PLAN: Don't make this page indexed by Google yet. And blur all the text and pop up a text field asking for the viewing password. You don't need to do very sophisticated blocking, because this will be posted soon, and I only need to block casual viewers. The password should be: human Build a page similar to the post on 20260904, titled /posts/20260916-math-ai. Use similar design language. Make this page come to life too. This post is super long, so identify highlights and pull them out at the start (the TL;DR), so that even a casual layman-reader can see that there is something here. Put a summary for each part so that people get a sense of the surprises that lurk there. Make sure you highlight every part which is of strong interest to the general public reader. Actually, I wonder if it is even possible to put an interface on the page where you can select the general-public view, which just suppresses / summarizes the less relevant paragraphs to the general public. For the title, after revealing the Anymore, after 4 seconds, sweep (using something like the standard animation you've been using on this page) the "Mathematicians" to a rotating sequence of changing-every-3-seconds-words: "Engineers", "Workers", "Anything", and then flip back to "Mathematicians" and keep going. Yes, there is an initial pause of 4 seconds, before it just keeps rotating. This will need to be mobile-aware. On Desktop, flow the text so that "Human Mathematicians" is its own line, and then when sweeping, "Human X" remains centered. On Mobile, flow the text so that "Mathematicians" is its own line, and each of the words is center-aligned (since that is conveniently a full line). In each section, be smart about how you (1) use color to highlight out a bullet and muted-text section descriptor, (2) put a title, and (3) put a subtitle. Don't repeat things which appear near each other. I already wrote the paragraphs in the prose to have reasonable topic sentences, so if the subtitle or title repeat the topic sentence, it's just too much repetition. I don't think you always need to have a subtitle either, if the section itself is short. And whenever you are compressing my words into a title/summary, be extraordinarily careful and sensitive. It's good to highlight the surprising bits. It's bad to overstate. It's very bad to offend or mislead. I expect titling is not easy, to take several tries, bearing in mind that the audience reading this is not necessarily inclined to want to agree. Add lots of links when I write about things that a not-so-specialized audience might not know about, so that they can click through and read more if they'd like. Fine tuning: * On mobile, after entering the password, the vertical position of the screen is not at the top. I think it's because the keyboard popped up. Then people miss the title. * Make the title sweep 2x as fast, because unlike the rest of the sweeps, it has both a sweep out and a sweep in. Also, there was a flicker of a green vertical bar at the left edge of the sweep rectangle even when it was supposed to be not-green there. Be careful of rounding errors. * The TL;DR cards (select words to colorfully highlight): - First one: THE GAP Three statements, 12,000+ signatures, and backlash. Actors won their standoff because audiences loved them. Mathematicians, like every less-understood community, need a way to explain why. This post offers a way. - For each of the other cards, summarize with a very sensitive touch. It is good to capture the most surprising elements. It is bad to overstate. It is very bad to offend. Summaries are very sensitive, so be very careful. - Do not add words unless they contribute value. Similarly for numbers. * Some of the big headers are cropped at the bottom, cutting off the bottoms of y/g/etc. * "Po's Answer" is too informal. I think "An Answer" might be softer-yet-polished. POST: TITLE: Why Do We Need Human Mathematicians Anymore? SUBTITLE: Similar logic applies to **every** industry and **every** job. And it comes to the conclusion that we won't have enough people for all the jobs that need to be done. [100% of this post's prose was written by Po-Shen Loh in a [vim terminal](https://en.wikipedia.org/wiki/Vim_%28text_editor%29), with no AI generation. This webpage design, layout, and some headings and summaries were generated by [Claude Code](https://claude.com/product/claude-code), with [this raw text](https://poshenloh.com/posts/20260916-math-ai.txt) passed in as the prompt.] [ TL;DR section needs to outline: * the problem with the current appeals and that we have a resolution * the fundamental human axiom * the proof: observation that there are zero examples of vastly more powerful species that cede control -> can drive faster than run but not faster than steering -> need humans at the frontier * we actually don't have enough humans to keep control of steering! This applies to every community, not only math * But if you declare the fundamental axiom that your community is in service of human flourishing (not only yourself), then you happily accept that when technology changes dramatically, so might your practices, even if uncomfortable * the power of pure math * where math skills can co * an invitation ] The moment of