显然在当下或者以后的未来时代，掌握构建复杂agent系统的能力，是一种类似浪尖的能力。对于我所学的软件工程，虽说不像其他那些工程类的更加实际，但是的确是构建一个复杂系统的最适合的专业了。关于保研的方向，所以我想尽量往这边靠。

We used a system of coordinating agents powered by our internal model. The agents had access to tools such as the ability to read from a cached version of the internet and the ability to run code. Agents were subdivided into groups with the ability to communicate within the group. The groups varied in size, and the group that produced the Navier–Stokes resolution involved on the order of 10,000 concurrent agents. At all times we maintained the same strict safeguards that we apply to all our frontier model evaluations, including monitoring and isolation. 我们采用了一种由内部模型驱动的协调代理系统。这些代理可以访问各种工具，比如从缓存的互联网数据中读取信息，以及运行代码的能力。代理们被划分为不同的小组，这些小组之间可以互相通信。各个小组的规模各不相同，而负责生成 Navier–Stokes 解算结果的那个小组，同时运行的代理数量达到了约 10,000 个。在任何时候，我们都遵循着同样严格的防护措施，这些措施是我们对所有前沿模型评估所采用的标准，包括监控和隔离措施。

For each problem, we prompted different groups of agents with different variants of the problem statement, covering all variants of the problem. For the Navier–Stokes problem, we suggested versions “A” and “B” (particular forms of the Navier–Stokes problem which would result in a proof) and versions “C” and “D” (which would result in a disproof) to separate groups of agents. 对于每个问题，我们向不同的代理组展示了问题的各种变体，以涵盖所有可能的情况。对于纳维-斯托克斯问题，我们为不同的代理组分别提供了“A”和“B”两种版本的问题（这两种版本能够促成证明），以及“C”和“D”两种版本的问题（这两种版本则可能导致无法证明）。

In addition to the full Millennium Prize problems, we asked our multiagent system to try a set of “easier” problems. One of these problems was a similar blowup question for the limit of the Navier–Stokes problem with the viscosity term removed. This is known as the regularity problem for the Euler equations, and our agents surprised us by resolving this question. The specific variant of the question that they resolved was the unforced version, where no external force is applied to the fluid. Nearly 100 agents worked together for approximately 50 hours to produce our Euler regularity disproof. 除了完整的“千年大奖问题”之外，我们还让我们的多智能体系统尝试解决一系列“较简单”的问题。其中有一个问题类似于纳维-斯托克斯问题的扩展版本，只不过这里删除了粘性项。这个问题被称为欧拉方程的正则性问题。我们的智能体在解决这个问题时表现得非常出色。他们解决的具体问题是无外力作用的情况，即流体不受任何外部力的影响。近 100 个智能体共同工作了大约 50 个小时，才解决了这个欧拉正则性验证问题。1

Once we saw the Euler solution, we thought that Navier–Stokes was the most promising problem to work on. Thus, we decided to devote our resources to Navier–Stokes. To do so, we shifted agents away from the other Millennium Problems and prompted these agents with the Euler resolution. When a further trained version of our internal model became available over the course of the effort, we updated our agents to that model. 一旦我们掌握了欧拉方法的解决方案，我们就认为纳维-斯托克斯问题是最有前景的研究课题。因此，我们决定将资源集中在纳维-斯托克斯问题上。为此，我们让智能体不再处理其他千年难题，而是引导它们专注于欧拉方法的解决方案。当我们的内部模型经过进一步训练后变得可用时，我们就将智能体更新为使用这个新模型。

We encouraged different groups of agents to explore a diversity of approaches. After some time, we cross-pollinated the agent groups by using Codex to consolidate the most useful insights from each agent group. These follow-up prompts drew on the agents’ own intermediate results. The group that found the solution to Navier–Stokes was guided in such a way. 我们鼓励不同的代理团队尝试各种不同的方法。经过一段时间的探索后，我们通过 Codex 将各个团队的研究成果进行整合，从而实现了知识的交叉传播。这些后续的引导过程都是基于各个团队所取得的中间成果进行的。找到 Navier–Stokes 问题的解决方案的那个团队就是通过这种方式得到指导的。

The agents arrived at their resolution on Saturday, September 5, about 88 hours after the first agents were launched. Lean formalization and verification took an additional 17 hours via GPT‑6 Astra. 这些工程师们在 9 月 5 日星期六得出了他们的结论，这距离首次启动这些工程师大约过去了 88 个小时。而通过 GPT-6 Astra 进行精益形式化设计和验证则又花了 17 个小时才完成。

Across all attempted problems, the agents sent 4.9 million messages and used about 300 billion output tokens. In the process of resolving the Navier–Stokes problem, the agents sent 2.7 million messages and used approximately 130 billion output tokens. 在所有尝试解决的问题中，这些智能体共发送了 490 万条消息，并使用了约 3000 亿个输出令牌。在解决 Navier-Stokes 问题过程中，这些智能体发送了 270 万条消息，并使用了大约 1300 亿个输出令牌。