OpenAI 发布 722 份数学手稿与证明，引发数学界对 AI 的强烈争议

上周，OpenAI 分享了超过 400 项结果，涉及困扰人类数十年的长期数学公式；如今研究人员表示，人类可能需要数年时间，才能验证并证明所有这些由 AI 驱动的工作。不过，在分析人士试图核查这款未具名 OpenAI 内部前沿模型所发现的所谓解法之际，数学家们认为，这种由 AI 驱动的研究与发布方式本身就威胁着该领域。

甚至有人认为，AI 从提示词直接跳到解答、中间没有清晰推导过程，因此这些解答本身的价值有限。数学家和整个领域可能无法在这些结果的基础上继续推进，因为他们不知道这些结果是如何得出的，而且这类解法的产生也没有带来新的数学理解领域。

更糟糕的是，有观点认为，前沿 AI 不断汇聚的数学与网络安全能力，可能会使密码学本身的可靠性受到质疑。除对国家安全和现代数字系统引发严重担忧外，这还可能令价值数万亿美元的加密货币面临迫在眉睫的风险。

一次性发布逾 722 份手稿

OpenAI 数学解法发布的官方统计数字为 722 份手稿，但其中只有 300 项结果完成了形式化处理——即将人类可读的公式数字化，使其能够由计算机验证——因此很难判断哪些属于可靠研究。接受 The Verge 采访的一些研究人员在报告中发现了毫无意义的解释、不合逻辑的公式，以及其他研究者已经完成的研究。

证明 OpenAI 及其模型所作主张真实性的负担，也很大程度上落在数学界身上。OpenAI 没有公布用于生成这些结果的模型名称，也没有公开生成结果所使用的提示词——尽管数学家与人工智能咨询小组（AGMAI）曾提出这样的建议。

OpenAI 至少已经为其结果的 GitHub 仓库发布了更新日志，从而更清楚地标明错误出现的位置。但目前已经出现多次撤回与修正，这似乎清楚表明，该公司在发布前并未对结果进行特别细致的检查。

正是这种大胆冒进的态度、发布速度，以及 OpenAI 在这一领域似乎毫无放缓意愿的表现，让许多数学家感到愤怒。

数学并不是第一个因 AI 而遭遇重大震荡的领域。随着 ChatGPT 在 2022 年发布，作家最先感受到迫近的威胁；不久之后，视觉艺术家和音乐艺术家也面临了同样的担忧。人工智能正在以某种方式影响几乎所有行业，尽管它在数学领域的应用可能带来一些好处，但该领域的研究人员担心，这可能冲击数学研究的协作性质，并阻碍未来的数学家探索这一学科。

纽约大学数学教授 Tristan Buckmaster 在接受 Business Insider 采访时表示，OpenAI 的发布颠覆了许多职业生涯早期数学家的世界，甚至可能摧毁了他们整个研究计划。除了一些人的自身研究可能因 OpenAI 的部分解法而失效外，他还表示，一些人如今担心，研究人员此前使用 AI 工具时，可能在无意中为这些结果作出了贡献；这可能导致他们未来不再使用高级工具，也更不愿意公开谈论自己的研究。

西北大学数学教授 Bryna Kra 认为，这可能给整个数学领域造成巨大问题。她强调数学是高度协作的学科，研究人员会共享想法、研究数据和公式；如今她非常担忧，OpenAI 已令数学家变得更加保密，削弱了他们共同寻找解法、并在彼此研究基础上继续推进的能力。

加州大学数学教授 Terence Tao 在 Mastodon 上表示，与传统突破相比，“由这些结果带来的研讨会、工作坊、合作或其他活动要少得多”。他认为，数学界或许需要转向更“整体地重视进展”，即提升社区建设相对于单纯解答成果的重要性。

研究人员描述了一种极度焦虑的氛围：无论他们正在研究什么，都可能在一夜之间失去意义。这可能损害求职申请、科研经费提案，以及那些正在建立学术生涯早期基础的人。要在高水平上理解和发展核心数学能力，可能需要数年时间。AI 以如此随意的方式批量发布结果、抹去多年的努力，会使这项事业看起来近乎毫无意义。

随着有关 OpenAI 还将发布更多结果的传言不断出现，以及其他追逐相同头条的 AI 实验室可能推出配套发布，许多数学领域的士气极为低落。

密码学

数学为数字世界的关键组成部分提供了基础，因此其发展速度的重大变化可能在其他领域产生连锁反应，这并不令人意外。其中一个被提出的潜在雷区，是密码学这一充满发展空间的领域。

约翰斯·霍普金斯大学怀廷工程学院计算机科学副教授 Matthew Green 在社交媒体上表示，他认为数学进展与网络安全能力的结合，可能会催生能够破解现有加密体系的 AI。

这不仅会给所有依赖加密来保护敏感数据安全的领域带来潜在担忧，也可能令加密货币行业面临大规模盗窃风险，影响价值数万亿美元的数字代币。

并非所有人都同意 Green 认为这不可避免的看法。英国密码学家 Adam Back——也是少数曾被认为可能是比特币开发者中本聪的人之一——称这些说法是无稽之谈，并表示，没有多少迹象表明，仅仅因为 AI 现在能够完成某些数学工作，它们就会在未来某个未确定的时间点破解加密。

以太坊创始人 Vitalik Buterin 也呼吁保持冷静，他在 Twitter/X 上表示，任何人都不应急于将代币转移到新钱包，也不应对钱包安全感到恐慌。不过，他确实认为，AI 有朝一日可能成为比量子计算更危险得多的加密货币安全威胁。

虽然目前看来，密码学还不是一个即将被 AI 颠覆的领域，但显然，AI 对数学研究者以及其底层的“做事方式”构成了潜在威胁，就像它在几乎所有其他领域中所做的那样。

研究人员正在适应这一变化，但局面短期内不太可能平息；与此同时，OpenAI 及其同行可能会在持续追逐影响力和盈利的过程中，转向下一个重点关注的领域。

Last week, OpenAI shared over 400 results for longstanding mathematical formulas that have troubled humans for decades; now researchers say it could take years for humans to validate and prove all the AI-driven work. But while analysts try to check the work of the unnamed OpenAI internal frontier model that found these alleged solutions, mathematicians argue this kind of AI-powered research and release threatens the field itself.

