> One of the points I clearly remember him saying that having AI be able to solve many of the open problems, regardless of how important there are (there are many open problems that are not that important) greatly reduces the problem space for mathematics students to give new problems to work on.
The crux of the argument perhaps. It suggests that too many people are currently studying mathematics without making much progress.
> The issue of credit is a relatively minor point in the declaration.
What a load of croc. This entire debate is fueled by a perceived lack of attribution. The AI learnt from researchers and did not give them a sporting chance of being first before scooping them. They were expecting some sort of fair play, instead they got a ruthless machine. Every other tangent to this debate is irrelevant, the culture, the community, the shared symbolic growth. Every mathematician I know is secretly trying to one-up their peers.
> He doesn't see value in scrolling through unsolved problems asking an AI to please solve them.
Yet that's exactly how the field works. A new grad student is tasked with finding a suitably difficult problem from a list of unsolved problems. The sweet spot is obscure, so that fewer people are working on it, but not too obscure that no one knows about it. It works the same way in theoretical physics and theoretical Comp Sci, and I speak from insider knowledge. The rosy view of mathematicians in the media is largely a product of marketing.
The authors of the declaration agree with you that this is how the field works today. They think that fact causes AI use to produce bad results, and they want to reformulate how the field works so that AI use will produce good results instead.
That sounds shockingly like cognitive dissonance. So what would previously be a good thesis if produced by a student over 4-6 years is suddenly now a bad result because it was produced by AI in a few weeks. One would think mathematicians would not fall into such a simple trap but here we are.
I understand the perspective: The journey of a PhD thesis is a learning experience greatly beneficial to the student. Yet that journey is funded by society (esp. for domestic students) and society benefits from the results. The average person benefits when progress is made.
No, you're misunderstanding the perspective. They believe the journey is a learning experience greatly beneficial to the field, and that this experience rather than the headline result is where most of the value lies. They don't think mathematical progress consists primarily of finding answers to unresolved questions, so they don't think the average person will benefit if only this narrow kind of progress is made.
I'm not sure what's getting lost in translation here. The answer is quite clear: math textbooks are valued based on their ability to help readers understand mathematical principles, not based on the number or complexity of problems that they contain solutions to. If an AI lab announced they've released a new calculus textbook with hundreds of new integrals a human has never found before, that wouldn't be terribly exciting, because we all understand that finding new integrals isn't that important and not the point of textbooks anyway.
LLMs can help people understand mathematical principles too.
The idea that when LLMs produce solutions, people won’t try to understand them and won’t learn from it, is obviously not true. Terry Tao himself spent time digesting and simplifying LLM proofs.
So again we’re left to speculate what the actual problem is.
Math understanding will increase with LLMs. Not just professional mathematicians but amateurs.
Again, we’re not left to speculate, they’re being quite clear.
I think you’re struggling to understand what Tao and his cosignatories are saying because you’ve acquired a very specific kind of “AI-pilled” mindset from social media, where taking AI seriously implies accepting LLMs should be used at any time for any purpose. They’re saying in great detail that LLM solutions are unhelpful when presented in a particular way, but you can’t help but hear them saying that LLM solutions aren’t helpful at all, even as you rightly point out that this makes no sense and is inconsistent with their observed behavior.
> Yet that journey is funded by society (esp. for domestic students) and society benefits from the results. The average person benefits when progress is made.
Society doesn't benefit from results in research mathematics because it mostly consists of pure mathematics, which is completely useless for society.
Beautifully written post and true on many levels. The art of software stopped being an art once large amounts of capital started creeping in. There are no signs that we're returning to sanity any time soon.
Ok, I get how you might like the ideas there, but "beautifully written"?!? Really?
The goal of writing is to communicate. That means saying what you mean to say ... and not filling paragraph after paragraph with pointless and redundant things you don't need to say.
There is not an English teacher in this world who would argue that was even a well-written essay, let alone a beautifully-written one.
The pudding is in the proof. The field is mathematics, the proof can be rigorously verified. If there is a flaw, OpenAI is out to lunch. If the proof is valid, OpenAI has produced something new.
You seem to be unfamiliar about how research works. It's common to make an incremental advancement while citing prior work. The vast majority of papers out there fall into this bucket. Did the AI make incremental progress? Yes. Did it cite prior art? After some nudging, yes.
It seems to me the academics are upset that AI scooped them. But scooping is a time-honored tradition between researchers. First to print and all that. In a nutshell, they are upset that they lost out on a publication.
