We’re Entering Uncharted Territory for Math
But technology companies are trying to get it there. Recent, attention-grabbing generations of AI—even the almighty ChatGPT—were not built to handle mathematical reasoning. They were instead focused on language: When you asked such a program to answer a basic question, it did not understand and execute an equation or formulate a proof, but instead presented an answer based on which words were likely to appear in sequence. For instance, the original ChatGPT can’t add or multiply, but has seen enough examples of algebra to solve x + 2 = 4: “To solve the equation x + 2 = 4, subtract 2 from both sides …” Now, however, OpenAI is explicitly marketing a new line of “reasoning models,” known collectively as the o1 series, for their ability to problem-solve “much like a person” and work through complex mathematical and scientific tasks and queries. If these models are successful, they could represent a sea change for the slow, lonely work that Tao and his peers do.
he described a kind of AI-enabled, “industrial-scale mathematics” that has never been possible before: one in which AI, at least in the near future, is not a creative collaborator in its own right so much as a lubricant for mathematicians’ hypotheses and approaches. This new sort of math, which could unlock terra incognitae of knowledge, will remain human at its core, embracing how people and machines have very different strengths that should be thought of as complementary rather than competing.
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關於數學，科技正在進入未知的領域
**泰瑞斯·陶，全球最偉大的數學家，對AI有著獨到的見解。**
被譽為“數學莫紮特”的陶，作為加州大學洛杉磯分校的數學教授，已斬獲諸多榮譽，包括數學界的最高獎項。他被認為是當今世界上最頂尖的數學家。然而，當前的人工智能水平尚未接近他的高度。
盡管如此，科技公司正在努力縮短這一差距。目前大多數備受矚目的AI係統，諸如ChatGPT等，主要側重於語言處理，而非數學推理。早期的AI無法進行複雜的數學運算，而隻是基於詞語序列的可能性提供答案。然而，OpenAI的新一代“推理模型”（o1係列）正是專為解決複雜數學問題和科學任務而設計的。如果這些模型成功，將為像陶這樣的數學家提供前所未有的幫助。
陶設想了一種由AI支持的“工業級數學”形式，雖然AI本身不會成為獨立的創造性合作者，但可以作為數學家假設和推理過程中的輔助工具。這種新型數學，雖然前景廣闊，但核心仍然是以人為本，強調人類與機器的互補性，而非競爭。
（2024年10月4日）
