内容来源：https://www.technologyreview.com/2026/03/25/1134642/this-startup-wants-to-change-how-mathematicians-do-math/

内容总结：

初创公司Axiom Math发布免费AI工具，旨在革新数学研究模式

加州帕洛阿尔托的初创公司Axiom Math近日向数学界免费发布了一款名为Axplorer的新型人工智能工具。该工具旨在帮助研究者发现隐藏的数学规律，从而有望解决一些长期悬而未决的难题。此举被视为响应美国国防高级研究计划局（DARPA）推动数学与AI融合的“expMath”倡议的一部分。

Axplorer是该公司研究科学家弗朗索瓦·沙尔东早前在Meta参与开发的工具PatternBoost的升级版。PatternBoost曾依靠超级计算机破解了图论中著名的“图兰四圈问题”。如今，经过重新设计的Axplorer大幅提升了效率，据称在单台Mac Pro上仅用2.5小时就复现了PatternBoost耗时三周取得的成果，其目标是让更多数学家能在个人计算机上使用这种强大的模式发现能力。

公司创始人兼CEO卡丽娜·洪强调，当前许多AI工具主要专注于解决已有问题，但数学研究本质上是探索性和实验性的。Axplorer的设计理念正是辅助这种探索过程：用户提供一个初始示例，工具会生成类似案例，用户可筛选感兴趣的结果反馈给系统，从而迭代式地引导AI发现新规律。这与谷歌DeepMind的AlphaEvolve系统思路类似，但Axiom Math宣称其工具更易获取和使用。

尽管近期已有数学家利用大语言模型（如GPT-5）解决了一些历史难题，但沙尔东认为，许多悬而未决的“大问题”需要全新的思路，而非对已有成果的衍生。Axplorer的开源发布，有望让学生和研究人员更便捷地生成问题的样例与反例，加速数学发现进程。

不过，数学界对层出不穷的AI工具持审慎乐观态度。曾参与PatternBoost开发的悉尼大学数学家乔迪·威廉姆森表示，虽然Axplorer在理论上能适用于更广泛的数学问题，但其实际影响仍有待观察。他提醒，数学研究不应忽视那些更“脚踏实地”的传统方法。

Axiom Math团队承认，目前面向数学家的AI工具众多，其中一些还要求研究者自行训练神经网络，这提高了使用门槛。他们希望Axplorer通过一步步引导的交互方式，降低数学家的使用负担，真正融入研究流程。该工具的代码已在GitHub上开源，其能否如公司所愿显著加速数学研究，数学界正拭目以待。

中文翻译：

这家初创公司想要改变数学家的工作方式

Axiom Math公司正在免费提供一款强大的新型人工智能工具。但它能否如公司所愿加速研究进程，仍有待观察。

总部位于加州帕洛阿尔托的初创公司Axiom Math发布了一款面向数学家的免费新型人工智能工具，旨在发现可能破解长期数学难题的数学规律。

这款名为Axplorer的工具，是对现有工具PatternBoost的重新设计。PatternBoost由现任Axiom研究科学家的弗朗索瓦·沙尔东于2024年在Meta任职期间共同开发。PatternBoost需在超级计算机上运行，而Axplorer则可在Mac Pro上运行。

该工具的目标是让任何能在自己电脑上安装Axplorer的人，都能拥有曾用于破解"图兰四圈问题"这一数学难题的PatternBoost的强大能力。

去年，美国国防高级研究计划局启动了一项名为"expMath"的新计划，旨在鼓励数学家开发和使用人工智能工具。Axiom视自己为这一推动力的一部分。

沙尔东表示，数学领域的突破会对整个技术领域产生巨大的连锁反应。特别是新的数学成果对于计算机科学的进步至关重要，从构建下一代人工智能到提升互联网安全都离不开它。

Axiom Math创始人兼首席执行官卡丽娜·洪指出，目前人工智能工具的成功大多局限于为现有问题寻找解决方案。但寻找解决方案并非数学家工作的全部，数学本质上是探索性和实验性的。

上周，《麻省理工科技评论》与沙尔东和洪进行了独家视频访谈，探讨了他们的新工具以及人工智能将如何整体改变数学领域。

聊天机器人做数学

过去几个月，一些数学家已开始使用OpenAI的GPT-5等大语言模型来寻找未解问题的答案，尤其是已故20世纪数学家保罗·埃尔德什留下的数百个谜题。

但沙尔东对这些成果不以为然。他表示："大量问题悬而未决只是因为无人关注，从中找出几个能解决的瑰宝并不难。"他将目光投向了更严峻的挑战——"那些经过深入研究的、著名学者曾致力攻克的重大学术难题"。去年，Axiom Math使用其另一款名为AxiomProver的工具，成功解决了四个此类数学问题。