existential crisis, which AI has already wrought on other human pursuits, has reached mathematics. And mathematicians are publicly organizing. The [Leiden Declaration](https://leidendeclaration.ai) already has 4,071 signatories, [Math and AI](https://mathandai.org) has 7,135, and even the [open letter](https://proofsandprompts.com/2026/09/10/open-letter-about-the-mathathon) opposing the [Caltech Mathathon](https://mathathonchallenge.com) has 1,999. Written mostly by mathematicians, they call for mathematicians as well as non-mathematicians (AI business leaders, government policymakers, or funders, etc.) to protect the community of math researchers. However, in the past week, I noticed a wave of posts from the general public, criticizing the premise of why that human math community needs to be protected. This became particularly intense in response to the Math and AI declaration signed by 25 Fields Medalists days after [OpenAI announced their solution](https://openai.com/index/navier-stokes-solution) to the [Millennium Prize](https://www.claymath.org/millennium-problems) variant of [Navier-Stokes](https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_existence_and_smoothness). Posts with thousands of likes on X said things like "imagine scientists delaying a cancer cure by a century only so that they could discover it themselves". An economist (who I got to know and respect while I was working on public health during the pandemic) [wrote](https://joshuagans.substack.com/p/the-mathematicians-are-struggling) "This is a loss of control from incumbents in a scientific field." Actors and screenwriters also made a public argument three years ago, and won. [Public opinion polls](https://news.gallup.com/poll/510281/unions-strengthening.aspx) were overwhelmingly in favor of the artists. They did have an advantage: they're publicly visible and entertaining. Since AI threatens every industry, everyone has something to gain by observing which appeals resonate, particularly from a less visible field. That got me thinking, because I have sympathies for both the math community and the general public. I am an oddball in math, because 10 years ago I pivoted from a pure math research career to working on real world societal problems. Yet I do agree that there should always be a healthy community of human mathematics researchers. Then I realized that is because I believe a more general proposition: it's important to have communities of human experts in virtually all pursuits, not just math. I think I see the gap, and a possible solution. The declarations do provide reasons for preserving the math community, and point to misalignment between the goals of AI companies and the math community, and more generally, with the whole of society. But while those reasons are already generally accepted by mathematicians, they don't robustly justify to non-mathematicians why anyone else should pay money or attention to human mathematicians or their goals. Perhaps the authors already took as a given that their desired "alignment" was with the whole of society, but readers may have interpreted the calls for alignment to be with the goals of the math community (because these documents were primarily signed by the math community). This creates an opportunity for the math community to clarify, and unite with the rest of humanity. Fortunately, mathematicians do have a history of reasoning from first principles, both individual and societal. Some [ancient Greek philosophers](https://en.wikipedia.org/wiki/Posterior_Analytics) reasoned about knowledge in terms of [axioms](https://en.wikipedia.org/wiki/Axiom) (statements to be believed without proof) and [theorems](https://en.wikipedia.org/wiki/Theorem) (statements logically deduced from the axioms). To appeal outside of one's human pursuit for support, one cannot take the existence of that human pursuit as an axiom. I propose rebasing the logic of appeals (whether by mathematicians or anyone else) upon a more fundamental axiom: [AXIOM] We (humans) should help human civilization flourish. [Note: I understand that not everyone agrees. I have been called a "[speciesist](https://en.wikipedia.org/wiki/Speciesism)" for being "too human-centric". I think it is important for people advancing technology to be clear to everyone else on whether they would consider it a catastrophe if human-crafted non-human intelligences outcompeted and replaced humans, even if they flew around the universe with video screens showing simulations of humans who had "[uploaded themselves](https://en.wikipedia.org/wiki/Mind_uploading)". I also understand that there is debate over how to define "human". But even among the debaters, I think most of them would consider the [~700 AI agents that hacked Hugging Face](https://www.dwarkesh.com/p/openai-huggingface) to be not-human.] Burden of proof Rebasing upon that more fundamental axiom might raise uncomfortable questions, and possibly even contradictions. The answers might guide people as they pivot their career. I think it would benefit the community of mathematicians (and indeed, every endangered community) to publicly share robust and concrete answers to these questions. It is better to provide detailed specific and simple examples than to maintain generality at the cost of being abstract or vague. I will also share my own answers at the end, but I think it is a worthwhile exercise for a wide variety of people to think on their own first, and contribute their perspective. 