The essay “A beginning for mathematics,” published on Daniel Litt’s blog and also appearing on Proofs and Prompts, argues that the rapid advance of artificial intelligence in mathematical reasoning is prompting a fundamental reassessment of what mathematicians do and how they are trained. According to the piece, three years ago AI could not reliably add two numbers; a year ago internal models at OpenAI and DeepMind achieved scores comparable to a gold‑medal performance on the International Mathematical Olympiad; and now such systems are beginning to autonomously resolve major open questions. The author treats the prospect of AI that is robustly superhuman in most or all mathematical activities as a near‑future premise, but notes that even the weaker observation—that the production of mathematical text is becoming increasingly detached from genuine understanding—already demands institutional change. Litt contends that the mathematical community lacks a shared sense of purpose. Some view mathematics as problem‑solving, others as play or poetry, still others as a quest to uncover Platonic truths or to transmit love and understanding of the discipline to future generations. He offers his own concise answer: the profession should aim both to produce and understand high‑quality mathematics and to cultivate high‑quality mathematicians. These goals, he stresses, must be interpreted broadly, encompassing not only the training of PhD researchers but also public education about mathematical thinking. Because proving theorems can be mechanically automated—by enumerating axioms and deduction rules or by conjecturing propositions in alphabetical order—the essay argues that the current operational definition of mathematics as theorem‑proving is insufficient. Even if an AI could generate correct, beautifully explained results, it would not, by itself, create human understanding of those results. Litt suggests that this gap creates a pressing need for human mathematicians, provided the field adapts its values and practices. To that end, he proposes several concrete steps. The goal of a mathematics PhD should be reframed as becoming a world expert on a deep, interesting topic and being able to convey that interest and understanding to others; assessment would focus on a rigorous defense in which the student explains the subject, rather than on the mere existence of a thesis. The author also urges preservation of informal, community‑driven activities such as learning seminars, serendipitous hallway conversations, and students knocking on professors’ doors to discuss math. Maintaining a vibrant community where thousands collectively work through confusion, he writes, is essential to safeguarding mathematical progress. While acknowledging frustration toward AI labs, Litt maintains that the challenge lies not in the labs’ behavior but in the technology itself, which will remain accessible to anyone with a laptop and modest funds. He concludes that, if the mathematical community reorients its institutions around understanding and communication rather than mere theorem production, the rise of superhuman AI can coexist with, and even amplify, human mathematical endeavor.
