Comment by devolving-dev
8 hours ago
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
0: https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness...
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”
You could replace "math" with "programming" in your comment for a different perspective.
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.
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.
> 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.
Not the mathematicians I know. They’d happily drop the academic admin stuff, but they’d absolutely keep doing mathematics in much the same way.
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.
Some call that "entertainment", or "a hobby".
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.
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.
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.
Where was Terence Tao where other workers were being replaced by immigrants, robots and other automation?
Academics and white collars now get to experience what blue collar workers experienced in the past.
Same as what developers in USA experienced who were and are getting replaced by Indians.
He grew up in Australia, didn't he? He was the one doing the replacing I suppose.
He is a imigrant.