I will also point out for those unaware that any mathematics that is produced is automatically part of the public domain and can be used freely in derivative works. It is not a protected intellectual class like other works of art.
In my own ranking of favourite programming languages C is at the first place. C++ comes in last. I personally hate it when people write C/C++ as if it's the very same thing. I'm quite sure there's more like me out there. :)
Interestingly Perl comes in second, even I use it rarely (aka not at all) these days. But that's a slightly off-topic side note. :)
And yes, for the most part. C++ as simple shorthand for struct-attached functions and automatic memory management (no, not smart pointers; RAAI) is good. Every single thing added after that is misery and should push a modern developer to Rust, Go, or Zig (roughly in that order) where such things are implemented sanely or not at all.
And direct access to system calls. And the uncanny ability to look like it's going to do what I want and then five minutes into a run wind up in a small town in Arkansas blind drunk and crying vaguely about fluffy red squirrels taking its sandwich.
For me, C++ is always in first place. It allows me to do high-level abstractions to low-level hijinks all with total control (i.e. zero-cost abstractions, Templates for compile time programming etc.) across all levels of the software stack and the full spectrum of available hardware.
Furthermore, any C++ programmer who says they do not know C, knows neither C nor C++ (hence my preference in using C/C++ as a shorthand to encompass both and highlight the dependency of the latter on the former). I often see this in novice C++ programmers who started with "Modern C++" and identify it as something like Java/C# because of the now huge set of standard libraries and copious syntactic sugar which only compounds their confusion further.
> Furthermore, any C++ programmer who says they do not know C, knows neither C nor C++ (hence my preference in using C/C++ as a shorthand to encompass both and highlight the dependency of the latter on the former).
Right, but this dependency is one-way. There is an entire legion of C programmers who reject C++ (most notably Linus), so claiming that almost all C programmers are also C++ programmers is a bit off.
What i meant was that almost all C programmers are aware of and know C++ to varying degrees. But they choose to not use it for their application based on needs/expertise/etc.
Linus Torvalds objection to using C++ is perfectly logical for his use-case. I know many embedded programmers who refuse to use C++ even though they understand and agree with the benefits that it can bring to the table. Their C expertise is so good that when they program, cognitively the language just disappears and they "flow" through the problem solution implementation. This is the crux of problem-solving.
Many of us were there when yada yada white wizard. Hell, my first paid job was writing Perl CGI scripts. Well, script. Monolithic MFing thing spread across 100 files and running a whole company on text files with zero format documentation and RCS as version control. No need for CVS because the systems were incrementally archived with tar every hour...
Until they weren't. (I'm glad you saw that coming, because they didn't.)
Yeah I dislike it. Why are we babyducking sepples attributes? And what I assume to be namespace accessors? Why are logical assertions enclosed in backticks? I "get it", because it's actually kind of difficult to make a backwards compatible derivative of C that doesn't devolve into glyph soup, but this has a massive frankengrammar stink to it. The proof language is eyebrow raising to say the least.
That's good for the economy. Vanity projects help the wealth spread around. Think of all the people who received income by working on this house. It's a much bigger problem when wealth is hoarded.
Being silly and obstinate when knowledge is in arm’s reach? Making people spell it out for you because you don’t have the respect to look yourself?
OK here’s the short version: the economy has a limited amount of resources and the way they’re allocated matters. A yacht built means no hospital built. Making people work on useless stuff for the rich is demoralizing because their life’s blood is used on meaningless projects. Growing a luxury industry incentivizes gifted people to seek employment in it rather than in other fields where they’re. It matters what the economy does, not just that it grows.
Every LLM will tell you that if you ask. You just didn’t ask. Because you think nothing of others and their time.
LLMs will tell you whatever you want to hear. You subtly direct them with the way you ask the question, and then they give you the answer you want. That's basically what they're trained to do. So of course they always give you the answer you want -- but you can't just go around telling people to ask an LLM to back up your argument, as other people will get a difference answer.
I don’t think that’s true anymore. You can ask for weak points of a position (e.g. that luxury spending is good for the economy) and they will give you a reasonable answer.
You could do the opposite - what are the weak points of the position that accumulation of wealth leads to waste and see what are the weak points there.
And then think which position can be dismantled more easily and is therefore less well founded. Or ask for a steelman version of it.
But that's such a waste! 5 whole people taken out of the economy, no longer producing value, just going around consuming resources in retirement. How is that any better than me spending to build a nice house that facilitates my family's comfort and my friends' enjoyment of getting together to play games?
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