Why are we even doing all this?

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Why are we even doing all this?

What’s new Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao Home About Career advice On writing Books Mastodon+ Applets Subscribe to feed Why are we even doing all this? 15 October, 2026 in guest blog, opinion | Tags: Rikab Gambhir | by Terence Tao [This is a guest post by Rikab Gambhir. This blog post was initially written in a different file format and converted using AI. — T.]

最新动态:关于我的研究和说明性论文的更新、开放问题的讨论以及其他数学相关主题。作者:陶哲轩。主页、关于、职业建议、写作、书籍、Mastodon+、小程序、订阅源。我们为什么要搞这些?2026年10月15日,客座博客,观点 | 标签:Rikab Gambhir | 作者:陶哲轩 [这是一篇由Rikab Gambhir撰写的客座文章。此博文最初以不同的文件格式编写,并使用人工智能进行了转换。——T.]

First, they came for the artists, and I did not speak out, because I was not an artist. Then, they came for the mathematicians, and I did not speak out, because I was not a mathematician. Then, they came for the physicists, and it was actually really cool and they gave me free tokens and promised to solve my entire field for me and now I can finally devote myself to the important work of publishing papers instead of doing physics.

起初,他们抓走了艺术家,我没有说话,因为我不是艺术家。接着,他们抓走了数学家,我没有说话,因为我不是数学家。然后,他们抓走了物理学家,这其实真的很酷,他们给了我免费的代币,承诺为我解决整个领域的问题,现在我终于可以全身心投入到发表论文这一重要工作中,而不必再去搞物理了。

In early October, OpenAI fulfilled every mathematician’s childhood dream. I am not a mathematician myself (merely a theoretical particle physicist, which some argue barely counts as a scientist either), so I can’t 100% say for certain what inspires someone to pursue mathematics. But, I imagine this dream is common to all academics: Looking up at the stars in wonderment, or enjoying a complex puzzle game, or being inspired by an encouraging teacher, and dreaming that one day an unfeeling corporate robot[1] will burn a rainforest to compile a list of 700 highly obscure barely-readable facts that might be true that nobody can understand as part of a marketing gimmick to raise hype for an IPO[2]. This is probably why most of you reading this got into academia. At least, that’s why I did.

10月初,OpenAI实现了每一位数学家童年的梦想。我本人并非数学家(仅仅是一名理论粒子物理学家,有些人甚至认为这都算不上科学家),所以我无法百分之百确定是什么激励着人们去追求数学。但我猜想,这个梦想在所有学者中都很普遍:怀着惊叹仰望星空,或者享受复杂的益智游戏,又或者受到鼓舞人心的老师的启发,梦想着有一天,一个冷酷的企业机器人[1]会烧毁一片雨林,整理出一份包含700个高度晦涩、几乎无法阅读且“可能”为真的事实清单,而这些事实作为IPO[2]营销噱头的一部分,根本没人能看懂。这大概就是你们大多数人进入学术界的原因。至少,这就是我的原因。

In 1941, Jorge Luis Borges imagined a library containing every possible book that could ever be written. Somewhere in this Library of Babel is a proof of the Riemann hypothesis, the complete all-orders theory of quantum gravity, and all the papers I will ever write. Of course, there are also incorrect proofs, theories, and misleading Lean certificates, but that is besides the point. By the research standards of 2026, Borges’s Library of Babel would be the most successful research institution in human history, containing an inconceivably large number of potentially correct mathematical and physical results, blowing OpenAI’s mere 722 write-ups and even the physics community’s recent 2500 write-ups out of the water.

1941年,豪尔赫·路易斯·博尔赫斯构想了一个包含所有可能写出的书籍的图书馆。在这个巴别图书馆的某个地方,藏着黎曼猜想的证明、完整的全阶量子引力理论,以及我未来将要写的所有论文。当然,里面也有错误的证明、理论和误导性的Lean证书,但这无关紧要。按照2026年的研究标准,博尔赫斯的巴别图书馆将是人类历史上最成功的研究机构,它包含了数量大到不可思议的潜在正确数学和物理结果,足以让OpenAI那区区722篇文稿,甚至物理学界最近的2500篇文稿相形见绌。

Of course, most recognize that Borges was a visionless fool who failed to recognize the commercial potential of his library, as he never actually built it. He did not have the entrepreneurial STEM-spirit to raise venture capital, launch an IPO, and announce that he had the potential to solve all of mathematics. He was too concerned about the futility of sorting through randomized slop trying to understand what is correct and what isn’t and how to understand it all. But what did Borges know? He was only a writer, and we have already established that artists are obsolete.

