Terence Tao: Math 2.0 [pdf]

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.

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.

> 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?

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."

If you have not been following and focus on the cancer slide as an anti AI take, Tao has been involved and has a positive attitude towards AI for a while, he is just thinking a bit ahead on how the work of humans might change. https://teorth.github.io/tao-web/ai-views.html

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.

I think people are struggling to understand the way the world is changing. Entire modern philosophical contexts are being upended, for personal instance, I have been a big advocate of the philosophy described in Albert Camus’ “The Myth of Sisyphus”, particularly the concept of imagining Sisyphus fulfilled by the tedium of pushing the boulder up the hill, and deriving happiness from the struggle itself. But I bet Camus nor Sisyphus accounted for a self-pushing boulder.

Now what are we to derive happiness from? The joy of a boulder being on top of a hill?

I think that will be the most important thing for this transition, defining new purposes and meanings that people can assign themselves.

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.

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?

I think its valuable for mathematicians to think through how AI changes things for them. I think it's a bit premature to know exactly the impact AI will have. Math is one field that I feel will just naturally sort itself out without trying to predict or prescribe how it should work, it's a bit like software development, you adopt it in and see where it takes you. The presentation then sort of tries to argue for human understanding because AI might optimize for the wrong thing. That may well be what we need for the immediate future, but it's hard to know how things will play out. It might be such that it will become more important to people that AI understands something. ie, Does AI, with access to all current medical knowledge, think this cancer drug will be effective and safe? or has only humans said it's ok? At the moment we are in the chaos of change and its going to take a while for things to settle.

> Using AI to find and highlight new principles, methods, or insights, rather than merely new proofs.

I would have assumed that, by producing new proofs, the AI has either validated existing principles, or discovered new ones? Isn't that worth studying?

Are mathematicians complaining that reviewing AI's proofs is not as fun as writing your own? Try being a programmer... welcome to our world!

If AI lacks imagination and is not discovering new principles, then it's doing us a favour: it's crossing out the problems that don't need new principles. So the problems/conjectures that are still left are the more interesting ones.

Folks really want to decide if this is pro or anti and respond to that. It's neither.

In a world with only LLMs doing the day-to-day of proving, you still want more than just proof dumped out as soon as they pass adversarial review or formalization. The first proof code that passes checks may be a mess that's hard to build on; the path to a result, including failures, is full of interesting stuff; naming, generalizing, linking, and organizing things are tasks that move us from today's raw material to tomorrow's future directions.

Folks get this about code: "it works" isn't the same as "it's good." We knew it before LLMs, out of practical necessity as projects became hard to build on.

An odd thing to me is it would not be that big a concession for the labs to openly talk about the difference between the math artifacts they're releasing and what mathematicians do. It's analogous to the Claude's C Compiler post noting it wouldn't replace a prod C compiler. They could talk about paths from a rough initial product to 'production' math, say they hope future models will continue to improve as math collaborators and expositors, and so on.

They acknowledged the compiler's gaps because they'd be trivially evident to their customers, so they they could see it'd embarrassing not to. With their math output the differences from well-written, contextualized mathematical programs are subtle and deep enough the companies can't get themselves to acknowledge there are any differences, so they self congratulate and are then yelled at on the Internet instead.

(Ant seems to have wised up a tiny bit about this compared to OAI, and e.g. Ant handed a recent result to some experts in complexity theory to understand and refine and publish rather than just dumping a Claude-written PDF.)

And yes the drug discovery piece was weird. There are good relevant points: it'd be good to understand pharmaceuticals better (helps us find others, understand side effects, etc.); when we get a mystery result, it's worth effort to try to work our way to proper understanding; anything that could help us understand (reasoning etc.) shouldn't be hidden. But as presented it's both not a lot like math and accidentally a lot like those "would you choose..." questions that always get so much engagement on social media.

I think people have really misunderstood Tao as someone against "AI doing his job". That's at the core of this controversy in math, and it couldn't be further from true.

Putting aside the cancer question: I still don't understand how TT seems to be fixated on what models can do today instead of tomorrow. It's realistic and even conceivable that the models will also become better at explaining and presenting proofs too. Maybe he's not emotionally ready to accept that there may not be a future where his (and to some extent, my) skills are relevant and valued. It breaks my heart. I hope I'm wrong, but it feels like we've run out of higher ground to run to.

From the slide Beyond Problem Solving:

"Reaching these lighthouses [resolutions of open problems] prematurely by automated tools can disrupt the exploration of the paths not taken, and sterilize the surrounding field."

