数学即将永远改变之际，OpenAI内部研究人员报告了一项重大突破：人工智能几乎和一群小学水平的孩子一样聪明。
Before math changed forever, researchers inside OpenAI reported a monumental breakthrough: AI was nearly as smart as a bunch of kids in elementary school.
五年前，人工智能前沿的工程师训练了一个模型来解决数千道基础数学题。随后他们对其进行了测试。现在轮到你了。
Five years ago, the engineers on the frontier of artificial intelligence trained a model to solve thousands of basic math problems. Then they put it to the test.
小测验！（或者继续阅读。）即使你对数学过敏，大概也能应付这道简单的算术题。正如OpenAI研究人员所说：“一个聪明的初中生应该能解出每道题。”但小学生——或者人工智能模型——呢？
Now it’s your turn. Pop quiz! (Or just keep reading.) Even if you’re allergic to math, you can probably handle this simple arithmetic. As OpenAI’s researchers put it: “A bright middle-school student should be able to solve every problem.”But what about a student in elementary school—or an AI model?
当公司将这份考卷交给9到12岁的一群孩子时，他们得了60分。原始的人工智能系统参加了同样的测试，得了55分。研究人员欣喜若狂。
When the company gave this exam to a group of kids between the ages of nine and 12, they scored 60%. The primitive AI system was given the same test and scored 55%. And the researchers were elated.
“我还记得蹦蹦跳跳的感觉，”OpenAI首席研究官马克·陈告诉我，“对于那些我们现在会嘲笑的事情。”从未有过一次数学考试不及格感觉如此美好。当时，模型在逐步推理解决问题方面很糟糕。此后，人工智能变得比研究人员预期的更快、更强大。
“I still remember the feeling of jumping up and down,” OpenAI chief research officer Mark Chen told me, “for things that we would laugh at now.”Never had a failing grade on a math exam felt so good. At the time, the models were lousy at reasoning through problems step by step. Since then, AI has become more powerful in far less time than even the researchers expected.
它不再为四年级的作业苦苦挣扎。现在，它正在做前所未有的数学。
It’s no longer struggling to do fourth-grade homework. Now it’s doing mathematics that no human has ever done.
仅在过去几周内，OpenAI的一个内部模型就解决了一个传奇的千禧年奖难题，随后又解决了数百个其他未解决问题，这在几个月前还看似不可思议。这一发现的爆炸让整个领域震惊不已——证明数学将不再如从前。
In the past few weeks alone, an OpenAI internal model solved one of the legendary Millennium Prize Problems and then several hundred more open problems, which seemed inconceivable even a few months ago. This explosion of discoveries has left the field reeling—proof that math will never be the same.
数学已成为理解人工智能能力进步有多大、人们对其低估有多严重的最便捷方式。那么现在怎么办？如果模型在五年内从被长除法难住，发展到能够攻破类里曼假设，那么未来五年又将如何发展？如果人工智能能够掌握一门让大多数人脑子一团浆糊的领域，那么它是否只是时间问题，就会来对付我们中的其余部分？
Math has become the easiest way to understand how dramatically AI’s capabilities have advanced and how badly people have underestimated them. So now what? If the models went from being stumped by long division to cracking the quasi-Riemann hypothesis in five years, how will the next five years play out? And if AI can master a field that turns most of our brains to mush, is it only a matter of time before it comes for the rest of us?
这些问题比数独角兽和珍妮特卖鸡蛋要难得多——而数学家们原本以为，他们不会最先不得不回答这些问题。事实上，不久前，数学还被认为是人工智能最晚会改变的领域之一。
These are much harder questions than counting unicorns and Janet’s egg sales—and mathematicians didn’t think they would have to answer them first. Not long ago, in fact, math was thought to be one of the last fields AI would transform.
但随着公司利用数学来训练模型，这些模型在数学方面变得好得多、好得多。
But as the companies used math to train their models, those models became much, much better at math.
