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Terence Tao: Mathematics in the Age of AI [pdf]
- jimmy76615 3mo agoIt was an excellent talk. If nothing else, it really helps to establish some much needed vocabulary for us to constructively talk about the future of math
- doomrobo 3mo agoRecording of a talk with the same title. I’m not certain it’s the same content as the linked PDF though https://youtu.be/mS9Lr43cIB4 https://youtu.be/mS9Lr43cIB4
- pyentropy 3mo agoNote that the SAIR lecture is from 6 months ago, this Beamer presentation is from 2 days ago.
- layer8 3mo ago> Beamer Spotted the German guy. ;)
- jdm2212 3mo agothe software that generated the slides is called Beamer https://en.wikipedia.org/wiki/Beamer_(LaTeX) https://en.wikipedia.org/wiki/Beamer_(LaTeX)
- madcaptenor 3mo agoI believe the software was written by a German.
- Ar-Curunir 3mo agoAnd people all over the world use it, not just Germans
- pyentropy 3mo agoVedran Miletić doesn't sound German to me! :-)
- madcaptenor 3mo agoYou're right, but: - he works in Germany (https://vedran.miletic.net/files/cv-vedran-miletic.pdf https://vedran.miletic.net/files/cv-vedran-miletic.pdf) - the original author is Till Tantau (https://www.beamer.plus/Introduction.html https://www.beamer.plus/Introduction.html) who is German (https://www.tcs.uni-luebeck.de/en/mitarbeiter/tantau/cv/ https://www.tcs.uni-luebeck.de/en/mitarbeiter/tantau/cv/)
- jdm2212 3mo agosure, but the prior poster's "joke" was that Germans are bad at English and refer to overhead projectors as "beamers" when in reality the entire English-speaking academic world refers to slide decks as Beamers because they all use the Beamer software to generate their slide decks
- richard_chase 3mo ago[flagged]
- pretzellogician 3mo agoI would vastly prefer it to the current Zig News.
- onraglanroad 3mo agoI guess it's a better title than Dick News...
- richard_chase 3mo agoOr maybe Hacker Terry? He's such a hacker he's got a WordPress blog with unreadable images for his math expressions. Color me IMPRESSED. Let's not forget he's got some some excellent videos on YouTube of him vibe-coding some LEAN, with audio quality so good I can barely hear him!
- syndacks 3mo agocan't forget SimonWilson-News!
- megaloblasto 3mo agoThis is the thought process that I fail to see many people take (both here and other places). AI is changing many fields, ok what does that look like and how do we adapt? What can we do now that we couldn't before? What skills should I learn to adapt to this changing world? I think this is how we move forward. If you can get past the scary aspects of AI (not talking about datacenters or billionaires, that is a different subject) then you might be able to see how exciting this can be.
- Yokolos 3mo agoEven as somebody who uses AI every day and has integrated it in useful ways, I don't see how the rise of the AI industry can be anything other than terrifying. It signals the rise of a new feudal system. Couple that with the rolling back of democracy across the globe and growing trend of authoritarianism, even in Europe, and I just can't be excited. In Germany particularly, it feels like every week there's some new idea to increase surveillance and control over the populace while the AfD is knocking on the door.
- 2snakes 3mo agoOpen source intellectual power though. The promise of the personal computer.
- vouaobrasil 3mo agoThe fact is, open source was a solution to a different problem: closed source. Open source is not a panacea that will solve everything.
- knollimar 3mo agoWhats personal about a datacenter?
- 2snakes 3mo agoYou could have said the same thing about mainframes in the past? I am talking about smaller open source models not huge ones that need spaceships to run.
- 0x1ceb00da 3mo agoIs there a video for this?
- croemer 3mo agoTo be released imminently per this toot from 2 days ago (saying forthcoming in a day or two): https://mathstodon.xyz/@tao/116977934921819775 https://mathstodon.xyz/@tao/116977934921819775
- 4848488448 3mo agoIt really is sad that supposed leaders of technical fields have been reduced to TED tier clowns for profit
- pyentropy 3mo agoIn times when software eng teams push for maximizing token usage, Tao's public view is to encourage verification, limit AI use for tasks that have real-life consequences and prevent low-effort papers that exhaust the review pipeline? He also focuses on training the next generation of mathematicians and prioritizing the process of slow digestion of results, which to me sounds very.. reasonable?
- 4848488448 3mo agoTaos public view is to engagement farm and he'll swap to the new nfts or crypto when this is done because once you go down this road theres no going back with the lifestyle creep
- onraglanroad 3mo agoThere's no real point in engaging with these bot accounts. They'll keep making points that sound superficially correct but allow an argument against. TT has real results which is why his opinion is worth listening to even when you disagree. These random accounts are dismissable immediately. Except to make jokes about of course.