This crucial issue is centered in mathematician psychology and the incentive structure of academic/institutional mathematics worldwide. For mathematics to flourish going forward, we will need to realign our brains to think differently about the nature of mathematical progress. And we need to reorient our institutional incentive structures towards the promotion of meaningful mathematical progress itself rather than targeting proxies that are no longer faithful.

Regardless of the precise nature or the causes of the "sterilization" Tao refers to, we (the mathematics community) can only rely on ourselves to repair it. Though, since it will involve fundamental change at the level of ossified academic institutions with many stakeholders and divergent vested interests, any such repair will be slow, frustrating, controversial, and lacking any guarantee of success.

We still don't fully understand why Pepto Bismol and Tylenol work.

I'm a big fan of Tao. He must be so shaken by the AI storm that he's now writing arguments that even teenagers could quickly dismiss. A sad day.

This all seems precedented on model capabilities that came into play over the last 3-6 months. How do you establish this new paradigm when we don’t know what the models will be like in 1,2, 10(?!) years from now.

Jeez, TT made one bad example (cancer cocktail) and people in this thread can't stop bitching about this, even though the rest of the slide deck kinda makes sense.

In a nutshell, Math 2.0 is not fully compatible with Math 1.0 and the forced upgrade is breaking features, plug-ins, and we're tracking several new bugs, but this is still the fastest, most secure, and best version of Math ever released, with powerful new features and unrivaled privacy.

Can someone explain, why people understanding is important? Proof 1+1=2 was created in XX centery, but people before and now use it without understanding, use it as axiom. In computer science, a lot of people use CAP-theorem without understanding their proof, because we know someone else prove it and verified it.

This crisis exposes a conflation between A: The broader concept of [abstract] Mathematics and B: The contemporary Mathematics culture and community. This crisis is directly in B only. B will adapt: In how it attributes value, status, hierarchy, and career. There will be a death (Or something close to it), and rebirth. Through this, A will advance in a Kuhnian leap - habits will be broken as incentives changed, and paths ignored will be explored. Insights will flow to the sciences.

I'm excited!

> The future of mathematics — “Math 2.0” — will require both expanding the research frontier, while simultaneously decentering the traditional role of problem solving.

Seems to be the crux of the argument, but "use your imagination" isn't a great thing to tell people who are looking at degree irrelevancy, concerned about getting tenure or a research position. How do we measure if someone is a good mathematician or not, if they are one of the sanctioned few who get access to the biggest AIs?

I'm learning so much about specific vs. generalized intelligence through this entire ordeal.

Doesn't feel good slipping into irrelevance does it. This dude was complaining about having no funding and planning to leave the US just a few years ago, now he's all over the place giving talks and lecturing people about AI. He's got the classic case of epistemic trespassing

> This is in stark contrast to current AI performance on tasks which are subjective, dependent on real world interactions, or for which data is scarce. AI performance is thus extremely jagged: astounding in some directions, while inadequate in others. This is true both within mathematics, and more broadly.

underrated buried comment based in reality

The cancer arguement on slide 20 is pretty weak. I first need to be alive in the long term to worry about the long term effects. If I had terminal cancer I'd gladly take an AI developed 'cure'.

There are still a lot of treatments/medicines in medical science where we dont know 100% the real reason as to why it does what it does but we still prescribe them because the intended effect is what we are interested in.

Doesn't this assume that humans stop trying to understand problems and AI-provided solutions? Yes, the field is going to change and will require certain rethinking of mathematicians' motivation, but what stops humans from keeping to work on problems they want to solve and understand? The fun from math comes not from solving cancer, but from understanding something new with every approach you take

Reads in a lot of places a bit like a mix of anger and bargaining. There is no putting the genie back into the bottle.

But I understand that for people whose whole life was math and solving math problems this will lead to an identity crisis. Seen the same in my area of work (software engineering)

I think a better analogy would be conducting a marathon in a fog. If you can't see the path of the proof, how do you know it is completely true in all scenarios? If you can't see whether the AI runner ran through every part of the race, how do you know it didn't draw hallucinated shortcuts in the parts where humans can't see? Or worse, create obscurity and blow smoke to hide the shortcut section? If the same AI was to guide the last living humans to a star, because it found a path clear of danger, could you trust it to get in that ship? Or did it just forgot mentioning an asteroid belt the ship is not built to navigate? Truth is verifiable truth that multiple parties can agree upon. Can you trust with your life something you can't verify?

And what software developers should do?

Basically people are vibe coding their personal apps and anything that's expensive is being vibe coded open in the public. I don't see many software companies staying profitable for long.