沙尔东指出，PatternBoost破解的图兰四圈问题正是这样一个重大难题。该问题是图论领域的重要课题，图论这门数学分支被用于分析社交媒体连接、供应链和搜索引擎排名等复杂网络。想象一张布满圆点的纸，这个谜题的核心在于如何在尽可能多的圆点之间画线，同时避免形成连接四个圆点的闭环。

"如果你的目标只是对已有成果进行衍生，那么大语言模型的表现极其出色，"沙尔东说，"这并不奇怪——大语言模型是基于所有现有数据进行预训练的。但可以说大语言模型是保守的，它们倾向于复用已有内容。"

然而，数学中存在大量需要全新思路和前所未有见解的问题。有时这些见解源于发现前所未有的规律模式，此类发现可能开辟出全新的数学分支。

PatternBoost正是为帮助数学家发现新规律而设计。向工具输入一个示例，它就能生成类似案例。用户选择其中有趣的案例反馈给系统，工具便会生成更多相关案例，如此循环迭代。

这与谷歌DeepMind的AlphaEvolve系统理念相似，后者利用大语言模型为问题提供新颖解决方案。AlphaEvolve会保留最佳建议并要求大语言模型进行优化改进。

特殊权限

研究人员已运用AlphaEvolve和PatternBoost为长期存在的数学问题找到了新解法。但问题在于，这些工具需要大规模GPU集群支持，大多数数学家无法使用。

沙尔东表示，数学家们对AlphaEvolve充满热情，"但它是封闭系统——需要特殊权限才能使用。你必须去找DeepMind的工作人员帮你输入问题。"

当沙尔东用PatternBoost解决图兰问题时，他仍在Meta任职。"我当时能调用成千上万台机器运行程序，"他回忆道，"整整运行了三周时间，这种蛮力计算方式令人汗颜。"

Axiom Math团队表示，Axplorer的速度和效率远超前者。沙尔东透露，Axplorer仅用2.5小时就复现了PatternBoost在图兰问题上的成果，而且只需单机运行。

曾与沙尔东合作开发PatternBoost的悉尼大学数学家乔迪·威廉姆森尚未试用Axplorer，但他对数学家们将如何运用这款工具充满好奇。威廉姆森表示，Axiom Math对PatternBoost进行了多项改进，理论上使Axplorer能适用于更广泛的数学问题，但"这些改进的实际意义仍有待观察"。

"我们正处于一个奇特时期，众多公司都推出了希望我们使用的工具，"威廉姆森补充道，"可以说数学家们面对各种可能性有些应接不暇。新增这样一款工具会产生何种影响，目前尚不明确。"

洪承认当前面向数学家推广的人工智能工具确实很多，其中有些还要求数学家自行训练神经网络。身为数学家的洪指出，这种要求令人却步。相比之下，Axplorer将逐步引导用户完成所需操作。

Axplorer的代码已通过GitHub开源。洪希望学生和研究人员能利用该工具为他们正在研究的问题生成示例解法和反例，从而加速数学发现进程。

威廉姆森对新型工具表示欢迎，并坦言自己经常使用大语言模型。但他认为数学家们还不该就此抛弃白板。"以我的个人见解，PatternBoost是个绝妙创意，但绝非万能良药。希望我们不要忘记更务实的研究方法。"

