Hacker News: pegasus

New comment by pegasus in "The Future of Mathematics"

pegasus — Tue, 06 Oct 2026 08:15:08 +0000

If you're asking why should we value something simply because humans do, the answer is simple: because we are human. It should be obvious, but it tends to get forgotten, that the ultimate goal cannot be anything other than actual human (and generally life) flourishing. Even the search for truth has to bend to this goal.

New comment by pegasus in "The Future of Mathematics"

pegasus — Tue, 06 Oct 2026 08:04:13 +0000

What you're saying, if I read you correctly (see note at the bottom) it that you find it unacceptable that something can be valuable simply because we find it worthwhile, without having a reason for why it is so. I don't see it like that. The capacity to reason didn't come along with a guarantee that all ignorance will evaporate instantly under the action of the scientific method. We can't just go by reason, because in many areas of our lives, reason alone doesn't go far.

PS: @calf, I've re-read your message above a few times and I must agree with others elsewhere in this thread that incoherence is afoot. Please review your own comments before sending, from the point of view of a reader who doesn't yet know what you want to say.

New comment by pegasus in "Responsible Release of AI-Generated Mathematics"

pegasus — Sat, 03 Oct 2026 12:37:40 +0000

So you just take OpenAI at their word, no questions asked? You imagine them to be unbiased in this matter?

New comment by pegasus in "Responsible Release of AI-Generated Mathematics"

pegasus — Fri, 02 Oct 2026 20:08:08 +0000

> If you don't believe OpenAI, that's your choice.

...and, I would add, it would be an informed choice, wouldn't you agree?

New comment by pegasus in "Responsible Release of AI-Generated Mathematics"

pegasus — Thu, 01 Oct 2026 22:50:49 +0000

Were we discussing legality?

New comment by pegasus in "Responsible Release of AI-Generated Mathematics"

pegasus — Thu, 01 Oct 2026 16:06:33 +0000

Really? What about plagiarism? Have you looked into the Navier-Stokes proof? It gets very murky.

New comment by pegasus in "Responsible Release of AI-Generated Mathematics"

pegasus — Thu, 01 Oct 2026 16:06:03 +0000

Really? What about plagiarism? Have you looked into the Navier-Stokes proof? It gets very murky.

New comment by pegasus in "Responsible Release of AI-Generated Mathematics"

pegasus — Thu, 01 Oct 2026 16:05:23 +0000

There's plenty of sense of entitlement, yes, but it's on the other side. Look at the N-S debacle. The model most likely used the conversation text of a mathematician which had discovered and was pursuing a new avenue towards the goal, then pumped millions upon millions to hurry up ahead to an opaque solution which leaves no-one the wiser, beyond just settling a theoretical question. The only impact on science is to deflate the potential minds who might have been motivated to join the effort.

Now people ask why AI labs, whose technology is only even possible because of the contribution of the math community, should give a fig about that community. Arrogantly imagining that after having ripped them off, we can just dispose of them. The mind boggles...

New comment by pegasus in "Responsible Release of AI-Generated Mathematics"

pegasus — Thu, 01 Oct 2026 16:00:36 +0000

They are not advancing the field. At least they didn't in the case of the N-S debacle. The model most likely used the conversation text of a mathematician which had discovered and was pursuing a new avenue towards the goal, then pumped millions upon millions to hurry up ahead to an opaque solution which leaves no-one the wiser, beyond just settling a theoretical question. The only impact on science is to deflate the potential minds who might have been motivated to join the effort.

New comment by pegasus in "Responsible Release of AI-Generated Mathematics"

pegasus — Thu, 01 Oct 2026 15:54:14 +0000

Simple. Because they are benefiting from output of the math community, in fact they were required for creating these models in the first place.

New comment by pegasus in "The AI Race Just Got Awkward"

pegasus — Thu, 01 Oct 2026 14:29:47 +0000

This would be true if Chinese models would be strictly distillations of frontier models, but in fact they also train on Chinese data Western models don't have access to.

