildlife populations, cities and states in which data centers have been allowed to be built have seen skyrocketing prices to water and electricity prices and a degradation of natural water supplies. On this basis, one could argue that no AI use is truly ethical, as it contributes to this degradation of natural resources and increases the economic weight on communities local to these data centers, particularly among the most vulnerable populations.
Section 3: My AI Policies for Mathematics
With these ideas in mind, I now present my personal and professional policies for AI use in mathematics. For purposes in my research, scholarship, and teaching, I will abstain from almost all uses of AI until such a time as AI can be trusted at the same level as a human collaborator; that is, until I can trust that my use of AI is producing mathematics which can be understood by a human, can be trusted to properly cite its sources, and which is not run in a way that degrades our natural and human resources. The one very limited case in which I will consider AI use acceptable in my professional activities is in performing literature review. Although I recognize that this task still carries with it the same issues I expressed reservations about in the previous sections, my hope is that in restricting my usage to only this one task, I may offset the inherent issues with AI’s inability to properly cite sources by allowing myself to find and cite sources which may have gone unnoticed in a manual search. Furthermore, I hope to encourage the responsible, limited use of AI in such a way that will limit the need for large-scale data centers to exist. Of course, such an AI literature search may be flawed; as a responsible expert in my field, I will always perform the manual process of checking that the information provided is accurate.
In my teaching, I will commit to ensuring that my students are given proper, correct instruction led by an expert in the field (myself) rather than AI-produced lessons. All assignments, activities, and assessments will either be produced by myself or provided in collaboration with a trusted colleague. To encourage the growth of new understanding in mathematics and the struggle that is inherent to this process, I will disallow the use of AI by my students to the extent that I am able to do so. Rather, I will allow my students to try, fail, and try again in their pursuit of knowledge; after all, it is exactly this process which cultivates their intuition and understanding. In this way, I hope to help build a new generation of capable mathematicians (and other mathematical thinkers) who will continue to grow our collective understanding.
In my research activities, I refer to my earlier section on the purpose of mathematics: if an argument or discovery is not understood by sapient beings willing and able to communicate those results clearly and effectively, it cannot be considered progress. For this reason, I welcome and encourage collaboration with any and all mathematical thinkers with shared interests. This type of communication and collective thinking forms the basis of our mathematical community. However, as a matter of policy, I will not engage with any results or papers produced by an AI which have not first been reviewed, understood, and communicated by a human. At such a time as I can see considerable evidence that an AI can be considered a sapient being capable of true mathematical understanding, I will of course welcome the contributions of any AI which is responsibly and ethically run. Until then, I will neither read, respond to, nor acknowledge any purported claims of AI proofs. Quite simply, if these arguments are not or cannot be understood and communicated by a human, our collective understanding of mathematics has not changed; this is no different than the base state of the universe, in which all results within a system of logic are settled but undiscovered.