DHH is the biggest proponent of AI and let me know which of the 37 signals products can't be vibe coded in a month at a $200 plan that are suitable for that organization alone that just has to be accessible internally only? Hence scale and security aren't such an issue.

In that climate - for how long software companies would stay profitable and when not, who'll be employing developers?

PS: Don't underestimate vibe coded apps. Take a look at PDFCraft, VectorCraft, WordCraft. And imagine the feature parity in a year.

page 20 ("A thought experiment on alignment and understanding") is perhaps not likely to quite induce the reaction in most people that Mr. Tao expected.

One thing that AI can give me: time. Would I like to see all the rest of the Millennium Problems solved during my lifetime? Absolutely.

Also how many math and scientific discoveries do I want to see during my lifetime? "Just a little bit more."

> Before injecting this cocktail into your bloodstream, would you find it reassuring to know that there is at least one human cancer expert who understands– even partially the mechanism behind this cure

I mean... yes, most people will find it reassuring, but history has proven that's not necessary. People have been using medicines of which the mechanism wasn't understood for a very long time and greatly enjoyed their benefits. Even widely used one (e.g. Paracetamol).

It’s funny to see people in the STEM field focus more on the human aspect of creation. It used to be that the result mattered more than your feelings. Now we are moving the goal posts about how things should be done.

I wonder if we will begin to actual value human creation more at the end of all of this

It's quite noticeable how when Terence tao was sounding pro-AI the sentiment was much more positive and he was being held up as an authority to listen to. Then he puts out some limitations of AI in a presentation about how to work with it as an expert and suddenly on HN he is just some out of touch killjoy trying to hold back progress etc.

The workflow/understanding graphs really helped me understand his viewpoint on the field.

Can someone explain why there wouldn't be arrows from all three types of solutions back to human understanding?

I think people are missing the point that terrence is trying to make, especially on the cancer drug.

For nuance lovers - here are some basics for how you get your drugs: there is an established chain of trust from the first basic science paper to the phase 3 trial and the subsequent availability of the drug to general public

- someone publishes the first paper (basic science) explaining some biological phenomenon, which leads to 10s or 100s of other papers with some tweaks in conditions,

- after the above papers the pathway of the phenomenon is understood by researchers, they try therapies at cell level to see if they can control some behavior, 10s or more papers get published,

- then someone tries this in mice and other models, 10s and more papers get published.

- then researchers at pharma companies + hospitals create this therapy for human trials - phase 1, 2, 3 etc - data collections, then FDA - then approval.

Now, the people who worked on the phase 3 trial might not know the people who wrote the first seminal paper and they often don't exist in the same decade - but it absolutely does not mean that we (humans) don't know how these drugs work - if you take 1-2 researchers from each phase and put them in a room and ask them how that particular drug works - they will quickly be able to build a consensus. that is what the chain of trust means here. now of course there can be fraud in scientific research, but that happens in every human endeavor and is a separate topic.

back to terrence - he is saying that if there is suddenly a drug that nobody knows the origin of; passed phase 3 but it's unclear who conducted the phase 3 or if the phase 3 even happened or if it's fabricated - you would not want to take the drug. usually when doctors recommend these kinds of drugs - there is already a lot of information available about where the drug came from, if there are any case studies, which doctor tried it first, which country- they often even call those other doctors and find out who was behind the first trials going back as far as the university professors.

Your MD doctor might not know the chemistry and physics behind the drug you are taking but there is deifnitly a group of people, when put together, can tell how that drug is working. My wife is a fundamental researcher - understanding physics at DNA level and my brother is a MD doctor; our conversations are super fun.

Side effects are a completely different thing - they involve the above cycle on repeat.

It is nice to see some sanity back in the conversation!

I'm still not sure about math-2.0 (humans+AI will make fundamentally more progress):

- AI and computer usage take a mental toll on humans and humans will overlook radical improvements.

- AI may be good at finding useless things like "P==NP, but the complexity is O(n**4242424242424242)". In other words, useless.

- Humans become formalists and lose traditional sources of inspiration. Maybe interacting with Lean should be left to specialists, but not to creative blackboard mathematicians.

- AI exposure will further intellectual conformity, more than the Internet did.

As to the last point, a lot of progress (real, not measured in publications) seems to have been made when communication was slower and there were several different schools and approaches.

People are feeling devalued. We can't see where the ball is going...

Tao is continuously updating the cancer slide with the help of Claude in the past few hours.

https://github.com/teorth/tao-web/commits/main/

It reduces the badness somewhat.

