Why were we doing math in the first place? We should be happy that math problems were being solved, since presumably they were blockers for other problems in science and the like. But it feels like math was really more about seeking enlightenment, like a form of mental yoga or something. If so, we can just ignore AI proofs and continue on maybe?
There’s a somewhat famous lecture [0] by Wigner (one of the greats of 20th century physics if you’re not familiar) on exactly this topic. One of his points is that new tools and ways of thinking developed on the way to solving mathematical problems with no apparent application often find downstream applications in science and engineering. If we’re skipping the part where we identify and understand the new math, will we still reap the unreasonable effectiveness? Tao’s position in this post suggests that the current wave of LLM successes is not conducive to this dynamic
If you're considering an individual, maybe this makes sense.
But if you're consdiering a community, this falls apart. The maths community has universities, has professors who are paid, has students which are getting their degrees for varying reasons, it has conferences, has publications, papers, projects etc etc, all of which will get some negative impact some AI.
You know that line "when a measurement becomes a target it ceases to be a useful measurement". This line holds up to different degrees for various measurements and targets. For maths it holds up very well. The goal is "contribute to make the world better by increasing humanity's understanding of maths" and the measurement, which by evaluating an individual on it we're turning into a target, is "how much does the individual publish new findings". Measurement turned target holds up great. It's almost impossible to publish new findings and not contribute to humanity's understanding of maths. But with AI these two are being decoupled. You can produce lots of new findings, but the community is saturated and they don't get assimilated into humanity's understanding. Why do individuals use AI then? Because you've made the target "how much does the individual publish new findings" and they have to compete or lose.
If a coal miner or car mechanic would say something like this, they would be called a luddite by the same science people.
Its different when your own job is on the line.
When human manual arts were being automated away it was supposed to be not only acceptable but any complain and you were told you were a progress blocking luddite.
Now that mental labor is getting automated, the response to automation is very different.
This isn't about physical labour vs mental labour, it's about the dynamics of delivering a product vs contributing to a community.
For example, a software engineer is like a car mechanic or a coal miner. None of those are anything like a mathematician.
The person you're rallying against isn't me, it's an imaginary hypocritical person which exists in your mind. I do mental labour, I welcome AI developments hard, and I still think TT is 100% correct.
I'm a retired AI researcher and I still enjoy programming. However, I don't use any however assistance as I still want the thrill of learning new things. Unfortunately, it appears that the only way for most developers to enjoy similar activities is to be retired with enough money
The amount developers saying how "now we can focus on the bigger picture" rather than the code are just delusional. The bigger picture has always been a bigger problem than writing the code. It's the part that engineering stands for in "software engineering". If you couldn't code something well or weren't involved in bigger picture decisions in the past, you're just gonna engineer big picture spaghetti.
This is exactly why half the conversation conversations about AI eventually become a critique of capitalism. AI isn’t for fun or joy, it’s explicitly for business use. For replacing people. For extracting more out of each worker. That’s all the major companies (OAI, Anthropic, etc) are offering. None of this is designed to give us any more freedom or time to pursue the things we are passionate about.
I feel like we’re circling back to that 2010s energy of “everyone can be an entrepreneur.” Now it’s “everyone can build software”
Pretty much every published paper I see now is a combination of Chinese and Indian immigrant authors. Given enough time they all become American. I don’t see what the problem is.
To many professional mathematicians it's a form of art. But at the end of the day, it's a profession done for money, and even if they like doing it as a day to day job, they'd probably be doing something else if they had absolute freedom over their time. This is how I personally classify things as art or chore. If people continue doing something the same way when there is no financial motive, it's art in its pure form.
Based on the research mathematicians I have known, I'd disagree with 'they'd probably be doing something else if they had absolute freedom over their time' for at least a large number of them, although it probably varies from individual to individual.
If we're going to be frank about it, higher level math is:
1) Intellectually challenging, to such a degree that those wishing to enter the field need to have a certain level of intellectual prowess to do so. This creates some levels of mystique, with a sprinkle of elitism and gatekeeping.
2) Driven (among other things) by prestige. And the more pure the math is, the more prestigious it is.
