人工智能（AI）如今正在解决长期困扰人类的数学难题，这促使全球数学家——包括中国的数学家——不仅思考机器是否会取代他们，还思考其领域内的成就与研究在未来将意味着什么。
Artificial intelligence (AI) is now solving maths puzzles that have long stumped humans, prompting mathematicians around the world, including in China, to ponder not only whether machines will replace them, but also what achievement and research in their field will mean in the future.
10月初，OpenAI发布手稿，展示了在372类数学问题上的进展，其中包括许多长期未解之谜。本周，这家美国AI公司宣布了三项新发现。
In early October, OpenAI released manuscripts showing progress on 372 categories of mathematical problems, including many which have long defied solutions. This week, the American AI firm announced three further discoveries.
OpenAI表示，人类团队目前正在解读AI在数学、计算机科学和物理学领域生成的成果。分析结果被视为AI演进速度的一个指标。
Human teams are now interpreting the AI-generated results in mathematics, computer science and physics, OpenAI said. The outcome of the analysis is seen as an indication of how fast AI is evolving.
数学界近期的讨论也加剧了关于该技术将如何影响一个曾被视为最困难、最枯燥的学科领域的辩论。
Recent discussions in the mathematical community have also sharpened debate about how the technology will affect a field once seen as one of the most difficult and tedious fields of study.
学术期刊《科学》主编H·霍尔登·索普周四在一篇社论中表示，近期AI的成就“让数学界震惊不已”。索普写道，这引发了一个更广泛的问题：“理解的满足感能否取代发现的快感？”澳裔美籍数学家陶哲轩多次批评OpenAI。这位2006年菲尔兹奖得主周三在一次公开采访中表示，AI在数学家之前给出解决方案，相当于对早期工作的“掠夺式开采”。
H. Holden Thorp, editor-in-chief of the academic journal Science, said in an editorial on Thursday that the recent AI achievements “sent the world of mathematics reeling”. Thorp wrote that they raised a broader question: “Can the satisfaction of understanding ever replace the thrill of discovery?”Australian-American mathematician Terence Tao has repeatedly criticised OpenAI. In a public interview on Wednesday, the 2006 Fields Medal winner said AI coming up with solutions before mathematicians amounts to “strip mining” of earlier work.
陶哲轩与其他24位菲尔兹奖得主——被誉为“数学界的诺贝尔奖”——上月在一封联名信中警告，AI生成的数学解决方案必须由人类来开发并融入该领域。他们表示，走捷径将破坏学科的传承方式以及学生的学习方式。
Tao and 24 other Fields Medal winners, known as the “Nobel Prize of mathematics”, warned in a joint letter last month that AI-generated mathematical solutions must be developed and integrated into the field by humans. They said short-cuts would undermine how the subject is passed down and how students learn.
陶哲轩还在周四发表于《科学》的社论中论证称，AI正在改变研究范式，让人类只能去解读和理解AI生成的证明，而非自行开发证明。
Tao also argued in the editorial published on Thursday in Science that AI is changing the research paradigm, leaving humans to interpret and understand AI-produced proofs rather than develop them.
中国对数学领域使用人工智能提出担忧。北京清华大学的丘成桐正牵头一个由1000多名科学家组成的联盟，专门开发用于数学的人工智能模型。
Concerns raised in China over AI use in mathematics China has raised similar concerns. Shing-Tung Yau of Beijing’s Tsinghua University is leading an alliance of more than 1,000 scientists to develop AI models specifically for mathematics.
丘成桐表示，人工智能在数学领域的发展“如海啸般汹涌”，中国在推动数学和物理学发展的人工智能系统方面落后于美国。
Yau said AI’s development in mathematics was “like a tsunami”, and China lags behind the US in AI systems for advancing mathematics and physics.
丘成桐将担任新创刊的《人工智能辅助数学杂志》主编，该刊计划于2027年开始出版。该杂志被定位为纯数学领域严谨的人工智能辅助研究论坛。
Yau will serve as editor-in-chief of the new Journal of AI-Assisted Mathematics, set to begin publication in 2027. The journal was described as a forum for rigorous, AI-assisted research in pure mathematics.