- kiaansaraiya 3mo ago[flagged]
- light_triad 3mo agoThis is the taste question applied to Mathematics in a similar way it's been applied to code. In an era of AI abundance, the question becomes what the goals are and what gets verified and digested (adopted by users). Goodhart’s law: the goal of producing code is not just about maximizing the number of tokens used, but the productivity gains and economic surplus. This could serve as the template for any field in the age of AI: "We are not trying to meet some abstract production quota. The measure of our success is whether what we do enables people to understand and think more clearly and effectively about math (or products, or science, or hardware...)"
- vouaobrasil 3mo agoThis is the template any field should have in the face of AI: screw AI, forget it. If you're using it, it's a disrespect to the field. Let's continue without it. I think that's the only sane approach.
- light_triad 3mo agoWilliam Thurston's argument (from the quote) was that the point of math isn't to produce more math but to better understand the nature of reality, just like the point of code is not to generate more code but to increase user value. AI is a tool that reshapes knowledge work but the ultimate goal remains about value.
- vouaobrasil 3mo agoI posit that one cannot decouple understanding from a healthy social environment in which to practise math. And AI destroys that.
- andybak 3mo ago> but the productivity gains and economic surplus. I think you might be missing out vast swathes of human experience here. Some things are about joy, or god help me - fun. (For the record I think AI has a role to play here as well)
- 230581abv 3mo agoThe man just cannot stop. First, a lengthy introduction with caveats which can be used to hedge later. Then he goes all in on AI again. He is sponsored by the AI for Math Fund (Renaissance Technologies) and I'd really like a yes/no disclosure about OpenAI stock options. People give him the benefit of the doubt because he always has been unable to stay off the Internet for more than a day. But this is really unprecedented.
- andyjohnson0 3mo agoA few predictions: 1. I fear that AI is about to change from being a human art to becoming something like a bulk-extruded, industrial product. 2. I also suspect that mathematics is about to become substantially less open. As the number of entities on the planet that are capable of top-level maths explodes, and because most of those entiries will have no interest in the validation that publishing papers brings, we will see balkanisation and hoarding of "secret maths". 3. Areas of science that are downstream of maths -- basically everything -- will, in time, be degrated by lack of openness, before suffering the same fate.
- vouaobrasil 3mo agoWell, that's what AI does. It makes everything about the final product and nothing about the enjoyment of the process. Now a lot of people here will say "you can still read the AI results and enjoy math on your own time", but that is completely at odds with how most people do things: a large part of most people's enjoyment comes from sharing results with others and AI devalues that. People can't help but feel less impressed when you can come up with a result but AI can also. People on here have also argued with me that enjoyment and fun should be decoupled from work but I'd argue that jobs that are enjoyable are important because I mean, what really counts in learning is inspiration. If no one is having fun, no one will be inspired to learn and do math in the first place. The best professors I've had are clearly having fun. And sharing that fun on a human level is exceptionally important. I just don't see the tradeoff (more math at the expense of people being able to have fun expressing themselves), as being worth it. The whole point of discovering knowledge is to enjoy the process and share that with the world to create hope an optimisim in it, not to product like a factory. Unfortunately, this website tends to bring in the rare type of person who loves to believe that they can enjoy things all by themselves, and maybe they can, but the problem is that they (not necessarily you) foist their unusual view of the world on the rest of the world by developing and supporting AI and get defensive when someone points out that it actually contributes to a horribly destructive social structure - a cognitive dissonance most of them can't handle.
- hannofcart 3mo ago> The whole point of discovering knowledge is to enjoy the process and share that with the world to create hope an optimisim in it, not to product like a factory. This is the crux of everything you've written and I strongly disagree. The purpose of knowledge is the sheer power it brings, and if there's factory scale churning out of it, I'll gladly take it. As a closer analogy, consider this probability (I'll be stealing from the game Stellaris here): let's say a few hundred years later, when we are spacefaring, we discover a vast cache/library of knowledge of an alien civilization, we won't just pass up on exploiting it because we need to "enjoy the process of acquiring it on our own" or "derive the satisfaction of sharing the discovery with others". No, I and I daresay most others will take as much as we can without restraint in a quest to make all our lives better/more enjoyable. And if that's ok to do, using machine intelligence to mine/grab any new knowledge or new math as Tao is suggesting here should also be acceptable and welcomed.
- yurimo 3mo agoI think it is important to divine what currently AI is good for and what it is not even in such verifiable environments like math. Current hyped announcements about breaking conjectures are notable and are a marker of how much improvement was made. But as I read them, and maybe I am wrong, I see it as a large model+ harness executing a broad brute force search and trying solutions until something sticks. There are lots of problems like that and they should be solved, as often they are perhaps less important or overlooked, or just a slog, any field of research has these, math even more so. However, this is very different from inventing new mathematical machinery that allows to break old problems, I think it will be a while until AI will be able to do it if at all. For now I think we will be moving to a symbiosis where an AI cracking a problem and giving a solution, inspires a human to invent new techniques.