"""An advanced AI is prompted: “Find a cure for cancer that passes a stage 3 clinical trial. Make no mistakes.” After a large amount of compute, it produces a cocktail of previously unknown chemicals which it claims, when mixed and injected into a patient, will kill all their cancer cells. While nobody truly knows how this cocktail was found, the AI (somehow) provides a Lean certificate for its prediction, and the cocktail does indeed manage to pass a stage 3 trial.

Could the AI solution be somehow misaligned by exploiting a weakness in the trial process or its math models?"""

Yes, absolutely an AI solution could exploit a weakness in the trial process or its math models. Would it remain uncaught? Unclear.

> Before injecting this cocktail into your bloodstream, would you want to know that there is at least one human cancer expert who understands the mechanism behind this cure?

> Or a human mathematician who understands the mathematical model used to locate the cocktail?

If we're being fair to AI - it contains collective knowledge from all fields, which means it's probably less likely to miss something that a human would.

While Tao is having existential crisis the community is quick to pick up the results and is trying to improve on them. The integer multiplication results is getting better bounds every few hours. Recent post explaining what's happening:

https://x.com/RohanArun/status/2109336015814959200?s=20

It seems like OpenAI opened the door for many more people to participate in math discovery process. It's fascinating to follow!

>" “Ablation studies”: taking an already proved theorem and seeing whether it can still be proved after

removing some key theories or inputs

(e.g., finding an elementary proof for a result currently only provable by non-elementary means)."

As usual, Tao is brilliant in all that he researches, all that he writes about.

I chose the above statement (which is brilliant, in and of itself!) to comment on, because it leads to the following idea:

There there exists, or should exist, a dependency map in the fields of not only Mathematics, but also of Computer Programs/Software, Engineering, and even a seemingly non-related field: The Law...

In other words, how do we get from the simplest of axioms or foundational things (aka "first principles", aka "self-evident truths") to much more complex entities?

In Law for example, how do we go from the simplest of historical legal constructs to the most complex of the most complex Supreme Court cases?

You see, there is, or should be a map, you could call it a dependency map, you could call it a dependency graph, which shows more and more abstract/complex mechanisms/things/assertions/statements/truths/functions which is mapped back to , that is, dependent on various chains, various stackings, various "stacks" of simpler ones.

In Engineering, for example, how do we get from the simplest of machines to the most complex of machines? What simpler machines and/or sub-components (aka "dependencies", aka "subcomponents") are required to build it, and how do those simpler machines work, and what's the dependency graph or map for their subcomponents?

More generalized, if we have something of complexity, then how do we get there, step by step, from individual subcomponents, individual inputs, individual proofs, individual software systems, step by step?

What is the map of those dependencies?

Note that in some systems, Math proofs, for example, there may be different paths which can be traversed to get to the same destination.

Ablation Studies could be thought of in Travel, in Geography as "if I cannot take one, or a specific set of routes to get to a place, can I still get there?"

A simple example would be in Google Maps, where you'd like to drive somewhere, but you'd like to avoid tolls. Is the route still traversable while avoiding tolls? Well, that's an example of one constraint. In Ablation Studies, you might wish to remove a bunch of routes with whatever criteria or characteristics , i.e. muddy roads, roads that have characteristic X, roads that do not have characteristic Y, etc., etc.

Getting back to Math, specifically proofs, it would be great to create a dependency map/graph of all of them, and then try removing inputs (aka, paths to them, dependencies on other mathematical proofs/objects that they may have) and see if they are still reachable.

In software, when we desire the tightest, cleanest, source code, the above is related to refactoring.

In the future, I'd love to see dependency maps/graphs (call them whatever you will) for not just Mathematical Proofs (although I'd love to see that too!), but also in such diverse subjects as Science, Engineering, Programming/CS, and even the Law!

Because they should exist in all of those subjects!

Anyway, another great piece of work by Terrence Tao!

Source: https://terrytao.wordpress.com/2026/10/10/math-2-0/

(https://news.ycombinator.com/item?id=50034337)

Just a ~~few~~ ton of things (sorry!), with the upfront caveat that Tao is a hero who's trying his damndest:

1. The use of semi-ugly slides to communicate this is just perfect and quite heartwarming, but it does highlight my main criticism of the mathstadon version of this thesis: he's myopically focused on mathematics as he has practiced it, rather than mathematics as a ~2400y old academy. Like, "stable for almost a century" sounds impressive, but should be a pretty obvious red flag in hindsight!

2. Glossing over "objective verifiability" feels like another place where he's ignoring a ton of relevant philosophy for no clear reason -- yes, mathematics is the only academy based in pre-conscious cognitive facts about our processing of time and space, but that's not the end of the story on "objectively verifiable". To say the least! He hedges with "broad consensus" which doesn't need to be absolute, but that seems to be not only dismissing a highly relevant question, but even implying that he might be unaware of it. I doubt he is, but still: not great.