丘成桐表示，无论人工智能扮演何种角色，定理都必须达到顶级纯数学期刊同样的证明标准，作者必须说明该技术如何促成研究发现，以及他们如何验证人工智能生成的主张。
Yau said theorems must meet the same proof standards as leading pure mathematics journals, regardless of AI’s role, and authors must explain how the technology contributed to the findings and and how they verified AI-generated claims.
其他数学家则认为，某些人工智能成果应被视为“菲尔兹奖级别”。
Other mathematicians have argued that some AI results should be considered “Fields Medal-worthy”.
常驻清华大学的德裔伊朗裔数学家巴巴克·哈吉哈特认为，在合适的框架下，人工智能是连接不同领域的有力工具，而个人过去需要花费一生时间才能学会这些领域。
Babak Haghighat, a German-Iranian mathematician based at Tsinghua University, argued that in the right framework, AI is a powerful tool for connecting fields that individuals could previously learn only over a lifetime.
哈吉哈特在10月20日于京都大学发表的演讲中表示，人工智能将有助于探索以前不可能的解决方案和研究任务。
In an October 20 talk delivered at Kyoto University, Haghighat said AI would help to explore solutions and research tasks that were previously impossible.
然而，他警告说，大型人工智能公司掌握着最先进的模型，加剧了国际不平等。
However, he warned that large AI companies hold the most advanced models, deepening international inequality.
他说：“人工智能模型如今已成为数学研究的必需品，但数学家无法获取顶尖公司的模型，也无法检查和测试其结果是如何产生的。”这位研究人员表示，数学过去专注于通过全球合作建设的公共利益。
“AI models are now essential to mathematical research, yet mathematicians cannot access the top companies’ models or check and test how their results were produced,” he said. The researcher said mathematics used to be focused on the public good built through global collaboration.
他表示，现在由大型人工智能公司决定谁可以使用这些工具，不仅中国研究人员，所有数学家都处于劣势，他警告不要让少数私人利益掌握控制权。
Now that large AI companies decide who can use these tools, not only Chinese researchers but all mathematicians are at a disadvantage, he said, warning against giving a small number of private interests control.
哈吉哈特呼吁中国与大学和数学家合作，训练先进的人工智能模型。他指出，目前的中国模型擅长编程，但不擅长数学，而擅长数学的模型在商业或安全领域也更有可能表现得更好。
Haghighat called on China to work with universities and mathematicians to train advanced AI models, noting that current Chinese models are good at programming but not mathematics, and that a model good at mathematics is also more likely to perform better in commercial or security fields.
专家认为利用人工智能寻找解决方案影响积极 该领域的其他人也认为人工智能的介入影响积极。
Expert sees positive impact from using AI to find solutions Others in the field see a positive impact from AI involvement.
热门数学类 YouTube 频道 3Blue1Brown 的创作者格兰特·桑德森表示，现在是学习数学的最佳时机，因为证明变得更容易获得，数学家可以专注于理论构建。
Grant Sanderson, creator of the popular mathematics-focused YouTube channel 3Blue1Brown, said now is the best time to learn mathematics, since proofs have become easier to obtain and mathematicians can focus on theory building.
桑德森说：“人工智能正在改变数学的学术文化和学分分配体系，学界正在寻找新的标准。”
“AI is changing mathematics’ academic culture and credit-allocation system, and the community is looking for new standards,” Sanderson said.
当 AlphaGo 在中国古老的棋类游戏围棋中击败人类大师时，许多人感叹该游戏失去了挑战性。如今，顶尖棋手利用人工智能辅助训练，这为数学家提供了一条可能的前进道路。
When AlphaGo defeated human masters in the ancient Chinese board game Go, many people lamented that the game had lost its challenge. Now, top players use AI-assisted training, offering a possible way forward for mathematicians.
桑德森表示，人工智能在解决问题上优于人类数学家，不应阻止研究人员变得更强。
Sanderson said AI being better at solving problems than human mathematicians should not stop researchers from getting stronger.
他说：“这就像去健身房：当然，机器能举起比你更重的重量，但这并不否定你举重所获得的价值。”
“The analogy is going to the gym: sure, machines can lift heavier weights than you, but that doesn’t negate the value you get from lifting,” he said.