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Comment by btilly | Hacker News Reader

I've heard the human understanding line a whole bunch.

But it begs the question. What is the value to the rest of humanity that a small group of people possesses something that can be called human understanding? Particularly when that group of people is historically terrible at communication (as is routinely demonstrated in Calculus classes), and most humans are not capable of learning that understanding (though more are capable than think they are capable - that is another story).

I am speaking as someone who nearly finished a PhD in mathematics. I understand why mathematicians would wish to continue in the age of AI. But, barring something like universal basic income, it isn't obvious why the rest of humanity would support them in this endeavor.

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> What is the value to the rest of humanity that a small group of people possesses something that can be called human understanding?

Okay, now, take the field of medicine and ask the same question.

Okay, now, when AI and robots can do surgeries and advise people better than modern doctors do (the bar is not that high, ask anyone with an autoimmune disease or gut issues)...

I think the central problem with that line of reasoning is that it supposes we are already living with AGI. Even the latest PR from Anthropic admits that we are not [0] there yet. If we don't have AGI capable of integrating and employing the mathematical results produced by an artificially superintelligent theorem prover so that they become useful to the rest of science and engineering, we will need humans to do at least some of the work in mathematics. Moreover if we freeze current AI capabilities today, "digestion" probably doesn't scale, so mathematical research will probably end up AI-assisted in ways not far off from what we're already seeing in the sciences.

[0] https://www.anthropic.com/research/claude-shaped-science

I am stating a counter-argument to a common argument.

You are simply giving a different argument than the one I'm giving a counter to. Yes, of course, if including human understanding results in strictly better results than AI, then there is an argument for the value supplied by human mathematicians.

But that's an argument that human understanding is on the path to better outcomes. It's not an argument that the intrinsic worth of human understanding is a reason to support mathematicians.

I kind of feel motte-and-bailey'd here. You began by questioning the value of human understanding in mathematics and I've explained (exactly as you've said) why it is currently on the critical path of outcomes in science and engineering with value to humanity almost nobody would dispute. This new question, where human understanding of mathematics isn't on the critical path of anything, is something I can't argue, in the same way that I can't argue for the intrinsic value or meaning of essentially any human activity without resorting to what amount to basically religious axioms.

The idea that the rest of humanity needs to support them is absurd. A couple billion in private trust funds could fund mathematics researchers in perpetuity.

The idea of being supported by the rest of humanity, is not a requirement that the rest of humanity support it equally.

The idea that "someone rich will take care of it", reminds me of a passage from https://en.wikipedia.org/wiki/The_Logic_of_Collective_Action. It talks about "the exploitation of the large, by the small". Where a public good (in this case mathematics) is provisioned by a large entity that finds it worthwhile for their own reasons, and the remaining players who value it, feel no need to contribute anything themselves.

What does it mean for a mathematics to be "provisioned"? A well-funded math foundation run like the Linux Foundation could cover the lifestyles of many elite mathematicians. I don't understand why you imagine it would be centralized behind one "large entity" or that this large entity, so long as it is not a government, can't be trusted to fund good things.

People unaffiliated with the Linux foundation contribute to Linux. Regularly.

For a public good to be provisioned means that the necessary resources and organization for that good, need to be supplied.

Supporting a group of elite mathematicians is not enough. There needs to be a path to becoming an elite mathematician.

Which either means that it becomes an unpaid hobby. Or there is some wider source of support for the profession.

>What is the value to the rest of humanity that a small group of people possesses something that can be called human understanding?

If you're going to ask that then you need to ask the same thing about essentially every non-STEM department.

People in the humanities regularly write things that many people find interesting and entertaining. One need not be a historian to understand https://acoup.blog/2026/01/30/collections-the-late-bronze-ag... and find it interesting. The value here is not that they possess human understanding. It is that they can share human understanding, in a way that many humans can be interested in.

But, for example, take my first paper: https://dspace.library.uvic.ca/server/api/core/bitstreams/66... The title was, "Derivations whose iterates are zero or invertible on a left ideal." In order to understand the title, you need to learn what a ring is, what a derivation on a ring is, what an invertible element of a ring is, what an ideal of a ring is, and why these are concepts that anyone would have invented. In order to read the theorem, you have to further understand what division ring is, a matrix ring is, the characteristic of a ring, and a polynomial over a ring. The proof is even worse.

Good luck interesting anyone who wasn't a mathematician. (And good luck interesting most mathematicians!)

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