Mathematics is a Journey, Not Just a Destination
A New Kind of Olympian Takes the Stage
In 2024, a computer system entered the International Mathematical Olympiad, the prestigious high-school competition. [1] It scored one point below a gold medal. By 2025, a more advanced model had achieved a gold-medal standard in the same competition, and the conversation among mathematicians shifted from surprise to something more nuanced.
Ravi Vakil, a mathematician at Stanford University and president of the American Mathematical Society, has firsthand experience with the Olympiad’s demands. He remembers the intensity of those sessions. The competition itself is a grueling test: six problems, nine hours, spread across two days, with competitors drawn from high schools around the world.
Vakil sees the models’ success as a genuine proof of concept, a milestone worth acknowledging. But he draws a sharp distinction between what the achievement means for a machine versus what it means for a student. When a student solves a problem for the first time, something profound happens - they have learned how to think. When a machine solves the same problem, it has simply completed a task. The seventh correct answer from a model is far less interesting than the first, and the same holds true for students, but for entirely different reasons.
Alex Kontorovich from Rutgers University offers a more pointed observation about the medal claims. No official body awarded these honors, he notes - the companies developing the systems declared the results themselves. Kontorovich predicted the models would stop competing altogether once reaching gold-medal standards became routine. Pushing a button on a sophisticated system and receiving perfect Olympiad scores had become routine, no longer worth the effort of the companies behind them.
The Competition Trap and What Mathematics Really Demands
The Olympiad’s role in mathematics extends far beyond the handful of students who compete at the highest level. Vakil emphasizes that the competition’s true value lies in how it encourages millions of young people to sharpen their minds. It serves as an entry point, a way to attract new talent into the field and to advertise what mathematics can offer. But he also acknowledges the danger: people can be driven away from mathematics because they did not excel in a competitive setting, and that outcome makes no sense given the breadth of what the discipline actually requires.
Akshay Venkatesh from the Institute for Advanced Study expresses mixed feelings about the competitive framing that the Olympiad and its AI successors reinforce. The focus on competition has contributed to an image of mathematics as a contest, even among mathematicians themselves. That image is not how he sees the field, and he finds it particularly unhelpful at this moment. When young people receive validation for being good at something, it can feel rewarding, but Venkatesh questions how healthy that dynamic truly is.
The discussion points toward a deeper tension in how mathematics is perceived and practiced. Solving problems is just one small component of what mathematicians actually do, Kontorovich explains. They find definitions, they discover new structures that interest them, and they create new questions and problems constantly. The competitive dimension, whether against other humans or against machines, captures only a narrow slice of the intellectual work that defines the field.
Steven Strogatz, a podcast host, picks up on this thread with a familiar saying: it is the journey, not the destination. The mathematicians on the panel seem to embody this philosophy, and Strogatz suggests it may be an embryonic idea that the field will need to confront more directly. If machines can match or exceed human performance at problem-solving, the question becomes whether mathematics is fundamentally about reaching answers or about the process of getting there.
The Storyteller’s
Craft in a Landscape of New Questions
Paul Erdős, the prolific mathematician known for posing thousands of problems, represents a particular approach to the discipline. He loved to ask questions and did not mind writing them down whether he was right or wrong. His collected problems, some of which have remained unsolved for decades, have become a testing ground for both human and machine mathematicians in recent years.
The recent advances in AI-generated proofs have raised challenging questions about what the machines can actually accomplish. Some mathematicians view the results with caution, while others remain unimpressed by what the systems have demonstrated. The conversation among the panelists reveals a spectrum of responses, from Vakil’s welcoming attitude toward the progress to Venkatesh’s concern about how it shapes perceptions of the field.
The deeper question that emerges from the discussion concerns what mathematicians value about doing mathematics in the first place. The answer, the panelists suggest, involves grappling with what proof and understanding really mean. It also involves the surprising importance of storytelling - the narrative that mathematicians construct around their work, the way they explain why a problem matters, and how they connect one result to another across seemingly distant fields.
Janna Levin, the other podcast host, frames the moment as historic. . Mathematics has had a good run for three or four thousand years done on its own, she observes, but there is a new participant in the field now. . Artificial intelligence is starting to play with mathematicians and their discipline. The stakes are high for the future of mathematics, and the panelists represent different perspectives on what that future might hold.
The conversation at the International Congress of Mathematicians in Philadelphia in 2026 captures a field in transition. The machines are producing proofs, spotting connections between distant areas of mathematics, and solving problems that had stumped humans for decades. The mathematicians on stage are asking what will be gained and lost as mathematics becomes more machine-assisted at the frontier, and what this means for the next generation who will grow up with AI as a constant presence.