3) So complex that people can spend their entire working careers chasing a handful of problems. The amount of time researchers spend on very specific problems is mind-boggling, if we think about the results.
4) Intensely captivating for the people deep in the weeds.
And the deeper you get, the longer you study, the more you start to value things like "mathematical beauty", and may start to view math as a form of art.
Like many similar fields, you end up with this ivory tower where people can dedicate their whole lives to thinking deeply about extremely niche and theoretical problems.
Similar things are happening in the competitive programming world.
Quite a lot of people are not happy they aren't elite anymore, and many have spent years to decades to arrive here.
Simply put you invest years of your life to establish a kind of distinction over others, and that goes away. That hurts.
But its not something surprising. Most of these competitive programming problems were actually English languages puzzles, because you couldn't dial up the mathematical difficulty anymore making it a fields medal problem. And in most cases in simple language weren't even that hard to begin with, and you could look up solutions to these problems in an hour of Google searching.
I'm not totally against "math as art" but I don't think that formulation goes deep enough towards what's really going on with mathematics. There is something deeper where I lean more towards the philosophers who have said that mathematics is essentially ontology.
Since the Greeks we've had the idea that "Being and thinking are one," or that Being (in the sense of all of existence as such) has some essential unity with thought, and therefore can be thought, and expressed or submitted to the logos or reason. Being is in some sense fundamentally intelligible, and mathematics is the most developed, exacting, and articulate expression of Being.
Logic was understood in this older sense up to roughly the the mid to late 19th century. This is why a work like Hegel's Science of Logic begins not with syllogisms or propositions but with Being and Nothing. But this was forgotten after logic was mathematized by the English around the time of Russell, and its connection to ontology was gradually overshadowed by a focus on epistemology (still, it should be remembered, originally as a means of getting back to ontology).
There may be truth in art, but it's always haunted by its own historicity or contingency, which is to say untruth. Mathematics seems on the contrary the only really timeless, absolute thing we have. Part of what makes it captivating is stumbling on a construction or concept or proposition or theorem that simply must be, independent of us.
The AIs are certainly now more than automatic theorem provers, mechanically traversing some space of true propositions. They are able to push things forward and connect seemingly disparate domains to get to a proof, but to my mind it remains to be seen how well they will be able to form new concepts and definitions.
Imagine the controversy surrounding Cantor, for example, but put an AI in the place of Cantor. If an AI proposed something like the (infinite) hierarchy of infinity, would we have accepted it? What would the intuitionism debates have looked like? Would they even have taken place? And aside from that, has it actually been shown conclusively that an AI could propose such a thing?
There are lots of attempts right now to recover a humanism for mathematics, or restore man's pride of place with respect to it, but maybe we don't need to worry about that. Tao's attempts to preserve the mathematical community, while allowing for practices to change through the crisis may look like a kind of rearguard action, but seems reasonable to me and not really dependent on any kind of humanism. It's a way to avoid the question for now while things play out (and not conservative/reactionary like Scholze and others), which may be exactly what we need, because after all, perhaps we still don't understand why we do mathematics, what it's really for, and what our relation is to it. Whether it's enough to preserve funding is another issue.
If they pay market rate, the clearing price will go up making things more expensive for everyone. If they go off-grid they make the machines needed to produce water or electricity or whatever more expensive. If they borrow money, they make government bond yields go up and cause governments to start thinking about cutting pensions and stuff, not to mention increased mortgage rates for whoever wants to buy a home or is on a variable rate mortgage. There's no world in which this AI stuff doesn't increase costs for the rest of us.
I think that what's needed is a separation of concerns. Instead of a monolithic institution that is responsible for research, student enlightenment, self-discovery, vocational training, athletic competition, etc, we could move towards a micro-institution architecture and scale the different micro-institutions according to demand. Importantly, we wouldn't cross-subsidize the institutions, so if someone only wanted self-discovery for example, they could just pay for that and get a cheaper price than someone who wanted both self-discovery and vocational training. People could also decide how much of each they need according to their circumstances.
My universities football team is actually self-funding and actually funds a lot of other programs. The sports teams can be considered as courses unto themselves considering this is where the NFL and other professional sports teams find their players (employees). I don't think it's as cynical as tribal ties.