英文来源：

This startup wants to change how mathematicians do math
Axiom Math is giving away a powerful new AI tool. But it remains to be seen if it speeds up research as much as the company hopes.
Axiom Math, a startup based in Palo Alto, California, has released a free new AI tool for mathematicians, designed to discover mathematical patterns that could unlock solutions to long-standing problems.
The tool, called Axplorer, is a redesign of an existing one called PatternBoost that François Charton, now a research scientist at Axiom, co-developed in 2024 when he was at Meta. PatternBoost ran on a supercomputer; Axplorer runs on a Mac Pro.
The aim is to put the power of PatternBoost, which was used to crack a hard math puzzle known as the Turán four-cycles problem, in the hands of anyone who can install Axplorer on their own computer.
Last year, the US Defense Advanced Research Projects Agency set up a new initiative called expMath—short for Exponentiating Mathematics—to encourage mathematicians to develop and use AI tools. Axiom sees itself as part of that drive.
Breakthroughs in math have enormous knock-on effects across technology, says Charton. In particular, new math is crucial for advances in computer science, from building next-generation AI to improving internet security.
Most of the successes with AI tools have involved finding solutions to existing problems. But finding solutions is not all that mathematicians do, says Axiom Math founder and CEO Carina Hong. Math is exploratory and experimental, she says.
MIT Technology Review met with Charton and Hong last week for an exclusive video chat about their new tool and how AI in general could change mathematics.
Math by chatbot
In the last few months, a number of mathematicians have used LLMs, such as OpenAI’s GPT-5, to find solutions to unsolved problems, especially ones set by the 20th-century mathematician Paul Erdős, who left behind hundreds of puzzles when he died.
But Charton is dismissive of those successes. “There are tons of problems that are open because nobody looked at them, and it’s easy to find a few gems you can solve,” he says. He’s set his sights on tougher challenges—“the big problems that have been very, very well studied and famous people have worked on them.” Last year, Axiom Math used another of its tools, called AxiomProver, to find solutions to four such problems in mathematics.
The Turán four-cycles problem that PatternBoost cracked is another big problem, says Charton. (The problem is an important one in graph theory, a branch of math that’s used to analyze complex networks such as social media connections, supply chains, and search engine rankings. Imagine a page covered in dots. The puzzle involves figuring out how to draw lines between as many of the dots as possible without creating loops that connect four dots in a row.)
“LLMs are extremely good if what you want to do is derivative of something that has already been done,” says Charton. “This is not surprising—LLMs are pretrained on all the data that there is. But you could say that LLMs are conservative. They try to reuse things that exist.”
However, there are lots of problems in math that require new ideas, insights that nobody has ever had. Sometimes those insights come from spotting patterns that hadn’t been spotted before. Such discoveries can open up whole new branches of mathematics.
PatternBoost was designed to help mathematicians find new patterns. Give the tool an example and it generates others like it. You select the ones that seem interesting and feed them back in. The tool then generates more like those, and so on.
It’s a similar idea to Google DeepMind’s AlphaEvolve, a system that uses an LLM to come up with novel solutions to a problem. AlphaEvolve keeps the best suggestions and asks the LLM to improve on them.
Special access
Researchers have already used both AlphaEvolve and PatternBoost to discover new solutions to long-standing math problems. The trouble is that those tools run on large clusters of GPUs and are not available to most mathematicians.
Mathematicians are excited about AlphaEvolve, says Charton. “But it’s closed—you need to have access to it. You have to go and ask the DeepMind guy to type in your problem for you.”
And when Charton solved the Turán problem with PatternBoost, he was still at Meta. “I had literally thousands, sometimes tens of thousands, of machines I could run it on,” he says. “It ran for three weeks. It was embarrassing brute force.”
Axplorer is far faster and far more efficient, according to the team at Axiom Math. Charton says it took Axplorer just 2.5 hours to match PatternBoost’s Turán result. And it runs on a single machine.
Geordie Williamson, a mathematician at the University of Sydney, who worked on PatternBoost with Charton, has not yet tried Axplorer. But he is curious to see what mathematicians do with it. (Williamson still occasionally collaborates with Charton on academic projects but says he is not otherwise connected to Axiom Math.)
Williamson says Axiom Math has made several improvements to PatternBoost that (in theory) make Axplorer applicable to a wider range of mathematical problems. “It remains to be seen how significant these improvements are,” he says.
“We are in a strange time at the moment, where lots of companies have tools that they’d like us to use,” Williamson adds. “I would say mathematicians are somewhat overwhelmed by the possibilities. It is unclear to me what impact having another such tool will be.”
Hong admits that there are a lot of AI tools being pitched at mathematicians right now. Some also require mathematicians to train their own neural networks. That’s a turnoff, says Hong, who is a mathematician herself. Instead, Axplorer will walk you through what you want to do step by step, she says.
The code for Axplorer is open source and available via GitHub. Hong hopes that students and researchers will use the tool to generate sample solutions and counterexamples to problems they’re working on, speeding up mathematical discovery.
Williamson welcomes new tools and says he uses LLMs a lot. But he doesn’t think mathematicians should throw out the whiteboards just yet. “In my biased opinion, PatternBoost is a lovely idea, but it is certainly not a panacea,” he says. “I’d love us not to forget more down-to-earth approaches.”
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