Fields Medalist, UCLA Chinese Mathematician Terence Tao Claims the Romantic Era of Mathematics is Ending

Fields Medalist and UCLA Chinese mathematician Terence Tao expressed on Numberphile aired on October 15: "I think we are witnessing the end of the romantic era of mathematics, the era of heroes."

"Several centuries ago, other disciplines had already undergone this transformation. Mathematics has retained its traditions; we still use blackboards and the legendary story of Andrew Wiles working alone in an attic for seven years to finally prove Fermat's Last Theorem is still passed down."

"But now, we are entering an industrialized era. Mathematical research will become more large-scale, relying on large team collaborations, just like other scientific fields."

"Some things will disappear, including the romantic sense unique to that heroic era."

He stated that in the future, traditional mathematical methods should still be taught to students first, before introducing industrial tools, similar to teaching children to calculate by hand before using calculators.

"We are somewhat reluctantly entering a new era. Exciting new things will become possible, but some things are also fading away."

The interview focused on the impact of AI on mathematical research, with Tao pointing out that large-scale collaboration, computer-assisted verification, and AI tools are driving research from individual breakthroughs to team-based and experimental approaches, while emphasizing the need to retain an understanding of the proofs rather than just pursuing the quantity of theorems.

Source: Public Information

Terence Tao, a 2006 Fields Medalist, has made significant contributions in the fields of analysis, number theory, and combinatorial mathematics. In 2026, he promoted AI-assisted mathematical research, including public discussions on large-scale experimental projects like Equational Theories and participating in joint statements regarding the application of AI in mathematics. He has frequently compared the differences in collaboration scale between mathematics and other disciplines like physics.

In the Numberphile interview, he described the current transition as a shift from the "heroic era" (characterized by individual long-term research, blackboard traditions, and Wiles-style attic proofs) to an industrialized era (large teams, AI systems, and computer verification collaboration). He advocates for an educational path that first masters traditional hand calculations and reasoning before introducing tools, similar to arithmetic training before the introduction of calculators.

This is akin to the transition in physics from individual theorists to large-scale experimental collaborations like CERN, or the evolution of computer science from early individual hackers to large engineering teams. Currently, mathematics is in a phase where AI capabilities are rapidly improving, proof generation is accelerating, but understanding and standardization are lagging. Tao emphasizes that the discipline should proactively set rules for AI usage.

Essentially, this represents a technological substitution and structural change in the industry: AI and automated verification will shift theorem production from individual insights to scalable collaboration and machine assistance, reducing the value of "first to solve," while the stages of explanation, dissemination, and textbook standardization become bottlenecks. The narrative of individual heroes weakens, and teams and tools become the core of research infrastructure, while traditional understanding pathways need to be retained in education to maintain the significance of the discipline.

ABAB News · Cognitive Laws

The romantic era ends on the day of tool scaling.
Hand calculations before calculators; understanding precedes output.
As heroic narratives give way to team collaboration, meaning must still be preserved.

ABAB AI Insight