> 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?

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.

> 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.

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.

> 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.

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.

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.

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

> 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.

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.

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."

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.

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...

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.

> 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?

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.