ruilov

> "Math 2.0" will need to decenter the role of raw problem solving and value mathematical progress more holistically - for instance by elevating the role of exposition, but also that of community building and opening up new directions of study

It is interesting that AI is not yet superhuman at exposition, or at least exposition that can be understood by humans. But you haven't updated enough if you don't think that will happen soon. I'd also expect for AI to become superhuman at opening up new directions of study and theory building.

> Many fewer seminars, workshops, collaborations, or other activities are being generated from these results compared to traditional breakthroughs...the mere knowledge that a solution exists "contaminates" efforts by both humans and AI to find alternate routes to the problem that reveal additional insight

This is absurd. The mere knowledge contaminates...give me a break Tao! Of course having a (possible) solution changes how we're thinking about the problem. If that's what you mean by contaminate, fine. But if you're a person who's excited, curious, interested in mathematical knowledge for its own sake these AI results are a treasure trove. New approaches to old problems, some old approaches that we couldn't make work before. Why not whole seminars to take one of these results and dissect them, prompting the AIs to figure out where else we can use them, improving and simplifying, etc.

Look, I get Tao's anxiety. The ground is shifting and it's hard to solve for the equilibrium. How in the world do you write a grant proposal today when the person who will read it reads the headlines and thinks "math" is solved. That's something that the mathematical community will need to figure out over time. And it's possible that there'll less money for math research overall. When the marginal cost goes down, the market equilibrium changes (but don't forget Jevons paradox!). So I get the anxiety. I just expected better from some of the top people of the field.

Suppose I gave you a series of 1000 coin flips. I tell you they were generated by a fair coin. You’re suspicious, you think I hid a watermark in them. But you look at the sequence and 485 are heads, close enough to 50%. You look at the correlation between a coin flip and the next and it’s 0.0433. Close to zero. You do a bunch more stats and everything checks out. So you’re convinced.

Then I tell you: calculate the average of every 3rd flip minus the average of every second. It should come out close to zero, and unlikely to be higher than +/- 30 but for my sequence it comes out to +89. Ok, that’s very unlikely.

So from now on we share this secret. Whenever I generate sequences of coin flips they all came out with this particular statistic out of whack, but unless you’re looking for it, you can’t detect it. In fact, in the real world I use cryptography such that unless you know my secret key, the specific statistic in question is mathematically undetectable.

Now use this sequence of coin flips to pick amongst next tokens in an LLM. It doesn’t change the distribution of words used in the LLM. It doesn’t change its writing style. In fact, unless you know the secret key you cannot detect the watermark. So it’s not that some words are used more often. That would be detectable. It’s just that if you translate back to a series of 0’s and 1’s the average of every 3rd bit minus the average of every 2nd is out of whack.

the smartest people see AI as an incredible tool that enhances their productivity.

I'd like to see the base rate. Ie were there similar bets at similar times when Trump did not make an announcement

Look up Jeff Yass. Mega donor to Trump and large shareholder in ByteDance.

Only before Jan 19th and if a sale was in progress. After Jan 19th the law went into effect, and whatever Trump said or wrote in executive order became legally irrelevant

from the opinion: "[Tiktok] further argue that the Act is underinclusive as to the Government’s data protection concern, raising doubts as to whether the Government is actually pursuing that interest"

ie what you're saying...the Court replies:

"the Government need not address all aspects of a problem in one fell swoop...Furthermore, as we have already concluded, the Government had good reason to single out TikTok for special treatment"

Congress can solve one problem without needing to solve all problems.

it may be toothless but will they have an effect?

You're Apple or Google's lawyer - the CEO asks, should I take Tiktok down from the app store. What do you say?

Otoh there's a law and civil penalty. On the other, Trump says he won't enforce. Statute of limitations is 5 years, and the liability will exist whether Trump enforces or not. In 5 years, there will (may?) be a new president. On the other hand, trump saying he's not going to enforce may give us an out if we're ever sued over this (we just did what the Pres told us to do...).

Hard call, I give > 50% that they take it down whatever Trump says.

part D. "The record before us adequately supports the conclusion that Congress would have passed the challenged provisions based on the data collection justification alone"

agreed

they talk more about the motivations of the law in part D.

The "exclusion" referred to in this quote is not the exclusion of tiktok. The court is responding to one of the arguments that tiktok made. Certain types of websites are excluded from the law, and (tiktok says) if you have to look at what kind of website it is, then obviously you're discriminating based on content.

the court is saying that this would be an argument that this law is unconstitutional, period. That's a very hard thing to prove because you need to show that the law is bad in all contexts, and to whoever it applies to, very hard. So tiktok is not trying to prove that, that's not how they challenged the law - instead tiktok is trying to prove something much more limited, ie that the law is bad when applied to tiktok. It's an "as-applied" challenge. In which case, the argument about looking at other websites is irrelevant, we already know we're looking at tiktok. As the opinion says "the exclusion is not within the scope of [Tiktok's] as-applied challenge"

I'd use the term 'originalism' rather 'textualism', but you have a point. For 1st amendment cases, the court hasn't (yet) tried to use their new fangled originalist methodologies. In fact justice Gorsuch wrote separately in the Tiktok case to dig on the levels of scrutiny.

I think it's understandable, in a Chesterton's Fence sort of way - they better make sure that if they're going to start using a new methodology, it works better than what they use now, (these weird judge-created levels of scrutiny), but there's so much 1A precedent that is hard to be confident.

For 2nd amendment, they have used 'originalism' already. There isn't nearly as much precedent in that area, and so they were able to start more or less from scratch.

they found some of the arguments compelling and acknowledged that the law may burden free speech. But they also found that the law is not about speech, it's about corporate ownership. In these cases the court will often (not always) defer to congress / the state.

The replies here seem slightly off base. The Court acknowledges that 1s amm. free speech issues are at play. A law can regulate non-expressive activity (corporate ownership) while still burdening expressive activity, which is the case here. In such instances, the Court grants Congress more leeway compared to laws explicitly targeting speech. It checks that (1) the govt has an important interest unrelated to speech (it does), and (2) the law burdens no more speech than necessary (arguable, but not obviously wrong)