A Severe Misalignment of AI in Mathematics
人工智能在数学领域存在严重错位
Over the last few months, the mathematical capabilities of LLMs have improved dramatically, to the point that they can solve major outstanding problems in many fields of mathematics. However, the push by AI companies to solve mathematical problems as a benchmark is detrimental to the science of mathematics, and to the mathematical community. The goals of the AI companies and the goals of the mathematical community are severely misaligned. We see these as part of broader alignment issues impacting other scientific and creative professions, as well as the whole of society.
过去几个月，大文本模型的数学能力显著提升，甚至能够解决许多数学领域中一些重要的未解难题。然而，人工智能公司将解决数学难题作为衡量标准的做法，对数学科学本身以及整个数学界都造成了损害。人工智能公司的目标与数学界的目标严重不符。我们认为，这只是影响其他科学和创意行业乃至整个社会的更广泛协调性问题的冰山一角。
Research mathematics deals with understanding basic structures of shapes, numbers, and natural phenomena. Over the course of generations, it has built a large corpus of sophisticated ideas, methods, abstractions, and other tools to comprehend the mathematical landscape. In turn, modern technologies and sciences are based on mathematical tools.
研究数学致力于理解形状、数字和自然现象的基本结构。经过几代人的发展，它构建了庞大的复杂思想、方法、抽象概念和其他工具体系，以理解数学的奥秘。反过来，现代科技和科学也建立在数学工具的基础之上。
Famous problems have often served as landmarks and lighthouses against which one can measure an improved understanding of this landscape. Solving one of these problems has been a certain sign of new insights and interesting methods, which would then be studied by a community of mathematicians, through a long and arduous process of talks, discussions, simplifications. At the end of this process, one will ideally find a textbook presentation of the results suitable for any graduate or even undergraduate student to study. Some of the mathematical ideas pursue their journey even further to become, decades or centuries after, tools that are understood and used by the whole population.
著名的数学难题常常如同路标和灯塔，指引着我们对数学领域的理解不断加深。解决这些难题往往意味着新的见解和有趣的方法的出现，随后，数学家群体会通过漫长而艰辛的讨论、交流和简化过程，对这些见解和方法进行深入研究。理想情况下，最终会形成一本教科书，将研究成果呈现给任何研究生甚至本科生学习。有些数学思想甚至会延续其发展历程，在数十年或数百年后，成为被大众理解和使用的工具。
The mathematical community functions, in many ways, as a miniature version of humanity. It consists of individuals using a wide variety of different approaches, joined by core values. The most precious resources of our profession are students and ideas, and these we nurture with great care. We feel responsible to let them grow to their full potential, until they can live a life of their own in the mathematical world. For students we often suggest problems with the core intention of developing skills making them well-positioned for advances in research and elsewhere. Our ideas we disseminate in talks, private discussions and careful writeups, connecting them to the previous ideas of others. These processes invariably take time and are based on human interaction.
数学界在许多方面都像是人类社会的缩影。它由运用各种不同方法、秉持共同核心价值观的个体组成。我们这个行业最宝贵的资源是学生和思想，我们悉心培育它们。我们深感有责任让它们充分发挥潜力，直至它们能够在数学世界中拥有自己的一席之地。对于学生，我们常常提出一些问题，其核心目的是培养他们的技能，使他们能够更好地在研究及其他领域取得进步。我们通过演讲、私下讨论和精心撰写的文章来传播我们的思想，并将它们与他人的先例联系起来。这些过程必然需要时间，并且建立在人与人之间的互动之上。
In recent months, the success of AI in solving major mathematical problems has made headlines even outside mathematical circles. But solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight. Forgetting this in the world of AI may turn the tool against the primary goal. Indeed, the mass production at faster and faster pace of "true/false" statements could destroy fertile ground instead of breathing life into new ideas.