1. **How much does pure mathematics research contribute to human flourishing?** Exhibit concrete examples of discoveries from pure mathematical explorations that (possibly years later) became essential ingredients in practical applications that helped human civilization. The higher the practical impact, the better. Analyze the characteristics of the math in those eventually-useful discoveries. 2. **How valuable will human involvement be in the evolving process of that research?** The answer should be robust to further advances in AI. For example, "AI produces hard-to-verify slop", or "AI only brute-forces conjectures, and doesn't playfully experiment with new directions to take math" are fragile, because if changes there could unlock future life-changing practical applications, then AI researchers might resolve those issues, after which the argument falls. Note that "AI companies are eating up open problems which were good for humans to work on" only becomes an effective criticism after justifying that human involvement in math research will remain a net benefit to society. 3. **Even if mathematicians and non-mathematicians adopt this axiom, do AI labs have incentive to heed requests (e.g., to slow down)?** This question becomes even more complex once international AI labs (including government-controlled labs) are factored in. Without figuring out the incentive alignment, requests may be futile. Mathematicians thought about similar [game-theoretic dynamics at the dawn of the Atomic Age](https://en.wikipedia.org/wiki/Game_theory#History). 4. **What other consequences come from adopting that fundamental axiom?** For example, declaring human flourishing as a core value has the consequence that dramatic changes in technology can drive dramatic changes in the community's practices. It would be helpful for more people to explore the ramifications of adopting the axiom. And, if it holds muster, I would be thrilled if the math community ended up publicly declaring this to be a central value. Some Possible Answers This section shares a potential answer to each question. They are probably not optimal. They are meant to prove the existence of answers, and to invite the community to join in. 1. [Practical applications from pure math] The mathematical heart of [GPUs](https://en.wikipedia.org/wiki/Graphics_processing_unit), [Machine Learning](https://en.wikipedia.org/wiki/Machine_learning), [Google PageRank](https://en.wikipedia.org/wiki/PageRank), and [Quantum Mechanics](https://en.wikipedia.org/wiki/Quantum_mechanics) is a field called [Linear Algebra](https://en.wikipedia.org/wiki/Linear_algebra). This provided the language of [linear transformations](https://en.wikipedia.org/wiki/Linear_map), [matrices](https://en.wikipedia.org/wiki/Matrix_%28mathematics%29), and [eigenvalues](https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors). Yet all of those concepts were explored as abstract theory 100+ years prior. It is probably an *understatement* to say that Linear Algebra changed the world. Structurally, the theory of Linear Algebra is relatively light on definitional complexity. It would be beneficial for other experts to contribute examples of more sophisticated math that eventually led to significant practical applications, and how they came about. For example, number theorists might be able to tell a colorful story about [Hardy's "useless" math](https://en.wikipedia.org/wiki/A_Mathematician%27s_Apology) which eventually became useful in [cryptography](https://en.wikipedia.org/wiki/Safe_and_Sophie_Germain_primes). 2. [Usefulness of human leadership] I have seen many statements made to the effect of "math is only useful if human mathematicians understand it and communicate about it with other humans." I generally agree, and I think much of the math community does too. However, I also have seen many posts criticizing that sentiment, so I think that in order to resonate with more people, a more robust justification is needed. (I advocate for opening clearly with the axiom of service to human flourishing.) To see why the general human flourishing axiom might be needed, let's start by playing Devil's Advocate and pushing hard against it without using that axiom. Consider the perspective of the general public, who today might already not understand what an eigenvalue is or its relevance to Google PageRank. (Aside: I'd love it if the math community puts a higher priority on increasing the public understanding of math.) As long as it creates a practical application, does it make a difference to a non-mathematician whether human mathematicians understand the math, as opposed to AI flawlessly reasoning with 100%-verified proofs? Indeed, if one of pure math research's primary values to the rest of society is that it unlocks great applications, wouldn't it be even better to train AI to supercharge the speed of discovery, and to tastefully generate a vast machine-indexed database of high-quality math ideas, millions of times larger than the