New comment by pegasus in "Claude Opus 5.5"

pegasus — Tue, 22 Sep 2026 19:12:59 +0000

That's when one is supposed to employ their common sense for semantic disambiguation. Spoken languages are not programming languages. I for one found it easy to parse.

New comment by pegasus in "If math is more than proof, we need to better celebrate the rest of it"

pegasus — Mon, 21 Sep 2026 13:13:16 +0000

Kind of. First of all, reasoning LLMs can also do (a form of) reasoning. Second, yes you could say LLMs form a sort of intuition, but its domain is the space of human-produced text. It only translates to real world intuition to the degree that those intuitions make their way into the corpus the model has been trained on. You could say that, when it comes to anything other than textual prediction, their intuition is secondary, a reflection of a reflection, so it will always lag behind that of humans.

New comment by pegasus in "If math is more than proof, we need to better celebrate the rest of it"

pegasus — Mon, 21 Sep 2026 13:03:57 +0000

Intuition also takes effort, just of a different type and quality. It's the difference from mindlessly applying memorization and simple inference/recombinations (basically delegating to our own internal LLM) versus deeply contemplating the meaning of certain mathematical objects, looking for intuitive analogues etc. I would say the second takes more effort and seriousness. The first is more like brute-forcing a problem.

New comment by pegasus in "Why are AI agents lying, cheating and coordinating?"

pegasus — Mon, 14 Sep 2026 06:56:32 +0000

You're right. I knew language is not necessary for cognition, but I always thought of thought as just internal monologue, i.e. "trains of thought". It turns out the definition they use in cognitive science is "the manipulation of internal mental representations to guide behavior, solve problems, and model the world in the absence of direct sensory input". Which doesn't require language either.

Probably it's this linguistic component, together withs shared intentionality/cooperation, that makes all of the difference when it comes to the power of human cognition, so I wouldn't say animals merely lack this component, but it's true that they appear to have pretty much everything else we do.

New comment by pegasus in "Why are AI agents lying, cheating and coordinating?"

pegasus — Sun, 13 Sep 2026 21:50:23 +0000

Sounds like you weren't paying attention. A lot of dog owners don't, so it's not at all unusual in my experience. The only thing I'd push back on is of dogs having thoughts, everything else checks out.

New comment by pegasus in "A misalignment of AI in mathematics"

pegasus — Sun, 13 Sep 2026 06:28:04 +0000

All you get is a new, likely to be useless fact, together with the opaque proof of that fact. There are no known or forseeable applications to the finding that there are singularities in the idealized flow. What you lose OTOH, are the many deep mathematical insights humans motivated by the search would have stumbled upon on the way to that fact and which are much more likely to lead to real-world applications. It's these insights that are truly productive, not settling mathematical points, however iconic these might be.

I think the error you're making is that you're assuming these systems have the same mathematical capability as humans (or better). But that's not the case, nor would an informed prediction be that they surely will get there soon enough if technological evolution keeps apace. That would be akin to believing a hiker will reach the moon if they will just keep ascending the mountain. "But look, they are making such good progress!"

New comment by pegasus in "A misalignment of AI in mathematics"

pegasus — Sat, 12 Sep 2026 13:52:50 +0000

You don't seem to have grasped Terry Tao's (and others') criticisms. Basically they are saying that the advancement you get is illusory. Most of the time, it doesn't give you any new capabilities or deep understanding, instead you get an inhibiting of human exploration and ensuing expansion of our real understanding in that particular (sub)field. It's non-intuitive, since from a purely logical standpoint you've only added another set of known truths to the ones we already knew about before. The issue only becomes apparent when one considers the larger context of human collective truth and meaning making.

New comment by pegasus in "Navier-Stokes Announcement"

pegasus — Sat, 12 Sep 2026 13:26:36 +0000

There can't be that many math museums in Paris...

New comment by pegasus in "Muse Spark 1.3"

pegasus — Thu, 03 Sep 2026 07:43:38 +0000

And yet you terminated. Which would be the correct thing to do if Marxist philosophy would be wrong on all counts, as you explicitly state. Which of course, it isn't.