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.
It's really tiring that LLM skeptics will always talk about LLM fans every time AI comes up to strawman AI and satisfy their fragile fantasy world where everything is the sign of an AI bubble.
But, yes this is a good way to use LLMs. Just like many other mundane and not news-worthy ways that LLMs are used today. The existence of fans doesn't require a denouncement of said fans at every turn.
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".
One could say the same about these kinds of comments. If you don't like the content, simply don't read it?
And to add something constructive: the timeframes for enjoying a hype cycle differ from person to person. If you are on top of things, it might be tiring, but there are still many people out there, who haven't made the connection between, in this case, LLMs and mathematics. Inspiring some people to work on this may be beneficial in the long run.
GP didn’t say they didn’t like it. They criticized it. These things are not the same.
Discussions critical of anything are important to true advancement of a field. Otherwise, we get a Theranos that hangs around longer and does even more damage.
I don't think you read the comment you replied to correctly. He praised the article and approach therein, contrasting it to the LLM hype cycle, where effusive praise is met with harsh scorn, both sides often completely forgetting the reality in the argument.
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.
I read once that the general attitude of the group was that their publications were not meant to be widely read, but just to provide the foundation for better expository work.
I also heard that part of the bad reputation that Bourbaki got was due to their being used in graduate education, despite warnings that they weren't suitable. In the 1950s/60s, there was a lack of good graduate texts. Of course, then Serge Lang came along...
Yes, Whitaker & Watson (analysis), Hardy and Wright (number theory), Dieudonne (analysis and he was literally a Bourbaki member), heck, Euclid's Elements; Gauss Disquisitiones, etc. Bourbaki is more of a monument. Writing it was necessary, but for readers it suffices to know that it is there ;).
while it's certainly not read by most mathematicians, Bourbaki (especially set theory & general topology) are still quite often read by mathematicians in training I believe.
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.
they provided a unified point of view by explaining it all in terms of sets
ultimately they failed because they wrote such that it didn't matter if other people understood. it's a style that is only intelligible if you already know (from some other experience) what they are describing.
Bourbaki is known for their "definition-theorem-proof" style, which for a while influenced a lot of mathematical writing. It makes the logic of the presentation easy to follow. The proofs are complete and fairly clear. The logical order within books and in the series of books as a whole is also pretty good - if you read pages 1 through n in the books, you have the prerequisites to read a proof on page n + 1. There is a good index, a table of notation, exercises (at the back, not by section), and a table of contents (at the back, since the books are in French).
They probably originated the "dangerous bend" symbol (a Z-shaped curve in the margin) to indicate a tricky or subtle point.
They're pretty good as references (to look up the proof of a result, or read about single topic).
On the negative side:
There is little exposition in the sense of motivation for what is presented, or applications.
I'm looking at "Algèbre - Chapitre 10 - Algèbre homologique" (the only Bourbaki I own). In the introduction, they say:
"Le mode d'exposition suivi est axiomatique et procède le plus souvent du général au particulier."
"L'utilité de certaines considérations n'apparaitra donc au lecteur qu'à la lecture de chapitres ultérieurs, à moins qu'il ne possède déjà des connaissances assez èntendues."
Thus, you won't find applications, or many examples - just definition-theorem-proof.
It's assumed you know why you're reading the material, and so don't need to be told.
This particular volume is a little unusual for the series in that it has lots of pictures, but that's only because this is homological algebra, so there are many commutative diagrams. Most of the volumes are just walls of text (though the formatting and the production tend to be very clear).
(I believe they actually wrote some historical remarks in some of the books which were collected in a separate volume - I don't see any historical material in the volume I'm looking at, however. The members were not unmindful of things like history: Dieudonne wrote an excellent history of algebraic and differential topology, and Andre Weil wrote a book on the history of numbers.)
The fact that it took a while for many of the volumes to be translated from French to English may have deterred some English readers (though mathematical French is not too hard to understand even if you don't know French [like me]).
On the whole, (in my opinion) the presentation is too relentlessly formal for most people to try learning a subject (as opposed to a small topic) by reading Bourbaki. They did produce a "definitive exposition" of the subjects they covered, in the sense that the results and proofs are there. It's just that most people would have a hard time learning any of the subjects by reading through the books.
Wow, that's interesting. I guess that's like a US company being called "MRE". We would view that like a veteran's owned and operated company. Interesting.
And all the products would be "MRE-Phone", "MRE-Pod", hehehe :)
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.
It's luck of the draw with those guys. The job attracts people with nationalistic/fascist mindsets and if you look a certain way you can expect to be treated worse than others.
I wouldn’t describe them as nationalistic or fascist. There’s no need to bring in any sort of political view… the problem is when little people get a little power. It can get ugly.
It’s the same people. There’s always been an element of luck.
I travel a lot and I’ve interacted with a lot of border agents. I’d say luck is important for a lot of countries. I’ve had great experiences flying in US, Egypt, UK and Turkey I’ve also had terrible experiences with US, and Iceland. Most other places have been somewhere in between.
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.
It’s not an accident - if academics underestimated the quality of their own work or overestimated that of the journal, this would increase acceptance rates.
Authors start at an attainable stretch goal, hope for a quick rejection if that’s the outcome, and work their way down the list. That’s why rejection is inevitable.
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.
> 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.
That is messed up. Harsh. What is also messed up is that to become a math teacher, you have to go to teacher's college. That's one reason why I never became a teacher. I think I would do better than most at teaching (at least based on the comments I got in my student teacher reviews) but spending another two years at school is rather humiliating and costly.
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.
Computer Modern immediately signals to me "This was written in [Xe|Lua|]LaTeX". That alone has value; at the absolute least it tells me that the person writing it knows enough about computers to drive LaTeX to produce a compiled document.
If reviewing e.g. applications from undergraduates for a summer studentship, that signal is a subconscious hint saying 'read this a bit more closely' if nothing else.
Designers seem to prefer other fonts. That seems to be true whether they work for traditional publishers, advertising agencies, news papers, or indeed web agencies. It just does not seem to be a popular choice outside the narrow niche of people who use latex. Who are of course mostly not designers. And having worked with some great designers in recent years, I tend to follow their lead when it comes to making things look good.
But beyond me being conditioned to be bored out of my head reading scientific papers (being an ex-academic who definitely does not miss having to read lots of poorly written papers) written with latex and having that look, I shouldn't have much of an opinion on the matter.
IDK. I never had any problem reading the default font on screens, which seems to be the problem according to some commenters. It's more that the default style overall feels unappealing and space-wasteful (I get leaving margins for note-taking is a thing, but come on), and yes, also reminiscent of super-boring math stuff. And more than that still. I find myself disliking the style holistically, and can't put my finger on why exactly.
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.
In my view, prosecuting the bad actors alone will not fix science. Science is by its own nature a community because only a small number of people have the expertise (and university positions) to participate. A healthy scientific discipline and a healthy community are the same thing. Just like the "tough on crime" initiative alone often does not help a problematic community, just punish scientific fraud harshly will not fix the problem. Because the community is small, to catch the bad actors, you will either have insiders policing themselves, or have an non-expert outsiders rendering judgements. It's easy for well-intention-ed policing effort to turn into power struggles.
This is why I think the most effective way is to empower good actors. Ensure open debate, limit the power of individuals, and prevent over concentration of power in a small group. These efforts are harder to implement than you think because they run against our desire to have scientific superstars and celebrities, but I think they will go a long way towards building a healthy community.
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.