2023年，OpenAI的顶级模型轻松通过了之前机器不及格的小学数学考试。这种快速的进步意味着，它已经准备好迎接更严苛的数学知识测试。是时候让人工智能参加SAT考试了。
In 2023, OpenAI’s top model breezed through the grade-school math exam that previous machines had flunked. That rapid improvement meant it was ready for a more grueling test of mathematical knowledge. It was time for AI to take the SAT.
该模型在SAT数学部分拿到了800分中的700分——这表明这些系统已经走得多远，以及它们还有多远才能达到目标。即便如此，人工智能仍不如那些将去大学主修英语、以便不用思考代数的青少年。
The model scored 700 of 800 on the SAT’s math section—a sign of how far these systems had come and how far they still had to go. Even then, AI was outperformed by teenagers who would go to college and major in English so they wouldn’t have to think about algebra.
大约在这个时候，人工智能工具在回答一道不会出现在任何标准化考试上的数学问题时，仍然臭名昭著地糟糕：单词strawberry里有多少个r？（提示：不是两个。）但实验室里的研究人员可以看到，下一代模型在计算水果名称中的字母数量时，不会有任何困难。
Around this time, AI tools were still famously bad at answering one math question that wouldn’t appear on any standardized test: How many r’s are in the word strawberry? (Hint: not two.) But inside the labs, researchers could see that the next generation of models wouldn’t have any trouble computing the number of letters in fruit.
人工智能从效果不佳，发展到效果好到令人害怕，部分原因在于数学本身的性质。与更混乱的领域不同，数学在数千年来一直受到精确逻辑规则的支配。它也是可验证的。答案是对或错，因此模型可以从错误中学习，就像9岁的孩子一样。
AI went from not working very well to working so well it’s scary partly because of the nature of math itself. Unlike messier domains, math has been governed by precise rules of logic for millennia. It’s also verifiable. Answers are right or wrong, so models can learn from their mistakes, just like 9-year-olds.
接下来，他们数学教育的下一阶段：来自许多AI研究人员自己也曾参加过的高中竞赛的题目。
Next up in their math education: problems from the high-school competitions that many AI researchers had once entered themselves.
起初，模型在需要复杂多步推理的棘手问题上举步维艰。但和其他数学基准测试一样，这个测试最终也会被彻底击破。
At first, the models stumbled on tricky problems that required complex multistep reasoning. But like other math benchmark tests, this one would eventually get obliterated.
2023年中期，OpenAI的顶级模型在该测试最难的问题上得分23%。2024年，该公司推出了其首个推理模型——代号“草莓”——该模型在数学和编程方面尤其强大。到2024年底，OpenAI的旗舰模型在该考试中取得了95%的得分。
In mid-2023, OpenAI’s top model scored 23% on the test’s hardest problems. In 2024, the company rolled out its first reasoning model—code-named “Strawberry”—and it was particularly strong in math and coding. By the end of 2024, OpenAI’s signature model hit 95% on that exam.
而在2025年初，这种进展对OpenAI的研究负责人来说变得触目惊心。
And in early 2025, that progress became personal for OpenAI’s research leader.
当他得知模型已经超越了他作为竞技程序员的最高评分时，陈突然对李世石产生了共鸣，李世石是世界顶尖围棋选手之一，在AlphaGo击败他的这场AI历史上的决定性事件中落败。
When he was informed the models had surpassed his peak rating as a competitive programmer, Chen suddenly empathized with Lee Sedol, one of the world’s top Go players, who was defeated by AlphaGo in a defining event of AI history.
“那对我来说是一个真正的情感时刻，”他说。“我觉得经历过那样时刻的人，对模型未来能做什么会有更深的体会。”陈对模型在臭名昭著的美国邀请数学考试中取得满分也有另一层体会。当他还是高中毕业班学生时，来自世界各地的8586名学生参加了AIME考试。其中九人取得满分。他就是其中之一。
“That was a real emotional moment for me,” he said. “I feel like people who have undergone moments like that have a greater appreciation for what the models are able to do in the future.”Chen had another reason to appreciate their perfect score on the notoriously difficult American Invitational Mathematics Examination. When he was a high-school senior, 8,586 students from all over the world took the AIME. Nine got perfect scores. He was one of them.
