数学家Grant Sanderson提出，随着人工智能生成证明的能力不断增强，数学界需要重新审视价值评判标准，将"动机清晰的解释"提升到与证明同等的重要地位1。Sanderson认为，数学的根本目标是促进人类理解而非仅仅生成证明，学术界应当通过重视清晰的解释、系统地阐述问题和教学贡献来更好地衡量数学家的价值1。
在Sanderson的构想中，"动机清晰的解释"是指新的数学构念应在其解决的问题被清晰确立后才被引入，允许从不完全正确的想法开始，并强调这些想法的来源可追溯性1。他指出，解释与证明存在本质区别：证明的目标是说明定理为何成立，而解释还需阐明为何该定理值得被提出及其应用背景1。这一观点呼应了三十年前数学家Bill Thurston在论文《On Proof and Progress in Mathematics》中的论述——Thurston曾指出，当Appel和Haken用大规模自动计算完成四色定理证明时，人们的争议反映的是对人类理解的持续渴望，而非对定理真实性的怀疑1。
为了推进这一理念，Sanderson提出了多项具体建议1：博士生可改为通过讲座展示而非论文提交来呈现小问题的解答；建立现代版的"开放阐述问题"清单，与开放研究问题相对应；创办专注于更广泛理解的数学期刊；在聘用和终身职位评审中重视教科书写作的贡献。2026年，Liam Price、Nat Sothanaphan、Jared Lichtman等人与数学家Terence Tao合作，将AI生成的Erdős问题1196解答转化为人类可读形式并扩展其关键思想，体现了这一新思路的实践探索1。
Mathematician Grant Sanderson has called for the academic mathematics community to redefine what constitutes mathematical achievement, arguing that as artificial intelligence becomes capable of generating proofs, human insight and understanding should be elevated to equal importance with formal demonstration 1. Sanderson, who specializes in creating mathematical educational videos, proposes that "motivated explanation"—where new concepts are introduced only after the problems they solve have been clearly established, allowing ideas to be traced to their origins—deserves recognition alongside traditional proof-based contributions 1.
The core of Sanderson's argument rests on a distinction between proof and explanation 1. While a proof establishes that a theorem is true, an explanation must also convey why the theorem deserves to exist and illuminate its practical applications and context 1. This vision aligns with observations made three decades earlier by mathematician Bill Thurston, who noted in his paper "On Proof and Progress in Mathematics" that when Appel and Haken completed the Four Color Theorem through large-scale automated computation, the resulting controversy reflected not skepticism about the theorem's validity but rather humanity's continuing need for genuine understanding 1.
To operationalize this shift in values, Sanderson recommends several institutional changes 1. These include allowing PhD students to demonstrate mastery through lectures rather than submitting papers on minor problems, establishing a modern registry of "open exposition problems" as counterparts to traditional open research questions, creating mathematical journals focused on broader understanding rather than novel results, and considering textbook authorship and teaching contributions as significant factors in hiring and tenure decisions 1. A practical example of this approach emerged in 2026, when researchers Liam Price, Nat Sothanaphan, Jared Lichtman, and collaborators working with Terence Tao transformed an AI-generated solution to Erdős Problem 1196 into a form comprehensible to human mathematicians while extending its core insights 1.
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