There's even the claim that by leaping from a prompt to a solution without a clear working in between, there is little benefit to these solutions in the first place. Mathematicians and the field itself may not be able to build on the results, as they don't know how they were achieved, nor has the development of such solutions produced new fields of mathematical understanding.

To make matters worse, there are suggestions that the growing confluence of mathematical and cybersecurity capabilities of frontier AI could bring into question the sanctity of cryptography itself. Alongside raising serious concerns for national security and modern digital systems, it could also put trillions of dollars worth of cryptocurrency at imminent risk.

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Over 722 manuscripts dropped

The official count for OpenAI's maths solution release was 722 manuscripts, but with only 300 of the results formalized — digitizing human-readable formulas so they can be computer-verified — it's very difficult to know what's legitimate research. Some of the researchers The Verge spoke to found nonsense explanations within the reports, formulas that don't make sense, and some research that has already been completed by others.

The burden of proving the veracity of OpenAI and its model's claims is very much on the mathematical community, too. OpenAI didn't release the name of the model it used to generate these results, nor the prompts that generated them — despite those recommendations from the Advisory Group on Mathematicians and Artificial Intelligence (AGMAI).

OpenAI has at least published changelogs for its GitHub repository of the results, making it clearer where mistakes were made. But with several retractions and corrections already, it seems clear that it didn't check over the results in any great detail before releasing them.

It's this brashness, the pace of releases, and OpenAI's seeming disinterest in remotely slowing down its progress in the field that have so many mathematicians up in arms.

Mathematics isn't the first field to suffer a major upheaval because of AI. Writers first felt the looming threat with the release of ChatGPT in 2022, and both visual and musical artists faced the same concerns shortly after. Artificial intelligence is impacting almost every industry in some way, but while there are some potential benefits for its use in the field of mathematics, researchers within the field are concerned about the impact this may have on the collaborative nature of the field and how it might discourage future mathematicians from exploring it.

Speaking to Business Insider, mathematics professor at NYU, Tristan Buckmaster, said that OpenAI's release had upended the world of many early-career mathematicians, suggesting it had wiped out their whole research programs. Alongside their own research being invalidated by some of OpenAI's solutions, he suggested that some were now fearful that, by using AI tools, researchers had inadvertently contributed to the results, raising the potential of them not using advanced tools in the future and being less likely to talk about their research publicly.

This could cause huge problems for mathematics as a whole, argued mathematics professor at Northwestern University, Bryna Kra. Highlighting how collaborative maths is, with researchers sharing ideas, research data, and formulas, she is now extremely concerned that OpenAI has made mathematicians more secretive, reducing their ability to work together towards solutions and build on each other's research.

Professor of mathematics at the University of California, Terence Tao said on Mastodon that "many fewer seminars, workshops, collaborations, or other activities are being generated from these results compared to traditional breakthroughs." He argued mathematics may need to pivot to value "progress more holistically," by elevating the role of community building over raw solutions.

Researchers have described an atmosphere of extreme anxiety, that whatever they're working on could be invalidated overnight. That can undermine job applications, grant proposals, and those building the early components of their academic careers. Understanding and developing core mathematical capabilities at a high level can take years. AI dumps eradicating years of effort in such a haphazard fashion risk making it seem a near-pointless endeavour.

With swirling rumors of yet more releases from OpenAI, and potentially companion releases from other AI labs chasing the same headlines, the morale in many mathematical fields is extremely low.

Cryptography

With how much mathematics underpins key components of our digital world, it's no surprise that major changes in the pace of its development could have a domino effect elsewhere. One proposed potential minefield is the fertile ground of cryptography.

Associate professor of computer science at Johns Hopkins Whiting School of Engineering, Matthew Green, said on social media that he believes the congruence of mathematical developments and cybersecurity capabilities could result in AI that can defeat encryption as we know it.

While that raises potential concerns for all manner of fields that rely on encryption to protect the security of sensitive data, it could open up the cryptocurrency industry to wholesale theft, potentially impacting trillions of dollars of digital tokens.

Not everyone agrees with Green that this is an inevitability. British cryptographer — and one of the few people accused of being Bitcoin developer Satoshi Nakamoto — Adam Back, described these claims as nonsense and that there was little suggestion that just because AI can do certain mathematics now, that they'll be able to defeat encryption at some unnamed date in the future.

Ethereum creator Vitalik Buterin urged calm too, stating on Twitter/X that nobody should rush to move their tokens to a new wallet or panic over wallet security. However, he did argue that AI had the potential to one day be a far more dangerous threat to the sanctity of cryptocurrency than quantum computing.

While it doesn't appear that cryptography is a field AI is set to invalidate just yet, it's clear that it poses a potential threat to mathematical researchers and the core underlying 'way of doing things.' Much like it has just about everywhere else.

Researchers are adjusting to it, but the dust isn't likely to settle anytime soon, and in the meantime, OpenAI and its contemporaries may just move on to a new field to focus on as it continues to chase relevance and profitability.