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- Hacker News
- I just watched Primeagen’s video on this and Tao’s point is that juniors no longer have the path of solving a proof to earn Field’s medals. He also argues that the community part is being hurt by AI discovering proofs because in the past people used to get invite to talk and collaborate. Now all that is being taken away. The community must adapt because Pandora’s box cannot be closed.
Prime also mentioned that software development is different. In Software development, the product is what you’re building towards, so the means to get there can be disrupted without the industry being cannibalized.
In math research, the process is the product. You take away the researching part and not much is left. But my question is, these math proofs OpenAI released, will math shift to actually using the proofs to change the world instead of just finding new ones?
- Some of this feels like at times a public frenetic grieving process. Some of the rationalizations are fairly tortured, the seeking to place the world in some definite order is bordering on obsessive.
We don’t know where this technology advance will lead or settle, so it’s absurd to try to establish a working paradigm at this point. It’s like any system, the initial conditions can be extremely chaotic and impossible to model, but with time often a stable state emerges. But the stable state is impossible to identify from early initial states.
I know a lot of folks feel this, to torture other physics metaphors, sensation of jerk - acceleration of acceleration. It’s an unpleasant and dislocating sensation. A world that felt safe and stable suddenly isn’t, and not in a micro tragedy sense but in a global realignment sense. This happened to factory workers who had enjoyed generations of stable work, farmers more slowly and just as surely.
This is what the late stages of scarcity feels like. Labor of various types devalues rapidly. Our exchange of meal and health coupons for toil cracks, and people realize their labor wasn’t godly as great books told us, but simply needed for want of an alternative. The realization that our labors might not be valued any more, and that our sense of purpose is shaken, coupled with the fact we’ve tied bare survival to our toil in our labor, is mortally tightening. No wonder people are grieving publicly.
But maybe our purpose isn’t to toil? Maybe we’ve passed peak population, and as toil is less valuable, we need less people and that’s why population is declining. Maybe we don’t need to exchange food and health coupons for toil, maybe mathematicians don’t need to rationalize their value to pursue mathematics. Maybe they can pursue it because they can’t help but pursue it, and our ever improving automations can produce their meal and health coupons?
But it might require Dr Tao to take an AI generated cancer medicine some day.
by fnordpiglet - A question: How long does it now take for someone reasonably good at undergraduate mathematics and motivated to spend some time, get really good in at least understanding the frontier in some sub-field? For example, something in number theory. Has AI really helped accelerated motivated learners to reach the frontier fast? Has anyone tried this?by ChaitanyaSai
- The bad cancer example is interesting to the extent it reveals that one of the world's top mathematicians is apparently unaware that applied science runs almost entirely on half-understood semi-empirical methods. That's most true for medicine, given the extreme complexity of human life; but if you look at a modern SPICE model for a transistor, a device that we claim to understand at the level of subatomic particles, then you'll find it's full of curve fits. As an engineer, I find that perfectly normal. My job is to use all the tools at my disposal to meet some human desire (to not die of exposure, for a slightly thinner phone, etc.), and whatever fundamental understanding I might have is only one tool to that end.
My impression is that since pure mathematics doesn't attempt to meet those human desires they need some other objective, and that objective is human understanding. The loss of that is thus felt more heavily than in other fields. We could say it's their problem, and they need to get over it just like the chess players did; but the outside implications are broader here, since mathematicians working in fields they themselves considered useless have so frequently been wrong--in Hardy's Mathematician's Apology, he gave number theory as an example of such a field, unaware of what the cryptographers would achieve just decades later.
It's possible that AI-generated pure math will continue this trend of delivering extraordinary unexpected societal value. It's also possible that the humans won't ever sufficiently understand that math, and the machines won't ever sufficiently understand human desires, and that connection won't be made. I've never met a pure mathematician who considered those downstream applications to be an important contributor to their motivations; but as AI-generated math contributes to the argument to allocate a large and increasing share of GDP to datacenter buildouts, that question of whether downstream value requires human understanding seems pressing.
by tripletao - Explaining Tao's point in software terms: the point of pure mathematics is to build and maintain a high quality "codebase" of theory, definitions and proofs.
"Open problems are lighthouses not destinations" mean that these are currently not well explained by the theories and people should look into extending the codebase on that direction.
The current generation of math AI is not a "good citizen" in that it doesn't try to make the most elegant additions to the shared framework, but will often just rebuild everything from scratch til get to some endpoint.
Sure, we learned if the statement is true or false; but the proof can't be merged into the pure math codebase unless it's completely rebuilt. This is thankless work that humans are unlikely to want to do, and so the "solution" instead risks leaving a desolate patch of land, where existing efforts in extending the codebase lost their motivation.
As with all things AI we can't take more than a 1-3 year horizon, if even that much. Probably AI will become better at respecting and working within the existing theories as it has with large software codebases.
by thomasahle - Slide 12 and 13 sum up my conclusions from the Oct 8 100+ reactions to 100+ solutions. Several reported OpenAI drop included answers put a wrap on problems they had been working for years. Several said that they have to completely rewrite grant requests that they had just submitted. Others described learning of the solutions problems they had been working on like losing an old friend or a lover. The general sentiment was to bemoan the loss of a field, as if it would have been better be born in the early 20th century and conclude their career arc before reaching this point. My take away is that the field needs to get it through their heads that their old problems are no longer ambitious, and that their job in the short term is to find the new frontier.
One idea Terrance Tao conjectures, which is highly doubtful, is that spamming the AI button will solve open problems without producing insightful new methods. But the OpenAI drop would seem to disprove this. The sub O(nlogn) proof for DFT for example violated very old human assumptions. Decades of work in the field was incremental progress on sub optimal method that nobody questioned hard enough. More generally, we should always be able to go back to a super-human AI and say, "Attack this problem, but don't use a method tried before."
by samuelknight - > Before injecting this cocktail into your bloodstream, would you want to know that there is at least one human cancer researcher who understands the mechanism behind this cure.
Tao is out of his lane; lots of medicines don't have understood mechanisms. We don't even have the mechanisms behind general anesthesia nailed down; do you want to forgo it when the docs cut you open to remove your tumors?
by squidmaster - I work in drug discovery and AI and his slide about cancer medicine isn't very well informed. We have models and narratives about how drugs work, but they are woefully incomplete.
I ask nearly every doctor/researched in the medical field: if you had a AI-created drug that tremendously improved cancer treatment outcomes for your patient, would you hesitate to prescribe it because nobody understood how it worked? I have yet to hear "yes, I would hesitate", most people say "it would be cruel to deny a person a treatment that worked".
I think Tao is focusing too much on second order effects of AI on math and other fields; humans are terrible at reasoning about second order effects, especially ones that are happening dynamically, in real time, using the most advanced mathematical models the world has yet created.
by dekhn