The AI Takeover of Mathematics

Recently, artificial intelligence (AI) has solved various problems in mathematics research, some of which had remained unsolved for hundreds of years. From finding the most space-efficient way to pack high-dimensional spheres to addressing other, more complex concepts, AI tools have now surpassed human ability to prove theorems. Now that AI is more efficient than humans and constantly improving, the important question remains: what will be left for humans to do?

In “The End of Mathematics,” University of Toronto mathematics professor Daniel Litt explains how AI is replacing many aspects of math research, including the creation of new proofs, validation of existing solutions, and discussion among mathematicians. In fact, it is argued that it will soon be more effective—in regard to both time and money—for humans to converse with AI than attempt to solve complex problems themselves. Currently, mathematicians are awarded for solving outstanding problems; in the future, this may be less ideal to promote advances in research. If the current system is kept, the “best mathematicians” will be the ones who have access to the best AI and have the most money, or tokens, to spend on running that AI. Additionally, if mathematicians don’t spend their own time working on solving these problems, they may become too disconnected from the AI’s train of thought and be unable to continue the AI’s work or think in the bigger picture. Since problem-solving will become much more efficient and predictable, researchers may need to shift their focus to figuring out which problems are most worth solving, as well as coming up with new mathematical strategies altogether. 

This issue extends beyond that of a professional level. If AI is able to become more efficient than humans at these defined tasks, such as proving theorems and solving problems, learning how to efficiently solve math problems may no longer be considered essential for students. Therefore, teachers should redirect their focus to teaching students bigger-picture ideas, including critical thinking skills and understanding AI’s solutions to certain problems. Students should also be encouraged to learn and understand the purpose of artificial intelligence in mathematics, perhaps switching some assignments from solving problems to analyzing an AI’s solution to those problems. For instance, through the instant feedback and personalized assistance provided by AI tools, many students may gain greater access to tutoring, boosting overall exam results and understanding of the topics.  

Still, the presence of AI has become a significant issue in schools, particularly in terms of cheating. It is crucial for students to understand the difference between AI use that speeds up learning and AI use that stalls it completely. An article from the OECD distinguishes beneficial AI tutors from general-purpose AI tools. While general-purpose AI can speed up the rate at which students complete assignments, statistics show that this boosted performance during practice decreases the students’ performance on exams. Other studies have found that students using AI to study subsequently scored 17 percent lower on a math exam than those who didn’t have access to AI. 

But the use of AI for cheating is not only limited to school; it is also prevalent in math competitions. The most important of these is probably the AMC/AIME examinations, which can qualify students for the USA Mathematical Olympiad, and later, for America’s international team. Recently, the MAA recognized the breaches of integrity on these exams in recent years—indicated by abnormally high cutoffs and students choosing not to attend the national olympiad—and made many changes to restore this integrity. One of these changes mandates that the AIME be taken in an official testing center. The rise in cheating can likely be explained by the public’s access to AI to solve these competition problems. 

From math research to teaching and learning math in school, artificial intelligence is changing the way everyone interacts with mathematics. In research, several changes will need to be made in order for math research to progress optimally. Solving the most problems may no longer be a good measure of an accomplished mathematician, and solving problems may not be the most effective use of time for researchers. Mathematicians will need to respond to AI’s growing computational and problem-solving capability, potentially by shifting their focus toward incorporating existing solutions into the theory of the field and coming up with more important open problems. In schools, teachers should be aware of their students’ future in math and the effect AI will have on it, as well as students’ potential to use AI for cheating. Likewise, students should learn how to use AI effectively, both for solving problems and for speeding up their learning. As the available technology changes, people will have to follow; everyone should be aware of AI’s advances and ready for permanent shifts in how mathematics is practiced around the world.