Earlier this year, Siddharth Hariharan, a mathematics graduate student at Carnegie Mellon University, received unexpected news that underscored the rapid advances in artificial intelligence’s role in mathematical research. After working alongside Maryna Viazovska, a Fields Medal–winning professor at the Ecole Polytechnique Fédérale de Lausanne, on formalizing her celebrated proof addressing the eight-dimensional sphere-packing problem, Hariharan learned that an AI system had completed their task far ahead of schedule.

The AI, named Gauss and developed by the California-based start-up Math, Inc., had taken the team’s roadmap for breaking down Viazovska’s solution into formal logical steps and finished the entire formalization in just five days. The sphere-packing problem, famously visualized as arranging oranges in the most efficient way on a market stand, becomes increasingly complex in dimensions beyond three. Viazovska’s work, which had linked geometry and number theory in novel ways, initially spurred the collaborative effort to formalize the proof using Lean, a specialized software for mathematical formalization.

Despite an initial enthusiasm for AI assistance when Gauss solved around 30 incomplete segments last fall, the relationship soon became strained. Math, Inc. went silent for months before returning with an upgraded version of Gauss that completed the whole formalization. While the start-up’s CEO Jesse Han intended to announce their achievement promptly and move on to new projects, the academic team felt their original purpose—to deepen understanding of the proof—remained unfulfilled.

The development has sparked debate within the mathematical community about the implications of AI advancements. Some view these breakthroughs as a sign that AI can become a powerful tool or collaborator in exploring abstract problems, while others express concerns about the future for young mathematicians. Carl Schildkraut, a Stanford graduate student who contributed to follow-up research inspired by AI techniques, said his peers were generally pessimistic about prospects amid rapid automation, though he noted that current AI-generated mathematics still lacks the intuition and conceptual insight that human mathematicians bring.

This episode comes amid a broader surge in AI achievements within mathematics. In recent months, OpenAI and Google DeepMind have announced solutions and disproofs of longstanding theorems, fueling an arms race among technology firms to demonstrate AI’s capacity for high-level reasoning—a domain long regarded as a benchmark of human intellect.

For many graduate students, this acceleration of AI capabilities feels like a double-edged sword. Hariharan described the experience as disheartening, questioning the value of years spent on a project overtaken by automation. He now plans to focus first on proving theorems himself before formalizing them, underscoring a desire to retain creative ownership of his work.

Meanwhile, tension persists between academia and AI companies, amplified by differences in resources. Start-ups like Math, Inc. invest significant sums—reportedly exceeding $100,000—on computational resources for single problems, funding levels that outstrip typical academic budgets supporting multiple students. Some young mathematicians voice frustration over the limited recognition and compensation for human contributions that enable AI automation.

Math, Inc.’s CEO Han expressed regret over the backlash from academic peers, attributing current tensions to the swift pace of AI progress rather than any deliberate attempt to overshadow human efforts. As AI systems continue to push boundaries in mathematics, a complex dialogue is unfolding about partnership, competition, and the evolving role of mathematicians in an increasingly automated landscape.