3. Who is this for...? Why is an explanation of Lean needed in a talk given at CalTech? I suppose he's welcoming his role as a bit of an influencer, there?

4. Re:the focus-on/centrality-of 'highly digitizable' as a unique class of task that applies to mathematics in particular, I must sadly trot out the increasingly-common trop: Yudkowsky called it... https://intelligence.org/files/IEM.pdf

5. "the space of mathematical problems remains infinite" is, again, ignoring really important philosophy around academies as social structures, built for human means. Mathematics is only infinite if we decide that all knowledge is useful (the quintessential example being 'counting the grains of sand on a beach'). Not really important in the first place, but another worrying case of the above.

6. Problem solving is the goal of mathematics; he has a completely valid point here (that we shouldn't throw AIs at unsolved problems in bulk and thus lose human expertise), but it's obscured by the use of "[open] problem" being a too-technical one. IMHO. Slide 16 fails to disabuse me of this notion.

7. Slide 18 is describing the differences between functions and systems, and is arguably even talking about assemblages.

8. If we're gonna explain lean up-front, it feels like a baffling choice to throw the "maybe AI will solve cancer but use it to secretly plot to kill us all" slide in there. It's also already lead to misunderstandings and backlash on Reddit, where 'yes we want to not die of cancer!' is a pretty convincing counterpoint (if a ultimately a subtle strawman, ofc). It's also quite distinct from the rest of the talk.

As always, the best part of any Tao publication is his ability to inspire and rally and organize. I think Math 5.0 will indeed be a matter for creativity! Hopefully the IE levels off before we cease to be helpful in that capacity...

Far outside my expertise, but it feels like the shaky assumption here is that the understanding and proof need to come in a specific order to be valuable. Can't we get all the meaty goodness by simplifying and generalizing the proofs now we know they exist? Sure, some insights will live in the discovery itself, and I guess it's nice to be the person who got to a proof first, but the real work (according to the mathematicians, afaict) is in the understanding and processing. In this way, it feels like it's moving towards being like most other science: mostly understanding things that are already there.

I'm heartened to see that a decent number of slides in this isn't the run of the mill doom and gloom but some actually interesting and potentially productive offshoot ideas.

The popular perception of him (as popular perceptions generally tend to do) reduced his overall position to basically early adopter went sour grapes, and I'm really glad to see that substantively falsified.

Another example that people should not use medical analogies to illustrate a side point: Discussion boards will focus on the completely irrelevant side point to drown out the renewed AI caution that they do not want to hear.

"our work has brought about enormous advancements to the field of mathematics and we don't like it"

it's pretty ironic that AI being just a group of mathematical techniques after all is making mathematicians uncomfortable because it works. Instead of reacting like this, mathematicians should be excited to figure out how to use the new tools available and push the frontier of what's possible in service of science.

Terrence is asking the stupidest question he could ask: how can math better serve me? They completely forgot the point of science is serving humanity.

[flagged]

[dead]

[dead]

[dead]

> Before injecting this cocktail into your bloodstream, would you want to know that there is at least one human cancer expert who understands the mechanism behind this cure?

No. I'm gonna die, my man.

This guy might have the highest IQ on the planet, but it's clear he hasn't spent much time around average people.

This argument is so silly against reality, and already, almost nobody understands the things they put in their body to any significant degree, beyond the effect produced.

Will I take a cancer cure that no human understands? Yes. And so will billions of others. Just needs to cure cancer, that's nearly the only requirement.

[dead]

Has the world gone mad? In which universe would you get a mathematical model to produce a tonic of random chemicals that optimize said mathematical model, put that through stage 3 testing, and only THEN ask if you want to inject this into yourself. My Guy, you just did clinical testing on fucking humans for phase 3, it's a little late to consider the moral ramifications of the analysis-experiment dichotomy.

The real example is that you ask ChatGPT for a novel cancer cure, and it spit out some random chemicals, probably including bleach. Do you inject that into cancer patients that have no other hope? No, you don't. You absolute charlatan.

Man with a cozy and soon to be irrelevant sinecure grasping at straws.

It turns out research math was puzzling solving and we rewarded idiot savants.

This seems like cope to me.

Humans have a bias towards assuming that problems have solutions. Mathematicians probably more than average.

This talk is predicated on the theory that the problem of "maintaining the relevance of humans in mathematics" is tractable. Not sure I agree