kzz102
kzz102 on Hacker News
Human pursuits cannot be separated from the humans who pursuit it. In the pursuit of knowledge, what ultimately drives people is what they themselves can understand, and the meaning these understanding provides, both based on their own experience and people whose opinions they value. Humans do not pursuit Platonic knowledge for their own sake, and those who claim to do it, often are satisfying their egos in a different way.
I think this is an important point we need to grapple with more and more in the future. We like to think an act as either lawful or not lawful, either ethical or not ethical. We need to bring in scale as a separate axis. There's a world of difference whether an activity is done at human scale or machine scale. At human scale, it's an act of deviance that may contribute to the diversity of human experience. At machine scale, it's a distortion that threatens the society.
Yeah, while it's sad they are gone, the reality is that they have been zombies for a long time.
The aim is to produce a body of knowledge that will be useful to humanity. So far, the best way to ensure that knowledge is useful is to have a society of experts who understand them well. That may not be necessary any more with AI, but it's a scary thought -- because that logic can be applied to any human knowledge, not just mathematical.
AI tends to take nearly finished research directions and push it to the conclusion in one step. If deployed massively, it will pluck all the low hanging fruits causing a drought of near term promising research project. Because people who start promising research directions do not get to see it finish, over the long term fewer people will start new directions, causing the field to slowly whither.
The difference is the scale. A few incomprehensible long papers per year, sure, we will study it. A flood of AI results closing research directions left and right, that will be a problem.
On your second point: there is a more plausible explanation which David Bessis calls the "overhang". The short version is that there is a large amount of relatively low hanging fruits in mathematics, because no human has broad enough knowledge and enough time to try them all. AI is not constraint by that, and therefore can systematically pluck all those low hanging fruits.
Quote:
"The Overhang consists of the unrealized capital gains of past mathematical creativity, the latent value from connecting the dots in the existing corpus. It is a dividend of canonization. Mathematician X states problem A, mathematician Y crafts concept B, then mathematician Z notices that B trivially solves A and “captures” the social reward. But in the process of capturing the reward, Z usually introduces new concepts and new open problems, reinjecting latent value into the Overhang.
LLMs can be trained on the entirety of the mathematical corpus. Thanks to their phenomenal memorization and pattern-matching abilities (without always being able to map out their associative logic and attribute due credits), they are in a unique position to harvest the Overhang. By contrast, professional mathematicians have typically read a few hundred articles in their career, out of millions of existing references, less than 0.1% of the total.
This will lead to great discoveries, which is unambiguously exciting. But it could also lead to a sad new deal, where human slaves painfully curate the Overhang while AIs systematically beat them at the finish line."
source: https://substack.com/inbox/post/183753276
I think both the competitiveness and and lack of problems will mean fewer people will do mathematics. I think collaboration will always be there, but the community as a whole will be smaller and weaker.
The mathematical community was very competitive in its early years, but in the last 70 to 100 years, it has been generally less competitive and very collegial. The community was in a good place, and progress has been very good. In a few cases when competitiveness was ramped up, it lead to bad behaviour and destructive fights. Few would like to return to those competitive years.
It was copied from a pdf, maybe LaTeX generated. All the ligatures are wrong -- not sure where the problem lies, the pdf itself, pdf reader, or the clipboard on Linux.
Education is a complex topic. I don't claim to understand it, nor do I think we can sort this out in a hacker news thread. What I reject is the simplistic claims like "exams don't mean anything". There are certainly exams that are badly designed, but there are also exams that are well designed. A well designed exam can look very badly to different people, based on what they know and where they come from. It's a bad idea to think exam scores as the single metric of education quality, it is equally bad to reject them completely, because chances are any alternative measurement people come up with are going to be worse.
My apologies for coming off as over-enthusiastic, I am currently obsessed with this study. Here is another quote:
"The negative learning effects are larger for students with higher initial achievement. The differences in the estimated full (6-10 month average) effects are substantial, with a 50% gap between the most negative effect (-24 percent) for the highest tercile and the least negative (-16 percent) for the lowest tercile. "
Not top 10% as you asked, but the closest to what you asked. My working hypothesis is that top performance is highly correlated with willingness to work hard, and AI decreases the motivation to work hard.
The fact that exam scores are correlated with how much you study is not the same as exams only reflect how much you study. Two students who study the same amount could have very different exam scores. The reason that there still is a strong correlation between exam score and time of study is because if all other things being equal, students who studies more have higher exam scores.
It's not so clear that AI is an amplifier.. The paper has some fascinating analysis on this topic:
"At the other end of the distribution, AI students who spend more than 65 minutes on their homework receive homework and exam scores similar to those of non-AI students, suggesting that these students do not use generative AI for homework assignments. However, this group consists entirely of students who adopted generative AI no more than Öve months. Six months after adoption, no AI student spends more than 65 minutes completing their homework (see Figure A5). This is consistent with the gradual process of learning how to use AI tools. It also suggests that AI crowds out the highest level of e§ort."
"Interestingly, in the range of 50-65 minutes, the median and the interquartile range
of exam scores of AI and non-AI students are similar. This implies that, in the range
where AI students and non-AI students have overlapping homework times, students
who spend the same amount of time completing homework on average receive similar
exam scores."
