Mathematical Moments from the American Mathematical Society

Dr. Alex Best, of Harmonic discusses AI's struggles with technical and ethical limitations like uninterpretable methods and a lack of diverse datasets make facial recognition and medical software dangerously biased. If algorithms output answers without little explanation, how can one trust those results? Interpretability is a prerequisite to replace the work of human researchers. But using AI for formalizing mathematics offers some mitigation, Alex Best says. "Instead of asking for an answer, you ask for an answer and a machine-checkable proof that that answer is correct."

Dr. Kristen Lauter, director of FAIR (Fundamental AI Research) Labs, Meta, North America, discusses how cryptographers are using AI. Online, private information is secured using difficult-to-solve math problems. Researchers must test those problems thoroughly to be sure they are truly difficult - if hackers can solve the problem, they'll have access to your information.

Dr. Po-Shen Loh of Carnegie Mellon University, discusses how AI is changing the landscape of mathematics and looks ahead at what might come. As algorithms have matured, mathematicians have embraced computation as means to accelerate math discoveries. Researchers integrate AI with "proof checking" tools, like the software Lean, to avoid errors more quickly. According to Loh, this makes it easier for large teams to collaborate and for peers to check each other's discoveries for accuracy. According to a study in the journal Nature, mathematicians anticipate that AI will guide human intuition, and help to prove unsolved conjectures.

Dr. Abiy Tasissa of Tufts University, discusses the mathematics he and colleagues used to study particle collider data, including optimal transport and optimization. Collider physics often result in distributions referred to as jets. Dr. Tasissa and his team used "Earth Mover's Distance" and other mathematical tools to study the shape of jets. "It is interesting for me to see how mathematics can be applied to study these fundamental problems answering fundamental equations in physics, not only at the level of formulating new ideas, which is, in this particular case, a notion of distance, but also how the importance of designing fast optimization algorithms to be able to actually compute these distances," says Dr. Tasissa.