当然,大多数人都认为博尔赫斯是个缺乏远见的傻瓜,他没能意识到自己图书馆的商业潜力,因为他从未真正把它建出来。他没有那种筹集风险投资、启动IPO并宣布自己有潜力解决所有数学问题的创业型STEM精神。他太纠结于从随机的垃圾信息中筛选出什么是对的、什么是错的,以及如何理解这一切的徒劳感。但博尔赫斯懂什么呢?他只是个作家,而我们已经认定艺术家已经过时了。

Fortunately, OpenAI has brought us one step closer to realizing Borges’s vision. Rather than generating every possible mathematical paper, they’ve found a way to probabilistically generate things that look correct. An important aspect of this increase in efficiency is outsourcing the tedious, unprestigious, and unprofitable work of determining the actual correctness and understanding to the mathematics community (in the past, this was reserved typically for the group writing the paper), while also not wasting any time making the papers human-comprehensible. This is, of course, a tremendous breakthrough.

幸运的是,OpenAI让我们离实现博尔赫斯的愿景又近了一步。他们没有去生成每一篇可能的数学论文,而是找到了一种概率性生成看起来正确的内容的方法。这种效率提升的一个重要方面是,将确定实际正确性和理解内容的枯燥、无名且无利可图的工作外包给了数学界(过去,这通常是由撰写论文的团队负责),同时也不浪费任何时间去让论文变得通俗易懂。这当然是一个巨大的突破。

In centuries past, scientists and mathematicians were limited in their ability to solve problems by their ability to understand the solutions. This bottleneck has been removed, and now there is no theoretical limit to the amount of scientific and mathematical factoids we can fail to understand. From what I know about the academic community (mostly from Twitter and LinkedIn, which I assume are representative), there seems to be near-unanimous agreement that the purpose of math and science research is to gather a large quantity of potentially true factoids in a repository that nobody will actually ever read, in a ritual called “advancing humanity’s[3] knowledge”.

在过去的几个世纪里,科学家和数学家解决问题的能力受限于他们理解解决方案的能力。这个瓶颈现在已经被打破,现在我们无法理解的科学和数学事实数量已经没有了理论上限。据我对学术界的了解(主要来自Twitter和LinkedIn,我认为它们具有代表性),大家似乎近乎一致地认为,数学和科学研究的目的是在一个没人会真正阅读的存储库中收集大量潜在的事实,这种仪式被称为“推进人类[3]知识”。

That these results are well-written, understandable, pleasant to read or look at, or even completely correct is a secondary concern — in fact, in the pursuit of advancing humanity’s knowledge as quickly as possible, many academics will recoil in anger at the suggestion that it is worth spending any time making results understandable to humans. It is inefficient to explain or check a result when those resources can be spent generating another. This aligns with my own lived experiences — I didn’t become a theoretical physicist to learn about the universe or better appreciate the beauty of nature myself (that’s philosophy, which I would never be a doctor of).

这些结果是否文笔优美、通俗易懂、赏心悦目,甚至是否完全正确,都是次要的考虑因素——事实上,在追求尽可能快地推进人类知识的过程中,许多学者会对“花时间让结果变得通俗易懂是有价值的”这一建议感到愤怒。当这些资源可以用来生成另一个结果时,去解释或检查一个结果是低效的。这与我个人的生活经历相吻合——我成为理论物理学家并不是为了了解宇宙或更好地欣赏自然之美(那是哲学,我永远不会成为那方面的博士)。

Nor did I spend years learning to write code, make pleasing plots, or craft well-written papers for the simple satisfaction of creating something (that’s art, and we’ve already established that art is obsolete). Rather, I became a physicist to stare at large databases of histograms produced by a Lovecraftian-autocomplete of dubious correctness and say “yeah that’s probably ok I guess” to add to humanity’s knowledge frontier. I live to serve the knowledge frontier and nothing else.

我也不是为了创造事物的简单满足感而花费数年时间学习编写代码、制作精美的图表或撰写文笔优美的论文(那是艺术,而我们已经认定艺术已经过时了)。相反,我成为物理学家是为了盯着由洛夫克拉夫特式的自动补全程序生成的、正确性存疑的大型直方图数据库,然后说“嗯,大概没问题吧”,从而为人类的知识前沿添砖加瓦。我活着就是为了服务于知识前沿,别无他求。

Math and science are about cold, hard answers, just as art is about producing images, music is about producing sound waves, and literature is about producing strings of text. These things exist to be consumed as content. No rational person, least of all us masters of rationality in STEM, pursues these for the joy of creation, learning, or beauty — all of these are inefficiencies, and we mustn’t be inefficient lest we stifle humanity’s progress. LLMs are not burdened with these inefficiencies, and they will be merely the pursuits of those left behind with nothing more product.

数学和科学关乎冷冰冰的硬答案,正如艺术关乎产生图像,音乐关乎产生声波,文学关乎产生文本字符串一样。这些东西的存在就是为了作为内容被消费。没有一个理性的人,尤其是我们这些STEM领域的理性大师,会为了创造、学习或美的乐趣而追求这些——所有这些都是低效的,我们绝不能低效,以免阻碍人类的进步。大语言模型(LLM)不受这些低效因素的困扰,而这些(追求)将仅仅是那些被抛在后面、再无产出的人的追求。