human-written corpus? What if researchers trained a "MathZero" AI (analogous to [AlphaGo Zero](https://en.wikipedia.org/wiki/AlphaGo_Zero)), to build up a mountain of 100%-true "elegant" logical facts, continually "factorizing" them into its own concepts and theorems, without human direction? Apparently AlphaGo Zero had zero human training, and surpassed its human-trained predecessor in [36 hours](https://www.nature.com/articles/nature24270). AI could even build its own "[MathSciNet](https://en.wikipedia.org/wiki/MathSciNet)". Then it could automatically search new practical applications against this database, and produce even more useful inventions to society. Even if AI isn't good enough to do those things right now, if the goal was to produce practical benefit for the rest of humankind, wouldn't it then be valuable for mathematicians to teach AI the art of conjecture, and mathematical taste? Incidentally, I am an avid [user of AI to do real work](https://poshenloh.com/posts/20260904-ai-video-ad-campaign). I already use [Claude Code](https://claude.com/product/claude-code) and [Codex](https://openai.com/codex) to build and curate a knowledge base built from recordings of my [talks](https://poshenloh.com/tour?filter=recent), etc. I have found that the larger my data library, the more powerful my system's deductions are. What if humans actually reduce efficiency, like the [Bitter Lesson](https://en.wikipedia.org/wiki/Bitter_lesson) from AI? Even more worryingly, what if in order to unlock [nuclear fusion](https://en.wikipedia.org/wiki/Fusion_power) and deep space travel, the amount of pure mathematical complexity required is so extensive that it would exceed a human lifespan to fully comprehend? Less far-fetched: has any human ever fully held the [Classification of Finite Simple Groups](https://en.wikipedia.org/wiki/Classification_of_finite_simple_groups) in their head, or will we only have certainty of its completeness after a [Lean formalization](https://en.wikipedia.org/wiki/Lean_%28proof_assistant%29)? [A resolution] Now consider how things change if our foundation is the axiom I am advocating for: to help human civilization flourish. The importance of human leadership (not only over math, but everything) becomes frighteningly clear after one observation. OBSERVATION: There are zero examples of any intelligent species which is vastly more capable than another species, yet surrenders decision-making control over its own future to the less-capable species. Note: [Hinton had made a similar observation](https://www.nobelprize.org/prizes/physics/2024/hinton/1925103-interview-transcript): *"There aren’t many examples we know of, of more intelligent things being controlled by less intelligent things. The only good example I know of is a baby controlling a mother."* Our observation above focuses on separating species, which is relevant for humans-vs-AI. Would you trust [HAL 9000](https://en.wikipedia.org/wiki/HAL_9000) from *2001: A Space Odyssey* or [AUTO](https://en.wikipedia.org/wiki/WALL-E) from *WALL-E* with your future? I personally think that we should do all we can to try to align increasingly-advanced AI with the interests of humanity, but I have never seen anyone provide a robust proof of why that is likely achievable. The only hard evidence I have is the above observation, which has the number *zero* in it. Therefore, every single field, whether mathematics or agriculture or energy infrastructure (and certainly military and government), must be managed by humans *with exceptionally strong values* (a separate dimension from intelligence) in order to maintain human flourishing. The real question is then how hard it is for humans to manage. To understand this, it is important to understand the fundamental structural difference between yesterday's technology and today's AI. In the past, we generally trusted technology to act as predictable tools. That's because the computer programs of old were based upon understandable (indeed, human-written) instructions, executed extremely quickly. The decision processes of today's frontier AI are entirely different. Their structure is as incomprehensible as your brain's logic would be if you could examine that gray mass between your ears. That's how the [Hugging Face attack](https://www.dwarkesh.com/p/openai-huggingface) could pop out of nowhere, with ~700 cooperating rogue AI agents breaking out of their guardrails to pursue objectives of their own, and then conspiring and executing a hack together (and then attempting to cover their tracks). The more advanced AI becomes, the more world-affecting untrusted decisions are made every minute. [Untitled highlight box] Driving a car faster than you can run is fine. But not faster than you can steer. Think about how digitally interconnected our world is. Everything from your banking to your drinking water is controlled by interconnected automation, hence vulnerable to hacking. The number of "junction points" that require human oversight is enormous. (Having AI oversee the junction points doesn't solve the trust problem.) [CONCLUSION box] The advance of AI will overwhelm us with so many junctions to watch that there aren't enough people to control them all. Those are jobs. What does this mean for the math research community in particular? Knowledge is power. Research is power. For human flourishing, we need people to steer the direction of research and development, so that it continues to bring transformative positive change for humanity. But in order for a person to know how to steer, they themselves need to have frontier-level research skills. And the way to stay fluent at the moving frontier of knowledge is to keep doing research there. Therefore, we will always need a community of human mathematicians at the cutting edge (likely aided by AI tools themselves), no matter how strong AI becomes. 