- hodgehog11 3mo agoAgreed, AI is not capable at the moment of coming up with radical ideas to solve the tough problems. Sadly, I would argue many problems in math are likely to be found to be not actually tough in this sense, and those working in "comfortable" areas with fewer tough problems are having real crises of their own right now. But even for the tough problems, it is good at executing on a particular idea with reasonable competency. It's also quite decent at verification now. That can radically speed up proof development overall, since those aspects can become quite tedious otherwise.
- marysminefnuf 3mo agofinally someone is saying it our loud lol. mathematicans are just finding lower and upper bounds and having a computer input them into a theorem prover more times than a human is able to on their own. ai imo isnt solving anything.
- Syzygies 3mo agoI loved the appearance of Bill Thurston. He proved enough of what he saw to be considered one of our greatest mathematicians, but his brilliance was what he saw. The obvious question Terry Tao seems not to address: AI mops up our unsolved problems? Whose unsolved problems? The architecture of mathematics will remain a human endeavor long after we replace human construction workers with machines.
- calf 3mo agoHowever, the writing often dwells at length on trivialities, while passing very briefly through (or even obscuring) the most interesting and novel portions of the argument. This is consistently my experience chatting with LLMs. It's an very interesting anti-feature, what does it mean about them fundamentally, could more sophisticated machines one day surpass this, etc. Chomsky for example took the position that LLMs will never be able to explain things and he thought this anti-property was fundamental to their model of computation. But that was years ago.
- bobmarleybiceps 3mo agoI feel like at a certain point, there's is not necessarily a reason to go through the peer review publication process for some AI proofs. Not because "ai bad," but because at some point AI outputs should probably just be treated like public knowledge. Specifically stuff that's provable by "AI please output lean showing X is true," where anyone could kind of reach the same conclusion by asking ai.
- skybrian 3mo agoYou don't want people to have to rerun the prompt though. Collaborating on a registry for proven results makes sense. This probably looks like contributing Lean code to an open source project and writing docs.
- bobmarleybiceps 3mo agoYeah, I don't disagree with a registry. Especially for problems that are important to humans or are expensive for AI to prove/disprove. I partly just want to avoid a situation where the volume of hard-to-search-for results that are easily-ai-proved/disproved skyrockets... Basically, I think that for some stuff running a prompt is (or could become) easier than trying to do a search for an existing result. Partly why I think if something is fairly easily ai-proven, it should kind of be treated like it was already known, even if it wasn't actually known. :shrug:
- jabelli31 3mo ago[flagged]
- Schlagbohrer 3mo agoA pleasure to read such a presentation which carefully lays out its argument brick by brick.
- r00tanon 3mo agoMy first impressions and thoughts on the presentation speak to the need for human mathematicians to accept, absorb, and understand new AI-generated proofs—and to the fact that it takes time to do so, as well as the increasing burden of sorting through essentially unsolicited material, which robs that same group of the time to work. Software developers are seeing this same issue with AI-generated contributions of software changes in the open-source arena. What they are seeing is a very high number of trivial submissions, which Dr. Tao points out is a propensity of AI generation. The second problem is that submissions are often not good, forcing reviewers to read hundreds if not thousands of lines of intricate yet incorrect code—and they waste their productive time doing so, making them less amenable to future consideration of such contributions. This is a real problem. As to the issue of human mathematicians needing to accept work as useful before it can enter wider consideration—now that is an interesting problem if humans are indeed unable to understand work AI creates that is useful and correct, but not understood to be so (perhaps due to the above issues), and yet we have to consider a point in time when models become more capable. Let me put it another way: how long would you spend trying to get your dog to understand calculus? AI has inexhaustible patience (unlike humans), and it will keep trying to explain its ideas and theorems to us (or our dogs) far past the point humans would be willing to listen—though our dogs, at least, are amenable to treats and used to us talking a lot while handing them cookies.
- alestainer 3mo agoIt matters a lot what kind of tasks AI would be able to solve. Two completely different worlds arise if AI can do what I call a modern PhD grunt work vs it being able to produce genius of Nash/Einstein/Lovelace etc. And the way to test it is trying to produce modern math and science results with those historical LLM models or something similar: https://news.ycombinator.com/item?id=46319826 https://news.ycombinator.com/item?id=46319826 https://news.ycombinator.com/item?id=47927903 https://news.ycombinator.com/item?id=47927903 https://news.ycombinator.com/item?id=46319826 https://news.ycombinator.com/item?id=46319826