"This pattern shows that students who spend the same amount of time on homework
learn similarly, with or without generative AI. In other words, generative AI reduces
time spent learning for the majority of AI students but not learning efficiency for those who spend the same time studying as the non-AI students."
Even if we grant that education is to prepare for employment, which a lot of people disagree with, it does not follow education should do the same thing as what's done in employment.
Tenured professors do often fail large swathes of the class, and it's not hard to stand their ground because academic freedom is still very important in universities. This is not generally true for non-tenured and adjunct professors, but for a different reason -- their job review rely on a large part on student feedback forms, and failing students are not happy students.
The idea that if only all professors stood their ground then somehow students will be motivated to study doesn't pan out in practice, though. There is already a significant number of students who are perpetually struggling. They are missing basic prerequisites, and instead of catching up on them, they repeated try and fail at learning the same materials, passing only when they got a lenient instructor. The problem compounds because failing brings helplessness and exacerbates their mental issues, which brings more failing. The university cannot sit on their high ground and watch these students struggle, especially if their number reaches a critical mass.
I am criticizing how AI progress is reported and discussed -- given how important this development is, accurate communication is even more important for the discussion.
I think you inferring my motivation for the rant and creating a strawman yourself.
I do agree that directing my rant at the generic "fans" is not productive. The article Tao wrote was a good example of communicating the result. I should direct my criticism at specific instances of bad communication, but not the general "fans".
It's really tiring that LLM fans will claim every progress as breakthrough and go into fantasy mode on what they can do afterwards.
This is a really good example of how to use the current capabilities of LLM to help research. The gist is that they turned math problems into problems for coding agents. This uses the current capabilities of LLM very well and should find more uses in other fields. I suspect the Alpha evolve system probably also has improvements over existing agents as well. AI is making steady and impressive process every year. But it's not helpful for either the proponents or the skeptics to exaggerate their capabilities.
I was applying a unfair standard to them of course. Every field has a few classics that last a long time, but most old books are not read. But I think Bourbaki maybe had grand ambitions that were eventually unrealized. My theory is that the presentation of mathematics is not based on unifying principles, but rather on the collective taste of mathematicians. So what end up being the most popular books is based on how the collective taste evolve.
It's interesting that while Bourbaki had a large influence on modern mathematics, very few people read their books (at least among the people I know). In a sense, their project of producing a definitive exposition for a large part of mathematics has failed. I wonder whether it's because different branches of mathematics have their unique personalities, and therefore the attempt to provide a unified point of view are bound to fail.
This is one of the things that everyone gets the reference, but it won't be good to admit it publicly. This quote is known to almost everyone born in that area, and it's the first thing that come to mind when you hear the name.
I use to read about the power border agents have over foreigners and was amazed at how easily they can destroy me. The only reason this hasn't happened seems to be that they're mostly decent, professional people. And now that's gone.
In academic publishing, there is an implicit agreement between the authors and the journal to roughly match the importance of the paper to the prestige of the journal. Since there is no universal standard on either the prestige of the journal or the importance of the paper, mismatches happen regularly, and rejection is the natural result. In fact, the only way to avoid rejections is to submit a paper to a journal of lower prestige than your estimate, which is clearly not what authors want to do.
Even if we pretend nepotism doesn't exists, academia is still not a strict meritocracy. In addition to merit, at least two factors play an important role in success, which having a good mentor helps a lot.
1) Tacit knowledge. In many fields, there are important information only accessible from having a mentor like heuristics, insider information, in-lab techniques etc.
2) Investment opportunities. A good adviser is often good at spotting opportunities for their students. It's also common for an academic adviser to share their most valuable opportunities with their students.
It's clear to me that the ideal of meritocracy (talent and hard work leads to success) does not hold in academia, and maybe not anywhere. Having a good mentor gives you extremely valuable information that contribute to success. On the other hand, I am not sure this can be fixed or even needs fixing. I think it's healthy for academics to be partially siloed, so that they can develop their unique approaches and maintain a healthy diversity for the field.
One of the biggest problem of maths education is that they are
taught by people who dislike it. They think of maths as eating bitter medicine or training of a complex, rigid skill. The way maths is taught by them is clumsy and authoritarian, and this makes the students either passive or rebellious.
On a side note, recently the government of Manitoba in Canada removed requirement for maths teachers to take university maths courses. This is being pushed strongly by the education departments of university, which shows how much these maths teachers hate maths.
I am wondering how much of the hate of LaTeX document is due to the default font. Computer Modern seems to be disliked by many users of LaTeX as well. I personally am very conflicted, as I have come to identify it as the "vanilla" option so that I have lost any aesthetic sensitivity to it.
> That's not right. The primary task of management is alignment.
Fair enough.. at least they think they can add value by improving efficiency.
I think of efficiency as one example where naive economic thinking has poisoned common sense. Economists view inefficiency as a problem. Because a healthy economy is efficient, therefore inefficiency is unhealthy. Any inefficient market is a "market failure". Efficiency is also the primary way a manager can add value. But the problem is, efficiency assumes existence of metrics, and indeed is counter productive if your metrics are wrong.