近几个月来，人工智能在解决重大数学难题方面的成功甚至在数学界之外也引起了广泛关注。然而，解决问题仅仅是工具，是实现概念理解和洞察力这一根本目标的途径。在人工智能领域，如果忽视这一点，可能会使工具本身与根本目标背道而驰。事实上，以越来越快的速度大规模生产“真/假”陈述，可能会扼杀孕育新思想的沃土，而不是为其注入活力。
Often these solutions are announced in a rush, leaving no time for a proper writeup, the isolation of new methods and ideas, and citing relevant previous work of others. As in all creative professions, this raises severe attribution and plagiarism questions. Moreover, without the willing mathematicians who must take care of their development and integration into the mathematical canon, AI-conceived ideas would never become fully alive and the crucial human transmission chain between mathematicians would be lost.
这些解决方案往往仓促发布，没有时间进行充分的撰写、对新方法和新思路的梳理，以及引用他人相关的先前工作。如同所有创意行业一样，这引发了严重的署名和抄袭问题。此外，如果没有那些致力于发展和整合这些方案并将其纳入数学体系的数学家，人工智能提出的想法将永远无法真正落地，数学家之间至关重要的传承链条也将断裂。
We are witnessing a general threat to intellectual work, with misalignment between the outcome of the use of AI and its initial purpose. In many fields and activities, years of training have traditionally served not only to produce a final answer or product, but also to develop understanding and the ability to formulate new questions and ideas. However, building on a vast body of previous human work, AI systems are becoming increasingly capable of producing the results of such work directly, and these goals cease to align. The issues the mathematical community faces now are similar to issues that other scientific and creative professions are facing, and indicate issues that all of humanity might face: how to make sure that, as AI changes the way work is done, we do not lose sight of what that work was meant to achieve in the first place.
我们正目睹智力劳动面临普遍威胁，人工智能的应用结果与其最初目标之间存在脱节。在许多领域和活动中，多年的训练传统上不仅是为了得出最终答案或产品，更是为了培养理解力以及提出新问题和新想法的能力。然而，人工智能系统建立在大量人类先前工作的基础上，越来越能够直接产出此类工作的结果，而这些目标却不再一致。数学界目前面临的问题与其他科学和创意行业面临的问题类似，也预示着全人类可能面临的问题：如何确保在人工智能改变工作方式的同时，我们不会忘记这项工作最初的目标。
AI offers the potential of enhancing and accelerating genuine mathematical study and understanding. Mathematics as a profession will need to adapt to these changes in several ways. However, whether these changes ultimately benefit the field or have a destructive effect will in large part be determined by the decisions of the humans in control of this new technology.
人工智能有望增强和加速真正的数学研究和理解。数学作为一门学科，需要从多个方面适应这些变化。然而，这些变化最终是造福于该领域还是产生破坏性影响，很大程度上取决于掌控这项新技术的人们的决策。
These issues must be addressed urgently, in the mathematical community, by the companies developing these technologies and, more broadly, by a society that will confront similar problems in many other forms of intellectual work.
这些问题必须紧急解决，数学界、开发这些技术的公司以及更广泛的社会都必须重视这些问题，因为在许多其他形式的智力工作中，社会也将面临类似的问题。
签名者
Artur Avila (Fields Medal 2014)
Manjul Bhargava (Fields Medal 2014)
Caucher Birkar (Fields Medal 2018)
Pierre Deligne (Fields Medal 1978)
Yu Deng (Fields Medal 2026)
Simon Donaldson (Fields Medal 1986)
Hugo Duminil-Copin (Fields Medal 2022)
Alessio Figalli (Fields Medal 2018)
Martin Hairer (Fields Medal 2014)
June Huh (Fields Medal 2022)
Maxim Kontsevich (Fields Medal 1998)
Elon Lindenstrauss (Fields Medal 2010)
Pierre-Louis Lions (Fields Medal 1994)
James Maynard (Fields Medal 2022)
Curtis McMullen (Fields Medal 1998)
Shigefumi Mori (Fields Medal 1990)
Ngô Bảo Châu (Fields Medal 2010)
Andrei Okounkov (Fields Medal 2006)
Peter Scholze (Fields Medal 2018)
Stanislav Smirnov (Fields Medal 2010)
Terence Tao (Fields Medal 2006)
Maryna Viazovska (Fields Medal 2022)
Cédric Villani (Fields Medal 2010)
Wendelin Werner (Fields Medal 2006)
Efim Zelmanov (Fields Medal 1994)