一旦AI模型在AIME考试中取得高分，并在数学奥林匹克竞赛中赢得金牌，它们就从高中数学毕业，转向那些困扰人类数十年的未解决问题。
Once the AI models aced the AIME and won gold medals at the math Olympics, they graduated from high-school math to open problems whose solutions had eluded humans for decades.
我问陈，如果我在2021年告诉他接下来五年的进展速度，他会怎么说。
I asked Chen what he would have said if I had told him in 2021 about the velocity of the next five years.
“我会说那太疯狂了，”他说。“但这里的严峻教训是，人们真的很难内化指数增长——即使是OpenAI内部的人也是如此。”当我给德克萨斯大学的理论计算机科学家夫妇斯科特·阿伦森和达娜·莫什科维茨打电话时，我了解到为什么预测进步的步伐如此困难。
“I would have said that’s crazy,” he said. “But the harsh lesson here is that people are really bad at internalizing exponentials—even people inside OpenAI.”When I called Scott Aaronson and Dana Moshkovitz, a married couple of theoretical computer scientists at the University of Texas, I learned why it’s so hard to predict the pace of progress.
“事情发生的速度比你预想的快，”阿伦森说，“即使你根据上一次发生得比预想快的事情进行了更新，情况也是如此。”在被称为2026年8月的“从前”时期，莫什科维茨正和一位同事讨论独特游戏猜想，这是一个高度抽象的问题，困扰她十余年。当她提出AI有一天可能解决它时，这个想法听起来如此荒谬，以至于那位同事以为她在开玩笑。两个月后，她被证明是正确的，因为解决方案出现在OpenAI发布的大量论文中。
“Things happen faster than you expect,” Aaronson said, “even when you update on the last thing happening faster than you expected.”In the before times otherwise known as August 2026, Moshkovitz was talking with a colleague about the Unique Games Conjecture, a highly abstract problem that had occupied her mind for more than a decade. When she floated the idea that AI might solve it one day, the suggestion was so preposterous that he thought she was joking. Two months later, she was proven right when the solution appeared in OpenAI’s blizzard of papers.
莫什科维茨在接儿子放学时告诉了他这个消息。巧合的是，他今年9岁——与OpenAI研究中最年轻的参与者年龄相同。
Moshkovitz broke the news to her son when she picked him up from school. As it happens, he is 9 years old—the same age as the youngest participants in OpenAI’s study.
他们在解决数学问题上已不再比AI聪明，但9岁的孩子仍然相当聪明。
They are no longer smarter than AI at solving math problems, but 9-year-olds are still pretty wise.
“他告诉我，”莫什科维茨说，“他们应该去解决癌症问题。”来源：OpenAI；大学理事会；PLOS One；MATH数据集 注：部分问题已做轻微修改。小学问题来自OpenAI的GSM8K数据集，AI回答来自2021年OpenAI研究中测试的一个GPT-3版本。SAT问题来自大学理事会的模拟考试，AI回答来自2023年运行GPT-4的ChatGPT，如《ChatGPT作为潜在本科生和医学院学生》一文所报道。竞赛数学问题来自MATH数据集，AI回答来自OpenAI 2023年PRM800K数据集中的一个GPT-4版本。
“He told me,” Moshkovitz said, “they should solve cancer instead.”Sources: OpenAI; College Board; PLOS One; MATH data set Note: Some questions have been lightly edited. Grade-school questions come from OpenAI’s GSM8K data set, and the AI responses from a version of GPT-3 tested in a 2021 OpenAI study. SAT questions come from College Board practice tests, and the AI responses from ChatGPT running GPT-4 in 2023, as reported in “ChatGPT as a prospective undergraduate and medical school student.”Competition-math questions come from the MATH data set, and the AI responses from a version of GPT-4 in OpenAI’s 2023 PRM800K data set.