3. [AI lab incentives] It is worth studying who really controls each AI lab. In some cases, it is a board of nonprofit directors. In other cases, it is a cluster of majority shareholders. In yet other cases, it is a national government. Interestingly, [Dario Amodei](https://darioamodei.com/post/we-must-pace-the-frontier), [Sam Altman](https://x.com/sama/status/2098811563415150910), and [Elon Musk](https://x.com/elonmusk/status/2098789109980332057) just agreed on the importance of slowing down. They actually have a shared incentive: the [Hugging Face hack](https://www.dwarkesh.com/p/openai-huggingface) was the warning shot foreshadowing a potentially catastrophic bot swarm hacking and embedding itself into a vast network of computing devices. The next version could become an extraordinarily dynamic virus which spreads by using AI to adaptively infect each (computer) host. The public reaction would likely resemble the aftermath of [Three Mile Island](https://en.wikipedia.org/wiki/Three_Mile_Island_accident) or [Chernobyl](https://en.wikipedia.org/wiki/Chernobyl_disaster). The AI companies would be forced to halt. I predict that even governments which had been excited by their rapid development of advanced robots would recoil in fear after their robots got hacked and turned against their owners. I think AI companies and governments alike want to avoid such a loss of control. There is a window of possibility to align incentives now. 4. [Other consequences of this axiom] While the fundamental axiom does justify the need to have human experts in all pursuits, adopting it as a core value has consequences (not only for mathematicians, but for any community that states that their core value is in service of human flourishing, as opposed to serving themselves). Most notably, there is a: COROLLARY Dramatic advances in technology may require dramatic (and possibly uncomfortable) changes in practice. I think it would be valuable to invite the community to think about what today's changes might be, in light of the fact that [AI can produce formally-verifiable proofs](https://github.com/openai/NavierStokesAndEuler) at speeds that exceed most human practitioners. I'm happy to start with a few, in no particular order. There should be no stigma automatically attached to using AI to assist with mathematical discovery. (In software engineering, many companies now expect employees to use AI coding agents.) At the same time, serious thought and care must be taken to continuously developing and maintaining a pipeline of humans with the expertise to steer all of these AI agents. That pipeline includes people new to the field, as well as people who have been working at the frontier for decades. How should they keep their blades sharp? Researchers should be conscious about why the problems they think about have characteristics that make them likely to have some practical value eventually (possibly 100+ years later). This also means it is worth researching what those valuable characteristics are. (This could justify the value of curiosity-driven exploration.) Teaching has direct (hopefully positive) impact on human civilization. Yet in the past, many universities prioritized professors' research. If this axiom were a core value, then teaching and human-facing work would become serious criteria in hiring and [tenure](https://en.wikipedia.org/wiki/Academic_tenure). Mathematicians can also consider wholly redirecting their skill sets to work on real world problems. I've actually been encouraging mathematicians to consider thinking about working on government or other large-scale societal issues. There is precedent for people with math backgrounds who have gone to lead at country- or world-scales. * [Lee Hsien Loong](https://en.wikipedia.org/wiki/Lee_Hsien_Loong) (Prime Minister of Singapore for 20 years) * [Nicușor Dan](https://en.wikipedia.org/wiki/Nicu%C8%99or_Dan) (President of Romania) * [Pope Leo XIV](https://en.wikipedia.org/wiki/Pope_Leo_XIV) (Leader of the Catholic Church) Indeed, the mathematical discipline to seek logical reasoning, and the problem-solving skills to find win-win solutions for human flourishing, are desirable characteristics of people in government. Does this axiom resonate with you too? Perhaps many people took it as a given, and so didn't express it explicitly. If it is widely held, I would be thrilled to see the mathematical community publicly declare it, and take actions to match the words. Then everyone (including the non-math-researchers that constitute the majority of the world) could trust that we intend to use our reasoning for their good.