At the 2026 International Congress of Mathematicians in Philadelphia on July 24, Fields Medalist Terence Tao delivered a pivotal address titled Mathematics in the Age of AI, warning that the discipline is rapidly approaching an industrial paradigm shift. Tao argued that artificial intelligence is transitioning mathematics from an era of proof scarcity to one of proof abundance, fundamentally challenging traditional research methodologies, academic evaluation systems, and the core values of the mathematical community. Grounding his analysis in the newly released First Proof benchmark, Tao noted that contemporary AI systems successfully resolved 70 percent of novel, expert-level mathematics problems under controlled conditions, with verification costs ranging from 10 to 1,000 dollars per problem. While demonstrating that machines can now generate publication-quality proofs, Tao highlighted persistent limitations, including citation errors, incomplete explanations, and a lack of genuine conceptual understanding. He further cautioned against publication bias in AI capability reports, stressing that current data remains insufficient for definitive conclusions. The speech drew immediate context from recent developments, including an AI-assisted discovery of a three-dimensional counterexample to the Jacobian Conjecture, verified via Isabelle/HOL. Tao used this event to illustrate a critical gap: while machines can verify logical correctness, they cannot yet articulate why a result holds or contextualize it within broader mathematical frameworks. Citing Goodhart's Law, he warned that optimizing solely for theorem production will degrade research quality. As automated generation and formal verification accelerate, the community risks a proof indigestion crisis, where an influx of valid but uninterpreted results overwhelms peer review and knowledge integration pipelines. Tao proposed a five-tier framework for what constitutes a genuinely solved mathematical problem, progressing from raw proof generation to verification, expert exposition, community acceptance, and integration into standard theory and textbooks. He emphasized that human mathematicians must transition from primary proof producers to architects of verification systems, interpreters of machine-generated insights, and curators of disciplinary knowledge. The speech also reflected a broader industry shift, noting prominent mathematicians joining AI firms to develop theoretical safeguards and automated reasoning tools. Looking ahead, Tao urged the academic community to institutionalize transparent AI usage disclosures, recalibrate tenure and publication metrics to reward explanation and validation, and redesign graduate training to prioritize critical analysis over rote problem-solving. He concluded that the future of mathematics will not be determined by how many theorems machines can produce, but by how effectively human researchers can interpret, validate, and synthesize those findings into enduring scholarly knowledge. As AI capabilities continue to mature, the mathematical establishment must urgently rebuild its infrastructure for quality control, collaborative discovery, and knowledge transmission to navigate the forthcoming industrial era of research.