Mathematicians are witnessing a profound shift in their field. AI systems are now producing proofs, spotting connections between distant fields, and, in a few cases, solving problems that had stumped mathematicians for decades. The pace of progress over the past several months has raised challenging questions: What can AI systems actually do? And what happens to the more human, creative aspects of the field once machines can match – or exceed – people at problem-solving?

In this special live episode of The Joy of Why, recorded at the International Congress of Mathematicians in Philadelphia on July 26, 2026, hosts Janna Levin and Steven Strogatz are joined by three mathematicians responding to the rise of AI in math: Akshay Venkatesh at the Institute for Advanced Study; Ravi Vakil at Stanford University and president of the American Mathematical Society; and Alex Kontorovich at Rutgers University. Together they discuss what recent AI-generated proofs really demonstrate, what will be gained and lost as mathematics becomes more machine-assisted at the frontier, and what this means for the next generation of mathematicians. The conversation turns to a deeper question: What do mathematicians value about doing mathematics in the first place? The answer involves grappling with what proof and understanding really mean, and with the surprising importance of storytelling.

When an LLM answers a question, is it reasoning like humans, or just producing text that looks like reasoning? The distinction isn’t just philosophical, this determines what we can trust AI to do, how closely we need to supervise it, and ultimately what its real-world impact will turn out to be.

Melanie Mitchell at the Santa Fe Institute argues that we lack adequate methods for measuring machine cognition, and that AI is a form of “alien intelligence” that operates through non-human cognitive mechanisms. In this episode of The Joy of Why, Mitchell tells Steven Strogatz how methods that psychologists use to study cognition in other kinds of “alien intelligence” — babies and animals — can be adapted to probe AI, and she lays out six principles for better assessing machine cognition. Their conversation ranges from the challenge of interpreting what’s happening inside these systems, to recent AI-assisted breakthroughs in mathematics, to why a math-performing horse from the early 1900s offers a cautionary tale for how we assess intelligence.

Pain and pleasure seem like simple facts of life, but they are far from it. Neuroscientists still cannot say why physical pain differs from psychological pain, for instance, nor why a loved one’s touch soothes while a stranger’s touch repels.

To explore the science behind these sensations, Janna Levin talked to Ishmail Abdus-Saboor, a neuroscientist at Columbia University’s Zuckerman Institute. Their conversation covers how pain serves an evolutionary purpose, how researchers measure pain and pleasure in the lab despite the absence of any objective biomarker, and how touch functions as a social and emotional signal, not just a sensory one. Abdus-Saboor also describes his work with naked mole rats — a species that barely feels pain, shows no signs of aging, and lives in colonies built almost entirely on touch — and the ethical trade-offs when studying sensations in animals that cannot describe what they feel.