So you don't want the top scientists, engineers and thinkers training the next generation? And you don't want popular sexy things subsidizing inventing new things that haven't had time to be popular yet?
The “next generation” gets trained by adjuncts and grad students. “Top scientists, engineers, and thinkers” are too busy with grant proposals to be bothered with teaching.
When autonomy is solved, they could put a bed or office or dining table in the car. But I agree, this halfway autonomy where you have to watch everything is kind of useless.
> When autonomy is solved, they could put a bed or office or dining table in the car.
Have you ever tried reading a book while being driven around? You get car sick really fast, because your vestibular system does not like constantly getting jostled around with mismatching visual inputs. Eating dinner while being driven around is a similar story: anyone around you does something unexpected, and your dinner ends up being spilled all over the car.
Self-driving cars will never have the same smoothness as planes or trains, simply because they have to share the roads with the general public. You might be able to sleep, but your commute isn't going to neatly match up with your sleeping schedule, so that's only really useful for longer road trips.
> this halfway autonomy where you have to watch everything is kind of useless
No, it is actively dangerous. Humans are extremely bad at staying fully-focused and being ready to act in the blink of an eye, while at the same time having literally nothing to do 99.99% of the time. If you don't let your attention wander, it is significantly less exhaustive to drive yourself. Halfway-autonomous cars exist primarily so that car manufacturers can demand extra money without having to accept any of the reliability.
> Have you ever tried reading a book while being driven around? You get car sick really fast, because your vestibular system does not like constantly getting jostled around with mismatching visual inputs.
I don't suffer from this all, and judging by watching people in public transport I'm not alone.
I don’t know, it might just come down to how good a driver you are.
I agree with the proposition that people are horrible at halfway autonomy.
But I am horrible at driving, and I kind of think almost everybody is. I have a car that just does lane keeping and distance keeping cruise control. The number of times it is notified me that I’m sliding off the side of the road is large. Similarly it’s let off the gas a vast number of times when I was creeping up on the car in front of me and I didn’t notice.
Maybe it’s having just one long, largely empty commute for five years. But I suspect it’s that you can drive any modern car without 100% concentration at which point people are prone to getting distracted.
So I’m thinking the comparison should be halfway autonomy vs a modern “dumb” car and I think halfway autonomy is safer overall.
Like you said, I think skills are quickly subsumed by model abilities. I leave relevant notes about my own projects in agents.md and local comments around tricky bits of code that need them, but otherwise I just use vanilla codex.
I think a lot of people are missing some of the advantages of skills - they're to give an agent/harness the knowledge of how to do something or more context without it always being part of the prompt.
This could be to try and expand the capabilities of the model but in it can be used to store personal preference/workflow/organisational knowledge/improved efficiency etc. The harness could work through and build some of this on its own - but it's much more efficient if it has a document it can just look up. I use them for the database structure and it's quirks, how to use branded document templates, external document tone, system workflows, compliance requirements etc.
I wouldn't want these to load every time but being able to call them is really useful.
I don't think Arabic script is that hard. It's nearly phonetic, unlike English. It's not super broad and hard to memorized like kanji. I don't know, maybe I'm just removed from the struggles of people learning it for the first time.
(one of the blog post authors here) -> once you set up a finetuning pipeline, it's often trivial to rerun it on top of a new open weights model. so, it's orthogonal to base model improvements
I guess this ethics stuff is cool, but I'm more interested in how good it is at running a business and dealing with adversarial humans like in previous vending machine experiments. I hope they release something on that soon.
You'll make more money when you downsize or move to a cheaper city or country for retirement if your house goes up in price. If you own a house in San Francisco you can sell, move to a vlcol city, buy a new house, invest the remainder, and retire. You probably will want a smaller house once the kids move out too.
> move to a cheaper city or country for retirement if your house goes up in price
What kind of life experience would lead to such a conclusion? It's almost like you have no idea what a community is - with one's friends, neighbors, familiar shops, clubs, church etc. Money is not everything in life. Any policy which forces people in their late 60's to uproot and go somewhere else to rebuild their lives is bound to face a very angry backlash. A mindset like yours is why we got prop 13 here in California.
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